From a22e63a2c456858f2129731d267a0d8c3b868d3d Mon Sep 17 00:00:00 2001 From: DreamingOfClouds Date: Sat, 10 Oct 2026 13:28:42 -0500 Subject: [PATCH 1/2] research/complex-p10: the complex supplier at cube size p = 10 (7795/10^7 centre-sharing, 7737/10^7 #304 recipe; no new kappa) The source-assisted complex word of #184/#194 compiled with #304's frozen recipe at p = 10 (h = 20, 960 ports) on query modules re-annealed at p = 10, priced in Sussman's generic five-stage B2 layout at h = 20 (m = 100, W = 4v + R). Six gcert/1 programs (control, anneal, centre-sharing; parity and mw pairs), each regenerated and checked by verify.py (pair checks, PR #200 admission, PR #184 flow and lift, #194 contract, gx.check1 with the exact scalar identity and gxcore, exact five-stage price). Fixes two latent p != 11 bugs (pairs_mw gauge rank; dropped-gauge births in the record), documented. Co-Authored-By: Claude Opus 5.5 --- .github/workflows/complex-p10.yml | 35 + research/complex-p10/NOTICE | 85 + research/complex-p10/PROOF.md | 155 ++ research/complex-p10/README.md | 171 ++ research/complex-p10/SOURCE.json | 167 ++ research/complex-p10/aligned_word_p.py | 265 +++ research/complex-p10/centre46.py | 91 + .../complex-p10/certificate/expected.json | 1887 +++++++++++++++++ .../gcert1-p10-anneal-mw-flow.json.gz | Bin 0 -> 324061 bytes .../gcert1-p10-anneal-parity-flow.json.gz | Bin 0 -> 322438 bytes .../gcert1-p10-centre-mw-flow.json.gz | Bin 0 -> 323382 bytes .../gcert1-p10-centre-parity-flow.json.gz | Bin 0 -> 321824 bytes .../gcert1-p10-pr168-v4-cut-mw-flow.json.gz | Bin 0 -> 328803 bytes ...cert1-p10-pr168-v4-cut-parity-flow.json.gz | Bin 0 -> 326205 bytes research/complex-p10/discovery/README.md | 109 + research/complex-p10/discovery/add_centre.py | 30 + .../complex-p10/discovery/extend_floor.py | 99 + .../complex-p10/discovery/make_layer_p.py | 318 +++ 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create mode 100644 research/complex-p10/discovery/pr233/bundles.py create mode 100644 research/complex-p10/discovery/pr233/joint.py create mode 100644 research/complex-p10/discovery/pr233/matching.py create mode 100644 research/complex-p10/discovery/pr233/pairs_mw.py create mode 100644 research/complex-p10/discovery/pr233/physical_opt.py create mode 100644 research/complex-p10/gcert_emit.py create mode 100644 research/complex-p10/gx/gx.py create mode 100644 research/complex-p10/gx/gxcore.py create mode 100644 research/complex-p10/layers/anneal/kernel-pairs-mw.json create mode 100644 research/complex-p10/layers/anneal/kernel-pairs-parity.json create mode 100644 research/complex-p10/layers/anneal/matching-arcs.json create mode 100644 research/complex-p10/layers/anneal/physical-frames.json create mode 100644 research/complex-p10/layers/anneal/physical-pairs-mw.json create mode 100644 research/complex-p10/layers/anneal/physical-pairs-parity.json create mode 100644 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mode 100644 research/complex-p10/modules/pmod46_pc1_p10.json create mode 100644 research/complex-p10/modules/pmod_p3_p10.json create mode 100644 research/complex-p10/modules/pmod_pr168_p10.json create mode 100644 research/complex-p10/modules/qmod_pr168_p10.json create mode 100644 research/complex-p10/modules/qmod_sa1_p10.json create mode 100644 research/complex-p10/modules/tmod_pr168_p10.json create mode 100644 research/complex-p10/modules/tmod_t2_p10.json create mode 100644 research/complex-p10/normalize_scatter.py create mode 100644 research/complex-p10/paircheck.py create mode 100644 research/complex-p10/references/centre46_graph.diff create mode 100644 research/complex-p10/references/pr233-layer/NOTICE create mode 100644 research/complex-p10/references/pr233-layer/SOURCE.json create mode 100644 research/complex-p10/references/pr233-layer/baseline-pr202.tar.gz create mode 100644 research/complex-p10/references/pr233-layer/certificate.json create mode 100644 research/complex-p10/references/pr233-layer/verify.py create mode 100644 research/complex-p10/references/pr233-layer/witness/kernel-pairs.json create mode 100644 research/complex-p10/references/pr233-layer/witness/physical-frames.json create mode 100644 research/complex-p10/references/pr233-layer/witness/physical-pairs.json create mode 100644 research/complex-p10/references/sussman/pr193-blocks.json create mode 100644 research/complex-p10/scripts/moment.py create mode 100644 research/complex-p10/scripts/source527/NOTICE create mode 100644 research/complex-p10/scripts/source527/base_two_moment.py create mode 100644 research/complex-p10/scripts/source527/moment.py create mode 100644 research/complex-p10/verify.py diff --git a/.github/workflows/complex-p10.yml b/.github/workflows/complex-p10.yml new file mode 100644 index 0000000000..36ce70d39f --- /dev/null +++ b/.github/workflows/complex-p10.yml @@ -0,0 +1,35 @@ +name: complex-p10 + +on: + pull_request: + paths: + - 'research/complex-p10/**' + - '.github/workflows/complex-p10.yml' + push: + paths: + - 'research/complex-p10/**' + - '.github/workflows/complex-p10.yml' + +permissions: + contents: read + +jobs: + verify: + runs-on: ubuntu-latest + timeout-minutes: 90 + strategy: + matrix: + python-version: ['3.12', '3.14'] + steps: + - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7 + with: + persist-credentials: false + - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97 # v7 + with: + python-version: ${{ matrix.python-version }} + - name: Install the regeneration dependencies of the pinned pipeline + run: python -m pip install numpy==2.3.5 scipy==1.17.0 + - name: Regenerate the p = 10 words, check the frozen layers and pairs, run flow, lift and contract, emit the gcert/1 programs, run gx.check1 and gxcore, price the five-stage words at h = 20, compare with the committed certificates + run: python3 -B research/complex-p10/verify.py + - name: Require an unchanged tree + run: git diff --exit-code diff --git a/research/complex-p10/NOTICE b/research/complex-p10/NOTICE new file mode 100644 index 0000000000..923dacf2d9 --- /dev/null +++ b/research/complex-p10/NOTICE @@ -0,0 +1,85 @@ +Prepared by DreamingOfClouds with Anthropic Claude assistance. Apache-2.0. +Inherited files retain their original notices and assistance disclosures. +This package claims no exclusive priority over concurrent work and reports +no new kappa. + +What this package contributes: the source-assisted complex word compiled at +cube size p = 10 (h = 20) instead of p = 11; four query modules for p = 10 +(modules/: triple module p = 10, pair module n = 9, its centre-sharing +version with a 37th root, all-but-one module n = 8), each cut from a p = 11 +module file by zero restriction and then annealed at p = 10 against the +exact compile ledger of the aligned word (README, "Modules"); the control +modules (PR168 v4's modules cut to p = 10 by module_cut.py); one frozen +compilation recipe applied to three module sets (layers/); the cube size as +a parameter of PR304's builder (aligned_word_p.py) and discovery driver +(discovery/make_layer_p.py); centre46.py (the centre-sharing graph); the +gauge-rank fix of PR233's maximum-weight pairing for h != 22 +(discovery/pairs_mw_p.py); the record correction in aligned_word_p.py +(the births of gauges that PR194's source_aligned_local_v4.py drops are +removed from its record, so that PR200's checker can recount it); the six +resulting programs with their checks (verify.py). Everything else is +retained and credited: + +- icekylinx (OpenAI GPT-6 Astra and Codex assistance): PR144 paired cubes + and signed decoder (the K blocks and the star scatter of every program, + and Graph.finish, whose centre-sharing patch centre46.py reproduces), + PR184 source-assisted construction: source-parity local factorization, + frame flow, exact lifts, contract (complex_frame_flow.py, + exact_complex_flow_lift.py, and source_aligned_local.py, from which + aligned_word_p.py derives through PR194 and PR304). +- Avi Eisenberg (ikeboy): PR191/193/194, the rebuild of PR184's + construction on the PR168 v4 modules (source_aligned_local_v4.py, whose + code aligned_word_p.py keeps, contract_v4.py run here), the + parity-erasure-avoiding pairing of PR193 (the "parity" pair recipe) and + PR194's frozen pairs of the anchor. +- chafreaky / Chafik Boukhalfa (Anthropic Claude and OpenAI Codex + assistance): PR200 operation-frame descent (the frames of every layer), + maximum-weight late compensated reuse pairing (the "mw" pair recipe; + pairs_mw_p.py is his pairs_mw.py with the gauge rank read from h) and the + complete complex checker complex/physical.py (run here to admit every + layer); PR233 layer and package (vendored in references/pr233-layer/, its + discovery harness vendored in discovery/pr233/); PR256 gcert emitter + (gcert_emit.py, vendored unchanged); PR225 exact moment bounds + (scripts/moment.py); PR296, the five-stage package whose complex-supplier + checks (with PR234's) read the programs in star form. +- Jacob Sussman (Anthropic Claude assistance): the certificate format + gcert/1, the reference checker gx.py and the Python mirror of the two + Lean checks gxcore.py (both vendored unchanged in gx/, Apache-2.0, + Copyright 2026 Jacob Sussman, jacobalansussman/wht-power-saving-lean at + f010392c), the bridged five-stage layout B_2 (Lean-checked in his + repository, stated there for every h) in which the programs are priced, + the unit convention of gxconv.py reused by gcert_emit.py and + normalize_scatter.py, and the published certificate of #193 whose + histogram anchors the chain (references/sussman/). +- eumemic (Anthropic Claude and OpenAI Codex assistance): PR168 annealed + modules (the parents of the control modules and of the p = 10 pair module + pmod_p3_p10.json), schedules and physical frames; PR117/155/157/161 + module infrastructure, physical frames and reuse; the exact-DFT arena + (scripts/moment.py adapts eumemic/exact-dft-bounds, Apache-2.0); the + source527 package (PR210 lineage, OpenAI Codex assistance), whose two + rational moment engines are vendored unchanged in scripts/source527/ + (see scripts/source527/NOTICE). +- DaysSky: PR162 extended carrier closure (compile_closure, and the greedy + extension in discovery/extend_floor.py). +- DreamingOfClouds (Anthropic Claude assistance): PR304, the p = 11 + re-annealed modules (the parents of three of the four p = 10 modules), + the frozen-layer recipe, aligned_word.py, paircheck.py, + normalize_scatter.py, make_layer.py and verify.py, of which this package + is the p = 10 version; PR315, whose 10-line Graph.finish patch + (references/centre46_graph.diff, vendored byte for byte) defines the + centre-sharing graph, and whose two moment engines' fallback convention is + used for the coarse price. The annealing drivers used for the p = 10 + modules (numba simulated annealing on closed-form compile-ledger + evaluators, adapted from the bit side's annealer) are research code and + are not included. +- hcg890 (PR234: the five-stage architecture of the packages that consume + a complex supplier; the 10^-16 bad-class fallback envelope priced here is + the one their moment engines carry as an inherited assumption), + SovereignSteak (PR250: the five-stage ledger statement used for the + price), rohanarun (PR209/237). +- PR202 baseline lineage as credited in references/pr233-layer/NOTICE: + jamesyc / James Chang, DaysSky, GamingPuzzled, gupt1156, Abhinav + Ramachandran/geckods, jacklightChen / Zhihao Chen, Rohan Arun, an664, + Swapnil Jain, hpst3r, Aurel Prosz, dleen, Douglas Colkitt. +- OpenAI: the original complex phase network of "Integer multiplication + below n log n". diff --git a/research/complex-p10/PROOF.md b/research/complex-p10/PROOF.md new file mode 100644 index 0000000000..980cfc8c77 --- /dev/null +++ b/research/complex-p10/PROOF.md @@ -0,0 +1,155 @@ +# The complex supplier at p = 10: explicit numbered programs at h = 20 + +**Claim.** Compile the source-assisted complex word of PR #184/#194 at cube size p = 10 (h = 2p = 20, v = 8·C(10, 3) += 960 ports) instead of p = 11, with the query modules of `modules/` (triple module p = 10, pair module n = 9, +all-but-one module n = 8) and the frozen layers of `layers/` (carrier arcs, PR #200's descended operation frames, +reuse pairs of PR #193's or PR #233's recipe, kernel pairs). Each of the six words is one explicit program in Jacob +Sussman's certificate format gcert/1 with the star scatter, accepted by his reference checker `gx.check1` and his +Python mirror of the two Lean checks `gxcore.py` (jacobalansussman/wht-power-saving-lean, `tools/gx/`, commit +`f010392c`; both vendored unchanged in `gx/`). In the bridged five-stage word B₂ written out at h = 20 (m = 5h = 100, +W = 4v + R, idle climbs e₃₈, e₁₉, e₄₂, e₄) the exact rational bounds certify: + +- **centre-sharing set, PR #233's maximum-weight pairs: a = 7795/10⁷** (8,375 registers, R = 6,455, W = 10,295; + 7796/10⁷ rejected); with PR #193's pairs 7747/10⁷; +- **PR #304's recipe on the annealed set, PR #233's pairs: a = 7737/10⁷** (8,435 registers, R = 6,515, W = 10,355; + 7738/10⁷ rejected); with PR #193's pairs 7689/10⁷; +- same-recipe control (PR #168 v4's modules cut to p = 10): 7375/10⁷ and 7322/10⁷. + +Each claim holds with and without the five-stage packages' 10⁻¹⁶ fallback envelope, and the fallback-inclusive coarse +savings on the 10⁻¹⁸ grid are certified by two independent engines (§2, step 12). No new κ by itself: on the open +frontier the bit side (PR #320, 7.69199e-4, cited) lies below PR #315's p = 11 complex supplier (7727/10⁷) and below +both prices here; a κ package that adopts this supplier would see the complex cap rise from 7.727e-4 to 7.796e-4 +(whether it may is §5's open point). + +## 1. Inputs + +- **Modules** (`modules/`). JSON files in the formats of PR #168's sources, read by the rebuilt tree's own loaders, + which check the module contracts at p = 10: in the pair module every root sums exactly the inputs disjoint from its + pair, in the all-but-one module every root sums all inputs but one, in the triple module every root J sums the + inputs I disjoint from J, and every addition joins disjoint supports. The centre-sharing pair module has a 37th + root, the sum of all 36 inputs; `centre46.load_pmod46` checks the 36 pair roots and the full sum. All are zero + restrictions of p = 11 module files (PR #168 v4's or PR #304's), the non-control ones then annealed at p = 10; the + search is not part of the proof. The three control files are re-derived by `verify.py` (§3). +- **Frozen layer** (`layers//`): `matching-arcs.json`, `physical-frames.json` (the operations whose frame differs + from the closure frame, in the canonical form of `source_aligned_local_v4.py`), `physical-pairs-{parity,mw}.json` + (reuse pairs [donor, recipient, deadline]) and `kernel-pairs-{parity,mw}.json` (two kernel pairs on the control's + parity layer, none elsewhere). `discovery/make_layer_p.py` is how they were found; `verify.py` only checks them. +- **The word builder** (`aligned_word_p.py`). It is PR #304's `aligned_word.py`, i.e. `source_aligned_local_v4.py` + of PR #202 (Avi Eisenberg, PR #193/#194) with its four discovery steps replaced by inputs, with three changes: + the cube size is a parameter (`Graph(p)`, modules at p, p − 1, p − 2); `--centre46` builds the centre-sharing graph + (`centre46.finish_centre46`: the star centre S(2i + e) is the pair module's 37th root instead of a separate sum, + which is what PR #315's 10-line `Graph.finish` patch does); and when `select()` chooses gauges that the script then + drops, the record's gauge ledger is corrected to the kept gauges (§5). Everything else (local configuration, merge + f8:00111100, `compile_closure`, `select`, phase-one prefix, forward closure with future-cap clipping and local-pair + checks, gauge filtering, target histogram, `paired_cube_physical.physical()`, the encoding of the seven output + files) is the script's. + +## 2. Chain of checks (each of the six words) + +1. **Module contracts**: `triple_module_from`, `pair_module_from` (or `load_pmod46`), `all_but_one_from` at p = 10. +2. **Arcs**: `compile_closure` (PR #162, DaysSky) accepts the frozen arcs (one donor per use, a donor carries one of + its own operands, acyclic generalized dependency graph, every value span inside its backward-intersection frame, + exact positive-rank ledger with mass h·R + loss) and keeps them unchanged; `select` chooses the gauges. +3. **Frames**: the script's forward closure, run with every frozen frame as the preferred frame, returns every frozen + frame unchanged; the frozen list is the script's canonical list of moved frames. +4. **Pairs**: every pair is an edge of the script's candidate graph, one pair per donor and per recipient, and the + list is a fixed point of the script's last-late-control reordering. `paircheck.py` then re-checks the pairs from + the written word alone (kinds, one-to-one, every gauge paired, early and late chronology, donor frame inside the + gauge, no pair erasable by PR #184's source-donor purification) and rejects five mutations, each for the condition + it breaks. +5. **Physical checks** (`scripts/paired_cube_physical.py`, PR #168 lineage): nested role chains, pair legality and + read chronology, the exact spliced recount, and a randomized numeric replay of the aliased signed word mod 2⁶¹ − 1 + with random dirty scratch; `verify.py` recomputes this profile in-process and requires it to equal the file. +6. **Admission** (PR #200's complete complex checker `complex/physical.py`, Chafik Boukhalfa): exact signed scalar + pairs, full backward and gauge intersections, the positive-rank ledger recounted against the record, descended + frames, nested chains, aliases and target read chronology, the exact adjoint with a formal coefficient bound, + every formal source, target and dirty column; the early-read and missing-read mutations are rejected. +7. **Flow and exact lift** (PR #184, icekylinx): `complex_frame_flow.py --witness --purify-source-donors + --recycle-kernels` with the frozen kernel pairs, then `exact_complex_flow_lift.py`. +8. **Contract** (PR #194's `contract_v4.py`, as PR #233 runs it). +9. **Program** (PR #256's `gcert_emit.py`, unchanged) and **reference checks** on the emitted program: `gx.check1` + (E0/E1 labels, E2 the scatter cut, E3/E4 gate shapes, E5 the exact scalar identity, E6 the price data + N = R·h + 2v(h − 1) + cst) and Sussman's `gxcore.py` mirror (its block histogram equals the program's). +10. **Ledger**: 3(x + y + s + c) + 2v·e₂ of the program's block histogram equals the flow's child histogram. +11. **Star scatter** (`normalize_scatter.py`): all six programs are emitted in star form (every retained-total unit + is +1), so nothing is re-signed; `gx.check1` and `gxcore` accept the committed program again, and both reject it + with one scalar sign flipped (E5). +12. **Price** at h = 20: H₅ = 5·H_inv + 2v(e₃₈ + e₁₉ + e₄₂ + e₄), m = 100, W = 4v + R; W·m − |H₅| = 4v − 5·cst = 2,040 + (cst = h(h − 2) = 360). (a) The moment Σ n_r (r/m)^{1−a} is below W at the claimed a by PR #225's exact upper + bound (PR #304's convention), and also with the fallback envelope added (32·m²·Σn rank-one calls at weight + 10⁻¹⁶); at a + 10⁻⁷ PR #225's bound fails and source527's exact lower bound of the normalized moment exceeds 1. + (b) The coarse saving b: the largest 10⁻¹⁸ grid point at which the normalized moment with the fallback is below 1, + certified by `scripts/source527/moment.py` (with its `bad` envelope) and by `base_two_moment.py` (the envelope as a + separate rank-one term), the next 10⁻¹⁸ point excluded by both; the same without the fallback is recorded; a ≤ b. +13. **Reproduction**: the six programs equal the committed `certificates/` byte for byte (uncompressed JSON), and + every number above equals `certificate/expected.json`. + +## 3. Anchors + +- **(a)** `aligned_word_p.py` at its default p = 11, given PR #168 v4's modules and the source-aligned word's own arcs, + frames and pairs, reproduces the seven output files of `source_aligned_local_v4.py` byte for byte. +- **(b)** PR #194's word through this package's chain (at p = 11) gives PR #256's certificate of that word (same + sha256 of the canonical JSON) and the block histogram of Sussman's published certificate of #193 in every class and + rank; the generic idle-rank formula gives PR #304's (42, 21, 46, 4) there. +- **(c)** The control modules are `module_cut.min_cut` of PR #168 v4's three module files in the rebuilt tree (the + fewest-additions single-point zero restriction), byte for byte. +- **(d)** PR #315's patch `references/centre46_graph.diff` applied to the rebuilt `scripts/paired_cube/graph.py` + builds, on the centre-sharing modules, the same graph as `centre46.finish_centre46` in every field but the status + string, and leaves the graph of the 36-root pair module unchanged. +- There is no external histogram for any p = 10 word: nothing else compiles this word at p = 10. The control passes + the same chain and is the like-for-like baseline; the exploratory runs that first produced these programs (with a + script version of the same recipe) gave the same programs. + +## 4. Results + +| word | R | registers | blocks | N | W | certified a | rejected | coarse b with fallback (/10¹⁸) | +|---|---|---|---|---|---|---|---|---| +| control, parity pairs | 7,121 | 9,041 | 49,631 | 179,260 | 10,961 | 7322/10⁷ | 7323/10⁷ | 732209244332069 | +| control, mw pairs | 7,125 | 9,045 | 49,282 | 179,340 | 10,965 | 7375/10⁷ | 7376/10⁷ | 737511222939316 | +| PR #304 recipe, parity pairs | 6,515 | 8,435 | 48,602 | 167,140 | 10,355 | 7689/10⁷ | 7690/10⁷ | 768912365785154 | +| PR #304 recipe, mw pairs | 6,515 | 8,435 | 48,299 | 167,140 | 10,355 | 7737/10⁷ | 7738/10⁷ | 773718577669358 | +| centre-sharing, parity pairs | 6,455 | 8,375 | 48,278 | 165,940 | 10,295 | 7747/10⁷ | 7748/10⁷ | 774746506241368 | +| centre-sharing, mw pairs | 6,455 | 8,375 | 47,979 | 165,940 | 10,295 | 7795/10⁷ | 7796/10⁷ | 779597612622781 | + +Every program has m = 100, deficit 2,040, cst = 360, scalar denominators 2 (x, slots) and 6 (y), and the star scatter +as emitted. The fallback lowers the coarse saving by about 3·10⁻¹² (`certificate/expected.json`). Gains on the +certified grid points: annealed over control +4.91% (mw, 362/7375) and +5.01% (parity); centre-sharing over control ++5.69% and +5.80%; PR #304's recipe at p = 10 over PR #304 at p = 11 (7635 and 7586/10⁷) +1.34% and +1.36%; the +centre-sharing word over PR #315's p = 11 centre-sharing program (7727/10⁷) +0.88%. The centre-sharing set has no +control of its own: against the PR #304-recipe set (7795 vs 7737, +0.75%) it changes both the graph (the centre +patch) and the pair module (`pmod46_pc1_p10.json` vs `pmod_p3_p10.json`, different parents), so that gain is not +the patch's alone. + +## 5. What is not claimed + +- **No Lean build in this package.** `verify.py` checks the programs with Sussman's Python reference checker and his + Python mirror of the Lean checks. Separately, both mw programs were compiled with his unchanged generator and + kernel-checked locally (`wht_main_block_B2Gcc95x`, 1 − 7795973/10¹⁰; `wht_main_block_B2Gcp37x`, + 1 − 7737183/10¹⁰; `tools/Compare.lean` passed; axioms propext, Classical.choice, Quot.sound; see README). The + official comparator was not run, and the Lean files are not part of this package. +- **The five-stage layout at h = 20.** The ledger H₅ = 5·H_inv + 2v(e_{2h−2} + e_{h−1} + e_{2h+2} + e₄), m = 5h, + W = 4v + R is applied at h = 20 as the generic formula. PR #304 applied it at h = 22 only (as did every Lean run of a + complex program), and at R values other than #193's; that it holds verbatim here is the generic B₂ statement of + Sussman's repository (`bankPrice h`), not something this package re-proves. +- **The fallback envelope** (10⁻¹⁶, 32·m² rank-one calls per paid child) is the five-stage packages' inherited + assumption, here evaluated at m = 100; it is not a new m = 5h admission. +- **What a κ package must change to adopt these programs.** The outer assembly uses only the two coarse savings, + and the two suppliers' widths already differ in PR #315 (bit m = 100, complex m = 110). But PR #315's package + (and PR #296's, from which its complex checks come) pins the p = 11 complex program in five places, which must be + generalized or re-pinned before a p = 10 program can be used: + - `code/complex_labels.py`, `code/complex_scalars.py` and `code/complex_splice.py` hard-code h = 22, v = 1,320 and + 22 centres; + - `portable_complex.py` asserts (110, 9036, 22, 14316) and pins R, N and the reference histograms; + - `math_check.complex_supplier()` asserts m = 110, W = 14,316, the histogram totals (351,820 calls, 1,571,680 + rank mass) and the literal b. + + The programs here are in the star form those checks read. This package does not make those changes. +- **Record correction.** On the control's cut modules `select()` chooses 8 gauges of ranks 14 and 13 that the + script drops; `aligned_word_p.py` removes their births from the record so that PR #200's checker can recount it. + The correction is checked, not trusted: the checker recounts the ledger from the word. The programs do not read + the corrected fields (`physical()` reads other record fields, none of the three corrected ones). +- **Discovery is numerical.** Floating-point scores chose the modules, frames and pairs; every choice is a frozen input + that the chain checks exactly. The annealing effort is asymmetric (about 1.5 h at p = 10 against the p = 11 + anneals of PR #168 and PR #304), so the p = 10 prices are not a bound on what p = 10 modules can reach. Cutting + PR #304's p = 11 modules straight to p = 10 gives only 7235/10⁷, so the gain over p = 11 comes from re-annealing at + p = 10, not from the cut. diff --git a/research/complex-p10/README.md b/research/complex-p10/README.md new file mode 100644 index 0000000000..3c8a3fc030 --- /dev/null +++ b/research/complex-p10/README.md @@ -0,0 +1,171 @@ +# complex-p10 + +**The complex supplier at cube size p = 10 (no new κ).** PR #304 compiled the source-assisted complex word of PR +#184/#194 at p = 11 (h = 22, 1,320 ports) on re-annealed query modules, and PR #315 ships a centre-sharing version of +it. This package compiles the same word with the same frozen recipe one cube size down, at **p = 10 (h = 20, 960 +ports)**, on query modules cut from p = 11 module files and re-annealed at p = 10. Each word is one explicit gcert/1 +program that Jacob Sussman's reference checker `gx.check1` (exact scalar identity) and his Python mirror of the two +Lean checks (`gxcore.py`), both vendored unchanged, accept. Priced in his bridged five-stage layout at h = 20 +(m = 5h = 100, W = 4v + R; see "The layout at h = 20") with exact rational bounds: + +**centre-sharing modules (PR #233 pairs): a = 7795/10⁷ (7796/10⁷ rejected), against 7727/10⁷ for PR #315's p = 11 +centre-sharing program: +0.88%.** +**PR #304's recipe on annealed p = 10 modules (PR #233 pairs): a = 7737/10⁷ (7738/10⁷ rejected), against 7635/10⁷ +for PR #304 at p = 11: +1.34%.** + +Both claims also hold with the five-stage packages' 10⁻¹⁶ bad-class fallback envelope included; the fallback-inclusive +coarse savings that a five-stage package would consume are b = 779597612622781/10¹⁸ (centre-sharing) and +773718577669358/10¹⁸ (PR #304's recipe), each certified by two independent rational moment engines with the next +10⁻¹⁸ point rejected. + +**No new κ by itself.** On the open frontier (community stacks on PR #315's p = 10 bit word, best PR #320 at +κ 7.69199e-4; cited, not checked here) the bit side binds: it lies below PR #315's complex supplier (7727/10⁷) and +below both prices here. If a κ package adopts this supplier, the complex cap rises from 7.727e-4 to 7.796e-4 +(+0.89%), so that the bit side could pass 7.727e-4 without the complex supplier capping κ there. A κ package must first +generalize or re-pin the five places where PR #315's package pins its p = 11 complex program (listed in PROOF.md §5); +this package does not do that. + +| program (gcert/1, five-stage layout m = 100, W = 4v + R) | modules | pairs | R | registers | blocks | N | gx.check1 and gxcore | saving a | +|---|---|---|---|---|---|---|---|---| +| control, parity recipe | PR #168 v4 cut to p = 10 | PR #193 recipe | 7,121 | 9,041 | 49,631 | 179,260 | accepted | 7322/10⁷ | +| control, mw recipe | PR #168 v4 cut to p = 10 | PR #233 recipe | 7,125 | 9,045 | 49,282 | 179,340 | accepted | 7375/10⁷ | +| PR #304 recipe, parity | annealed at p = 10 | PR #193 recipe | 6,515 | 8,435 | 48,602 | 167,140 | accepted | 7689/10⁷ | +| **PR #304 recipe, mw** | **annealed at p = 10** | PR #233 recipe | **6,515** | 8,435 | 48,299 | 167,140 | accepted | **7737/10⁷** | +| centre-sharing, parity | annealed, centre pair module | PR #193 recipe | 6,455 | 8,375 | 48,278 | 165,940 | accepted | 7747/10⁷ | +| **centre-sharing, mw** | **annealed, centre pair module** | PR #233 recipe | **6,455** | 8,375 | 47,979 | 165,940 | accepted | **7795/10⁷** | + +Against the same-recipe control the annealed modules gain +4.91% (mw) and +5.01% (parity), the centre-sharing set ++5.69% and +5.80% on the certified grid points. Against the p = 11 programs: PR #304's recipe at p = 10 beats PR +#304 (7635 and 7586/10⁷) by +1.34% and +1.36%; the centre-sharing word beats PR #315's (7727/10⁷) by +0.88%, and +even PR #304's recipe at p = 10 passes it (+0.13%). [PROOF.md](PROOF.md) states the claim and the chain of checks. + +## The layout at h = 20 + +The price uses Sussman's bridged five-stage word B₂ with the h-dependent idle climbs written out: +H₅ = 5·H_inv + 2v·(e_{2h−2} + e_{h−1} + e_{2h+2} + e₄), m = 5h, W = 4v + R. At h = 22 these are PR #304's literals +(e₄₂, e₂₁, e₄₆, e₄); here they are **e₃₈, e₁₉, e₄₂, e₄**, m = 100, and the deficit is 4v − 5·cst = 3,840 − 5·360 = +2,040 for every program (20 scratch copies of 18 moves, cst = h(h − 2)). This is the generic formula applied at a new +h: PR #304's price, PR #315's complex supplier and Sussman's Lean build of #193 are all at h = 22. In his +repository the layout is stated for every h (`bankPrice h` +in `Work/BridgeGeom/B2.lean`, `bridge2_gcert` and `GX.wht_of_halves` parametric in the label dimension; `gxunit.unit` +builds the unit from `BANK['B2']` as functions of h). Both mw programs here were kernel-checked at h = 20 with his +unchanged generator (below). `verify.py` re-derives the h = 22 literals from the same formula on its PR #194 anchor. + +## Verify + + python -m pip install numpy==2.3.5 scipy==1.17.0 # for the pinned regeneration and the checkers + python3 -B research/complex-p10/verify.py # about 12 minutes; -O is refused + +The script checks every pin of `SOURCE.json`, rebuilds the 308 pinned files of PR #202 from the vendored PR #233 +package and regenerates the producer word and the source-aligned word at p = 11 (PR #194's pipeline). Four anchors +follow: `aligned_word_p.py` at its default p = 11 reproduces the seven output files of `source_aligned_local_v4.py` +byte for byte; PR #194's word through this package's chain is PR #256's certificate (same sha256) with Sussman's #193 +histogram; the control modules are re-derived from PR #168 v4's module files byte for byte (`module_cut.py`); and PR +#315's 10-line `Graph.finish` patch, applied to the rebuilt `graph.py`, builds the same graph as `centre46.py`. Then, +for each module set and pair recipe, it installs the modules and the frozen layer, builds the word with +`aligned_word_p.py --p 10`, re-checks the pairs with `paircheck.py` (five mutation controls), recomputes PR #168's +`physical()` profile and admits the layer with PR #200's complete complex checker, runs PR #184's flow and exact lift +and PR #194's contract, emits the gcert/1 program with PR #256's `gcert_emit.py` (unchanged), runs `gx.check1` and +the `gxcore` mirror on the emitted program, checks the ledger, writes the scatter as the star rule with +`normalize_scatter.py`, runs `gx.check1` and `gxcore` again, requires both to reject a flipped scalar sign (E5), +prices the five-stage word at h = 20 at the claim of `SOURCE.json` with and without the fallback envelope (next 10⁻⁷ +point rejected by an exact lower bound) and certifies the fallback-inclusive coarse saving on the 10⁻¹⁸ grid with +both engines, and compares the six committed programs byte for byte (uncompressed JSON) with `certificates/` and the +run with `certificate/expected.json`. `--temp-root` chooses scratch storage. + +All six programs come out of the emitter in star form (every retained-total unit is +1), so at p = 10 +`normalize_scatter.py` changes nothing; the step stays as a check. The committed files are the emitted programs in +canonical JSON (sorted keys). + +To check a certificate with Sussman's other tools (not run for this package): + + python3 -B tools/gx/refcheck.py /certificates/gcert1-p10-centre-mw-flow.json.gz # in his repository + python3 -B tools/gx/gxdry.py /certificates/gcert1-p10-centre-mw-flow.json.gz # mirror and price + +and to build it in Lean with his unchanged generator (about 10 minutes of kernel time per program at h = 20): + + GX_OUT= python3 -B tools/gx/regen_check.py /gcert1-p10-centre-mw-flow.json.gz CC95 B2Gcc95 --keep + cp -R /Work/GCert/Data/. Work/GCert/Data/ # then lake build each module in the printed build order + lake env lean --run tools/Compare.lean Work.GCert.Data.ChallengeB2Gcc95x Work.GCert.Data.SolutionB2Gcc95x OAI.PowerSaving.WHT.wht_main_block_B2Gcc95x + +A dry run of the Python half of that generator (`regen_check.py --keep` into a scratch directory; not part of +`verify.py`) accepts both mw programs at h = 20 (its `gxcore` mirror of both Lean checks; 6 data segments, 4 replay +segments, 2 scalar batches) and states the whole-block rates 1 − 7795973/10¹⁰ (centre-sharing) and +1 − 7737183/10¹⁰ (PR #304's recipe) for the theorems it emits. + +**Lean (run locally; not pinned in this package).** Both mw programs were compiled with Sussman's unchanged +generator (`tools/gx/regen_check.py`, wht-power-saving-lean at f010392, Lean v4.34.1, Mathlib d13f23b) and +kernel-checked, one module at a time (31 of 31 built modules each, 0 errors): + +| program | theorem | exponent | gcert sha256 (uncompressed) | +| --- | --- | --- | --- | +| centre-sharing mw | `OAI.PowerSaving.WHT.wht_main_block_B2Gcc95x` | 1 − 7795973/10¹⁰ | `370fae73…23ff` | +| PR #304's recipe mw | `OAI.PowerSaving.WHT.wht_main_block_B2Gcp37x` | 1 − 7737183/10¹⁰ | `433848305e…16e5` | + +The hashes equal the `certificate_sha256` values pinned in `certificate/expected.json`. `tools/Compare.lean` +passed for both, against challenge files that differ from his ChallengeB2Gp193x only in the module and theorem +names and the exponent. `#print axioms` gives `propext`, `Classical.choice` and `Quot.sound`. Nothing h-specific +broke at h = 20 (the generator emits 6 data and 4 replay segments). The official comparator and a clean build +from nothing were not run. This covers the Walsh–Hadamard power-saving theorem at these exponents, not any +integer-multiplication κ assembly. + +## Modules + +| set | triple module (p = 10) | pair module (n = 9) | all-but-one module (n = 8) | +|---|---|---|---| +| `pr168-v4-cut` (control) | PR #168 v4's, point 6 dropped (1,220 additions) | PR #168 v4's, point 4 dropped (256) | PR #168 v4's, point 1 dropped (24) | +| `anneal` (PR #304 recipe) | `tmod_t2_p10.json` (1,322) | `pmod_p3_p10.json` (269) | `qmod_sa1_p10.json` (24) | +| `centre` | `tmod_t2_p10.json` | `pmod46_pc1_p10.json` (291, 37 roots) | `qmod_sa1_p10.json` | + +Every module is a zero restriction of a p = 11 module file followed (except the control's) by simulated annealing at +p = 10 against a closed-form evaluator of the aligned word's compile ledger: the triple and all-but-one modules from +PR #304's `tmod_cmod_v2.json` and `qmod_cmod.json`; the pair module of the PR #304-recipe set from PR #168 v4's pair +module (the control's cut); the centre-sharing pair module from PR #304's `pmod_cmod_dropin.json`, annealed, given a +37th root (the sum of all its inputs) and annealed again with it. [discovery/README.md](discovery/README.md) has the +cut points, chains and energies. The annealing code is research code and is not included; the module files are inputs, +checked by the rebuilt tree's contract loaders (`load_pmod46` for the 37-root module) and priced by the chain. + +**The centre-sharing graph.** In PR #144's `Graph.finish` every star centre S(2i + e) is a separate sum of the +inputs of the pair module (i, e). The centre-sharing pair module returns that sum as its 37th root, and the graph uses +it as the centre: PR #315's 10-line patch (`references/centre46_graph.diff`, icekylinx's `graph.py`) does this inside +`Graph.finish`; `centre46.py` (`finish_centre46`, `load_pmod46`) does it without editing the tree. `verify.py` applies +the patch to the rebuilt `graph.py` and requires the two graphs to agree in every field except the status string, +and the patch to leave the graph of an ordinary 36-root pair module unchanged. + +## Two latent bugs, fixed for p ≠ 11 + +- **PR #233's `pairs_mw.py` hard-codes the gauge rank f = 18**, which is h − 4 only at h = 22. At h = 18 (p = 9) + every donor weight is then 0 and the maximum-weight pairing returns no pairs. `discovery/pairs_mw_p.py` reads + f = h − 4 (one line; identical at h = 22). The weights only choose pairs, which `verify.py` checks independently; on + this package's layers the literal happens to give the same pairs (discovery/README.md). +- **`source_aligned_local_v4.py` keeps the births of dropped gauges in its record.** The script keeps only the + selected gauges of rank h − 4 that are paired, but its record (`selected_roles`, `selected_rank_histogram`, + `remaining_internal_histogram`) still counts every gauge `select()` chose. On every p = 11 module set and on the + annealed p = 10 modules `select()` chooses only rank-(h − 4) gauges, so the record is exact; on the control's cut + modules it also chooses 8 gauges of ranks 14 and 13, and PR #200's complex checker (which recounts the record) + rejects the word. `aligned_word_p.py` reverses the births of dropped gauges in those three fields (and changes + nothing when none is dropped, which anchor (a) confirms byte for byte at p = 11). Only the verifiers read these fields; the + programs are unaffected. + +## Re-pinning after a module changes + + python3 -B research/complex-p10/discovery/make_layer_p.py --set anneal --tmod # ~90 s + python3 -B research/complex-p10/verify.py --write + python3 -B research/complex-p10/verify.py + +`--write` re-pins `modules/` and `layers/` (no other pin), sets every claim to the largest 10⁻⁷ grid point its exact +bounds certify, and rewrites `certificates/` and `certificate/expected.json`; the numbers in this file and in +PROOF.md are then updated by hand. + +## Files + +`verify.py`; `aligned_word_p.py` (PR #304's `aligned_word.py` with the cube size, the centre-sharing option and the +record correction); `centre46.py`; `module_cut.py` (zero restriction; re-derives the control modules); `paircheck.py` +and `normalize_scatter.py` (PR #304's, unchanged); `modules/` (seven module files); `layers/{pr168-v4-cut,anneal, +centre}/` (frozen carrier arcs, operation frames, reuse pairs of both recipes, kernel pairs); +`certificates/gcert1-p10-{pr168-v4-cut,anneal,centre}-{parity,mw}-flow.json.gz` (the six programs, star form, about +0.32 MB each); `certificate/expected.json`; `gcert_emit.py`, `gx/gx.py`, `scripts/moment.py` and `references/` +(`pr233-layer/`, `sussman/`) vendored byte for byte from PR #256 via PR #304; `gx/gxcore.py` (Sussman's, unchanged); +`scripts/source527/` (eumemic's two moment engines, unchanged); `references/centre46_graph.diff` (PR #315's); +`discovery/` (how the layers and modules were found; not run by `verify.py`); `SOURCE.json`, `PROOF.md`, `NOTICE`. +`.github/workflows/complex-p10.yml` runs the verifier on Python 3.12 and 3.14. diff --git a/research/complex-p10/SOURCE.json b/research/complex-p10/SOURCE.json new file mode 100644 index 0000000000..c4a690ff22 --- /dev/null +++ b/research/complex-p10/SOURCE.json @@ -0,0 +1,167 @@ +{ + "description": "Pinned inputs of research/complex-p10 (sha256). Vendored byte for byte; nothing is fetched at run time. verify.py --write re-pins only the package's own inputs (modules/, layers/) and the claims; every other pin is fixed.", + "files": { + "gcert_emit.py": "10d2fc3f1f3d8cda5f0b07720f51b5a6fd40cfc1490d361939ff93e5470805d3", + "gx/gx.py": "6f3dc8bb639933227a8dae181ec4a542e85c7276be9c9e330f49518e7b630b95", + "gx/gxcore.py": "eb972c06fe8c322db2d9a8d9a7d05596e8f40c4ca8e5f42eb6df3c7361b5d517", + "layers/anneal/kernel-pairs-mw.json": "e47454fb1838c9372a403b5156bc195630ba6f0cfcaf71b92170f05f111a11cc", + "layers/anneal/kernel-pairs-parity.json": "e47454fb1838c9372a403b5156bc195630ba6f0cfcaf71b92170f05f111a11cc", + "layers/anneal/matching-arcs.json": "96c87aac70b6ef0671872d142ccba66448ffa8f5f42c35f32c0f655668251f02", + "layers/anneal/physical-frames.json": "7b24c9d5498bcdf96a72a061a95ff7b4ff2cda0bef5d7c7307afe72685959422", + "layers/anneal/physical-pairs-mw.json": "2af485c88a240c1c96d0c5b5a31851587eb99a8513e18becd49b3a7e74bcf3a8", + "layers/anneal/physical-pairs-parity.json": "0bff907fa41409fb1269323001a2ef313fcfaf03937597af7a63f6c4dc6854e4", + "layers/centre/kernel-pairs-mw.json": "e47454fb1838c9372a403b5156bc195630ba6f0cfcaf71b92170f05f111a11cc", + "layers/centre/kernel-pairs-parity.json": "e47454fb1838c9372a403b5156bc195630ba6f0cfcaf71b92170f05f111a11cc", + "layers/centre/matching-arcs.json": "ea7300db2cdb324ddf680bee6d447e9a9994e0b77bf2cf7fbf25e7cd1f6cb16e", + "layers/centre/physical-frames.json": "1f9813eee92459b341fd437f4ec3a87ae9b440384a277450f483112481381b12", + "layers/centre/physical-pairs-mw.json": "6c910a4ed8fe325547d9da065edbe8176969048724c0f96ee43a075b2813bd53", + "layers/centre/physical-pairs-parity.json": "1ad1c36760848259270ab1710bb2ce0dea877195d3a763e0c9fb5c7624a751bc", + "layers/pr168-v4-cut/kernel-pairs-mw.json": "e47454fb1838c9372a403b5156bc195630ba6f0cfcaf71b92170f05f111a11cc", + "layers/pr168-v4-cut/kernel-pairs-parity.json": "d063546163d14e380747210cd0a060519d47061df1726aeb4707efc400c2a550", + "layers/pr168-v4-cut/matching-arcs.json": "22a28397c5c249438c36d087c14a16e99379891d45b2ad941af38944c971e166", + "layers/pr168-v4-cut/physical-frames.json": "8a1ae36d0d99d4dc9ee82a76422bcbd902dce360fcdd55a7a23fc17e4aa801c4", + "layers/pr168-v4-cut/physical-pairs-mw.json": "d12efcdd3091134c7506eed3e53c02dab1fa566d30bc3a0ad96559f767036dd3", + "layers/pr168-v4-cut/physical-pairs-parity.json": "5451e37e128850c6ae440ffda2010bd28d7fe8c127865387b662b4efd92cd744", + "modules/pmod46_pc1_p10.json": "7f0bfd151e7ec0b2a74bc6fd994acde477e23f1425f4da798202f510489b6a3c", + "modules/pmod_p3_p10.json": "5bb49c8befbbeb2f38a50c5b2ac836261074ef578a0a5697a8267b23551e96ab", + "modules/pmod_pr168_p10.json": "36053689bec46354916a6f412b891dd5b510edcb546ea6cf9bcbaddd34c1fe28", + "modules/qmod_pr168_p10.json": "c62504c96cb68658c4eade0f81cfb3a3733674519ebf7ddda1acbc18176e092b", + "modules/qmod_sa1_p10.json": "7f7f96efc14921c9dbd8a888a7f3a35b267f7c47d0a8e1e3926c3ff34011e8a6", + "modules/tmod_pr168_p10.json": "a81da2ba642ccf448a542825b02d678d430c9078e22f8a80813d409ae3c5cb48", + "modules/tmod_t2_p10.json": "4d39faeedfb5a5283a7ad34a8a18af93072e4d155d61dec6c28d7751bc2e4e04", + "references/centre46_graph.diff": "229eea46b56d19b262d1498f489f9bca84c347e33b16553079d38c4276700280", + "references/pr233-layer/NOTICE": "5826b9f155b70d496d729cbaddeadb881abfb68da77f82dfc1746ddfc753313b", + "references/pr233-layer/SOURCE.json": "9ad0549ba2403e8d84d7c0c8e71e5ca952a0604ad626f403426164bd4bc2982c", + "references/pr233-layer/baseline-pr202.tar.gz": "5d08386f71c421d2b83b21020e3b74198e9d0c75884d7d81987307740d98883f", + "references/pr233-layer/certificate.json": "691cb0aaeb0d6b993e1e1e5116ae7a5c57af058a8c413249016347d1b40d3b90", + "references/pr233-layer/verify.py": "cd61a8c61462b4eee95c0858335a9a11bdf1ff8e8e63ebb1e488da29f061ca71", + "references/pr233-layer/witness/kernel-pairs.json": "e33b753fc4519170373207b0527b9cb53e0b552e2a27f48f72381a881c7a227f", + "references/pr233-layer/witness/physical-frames.json": "1a6c215cdc58216f7ec96fb898a471e25d094fd86de085f6c06e86fd8997bfad", + "references/pr233-layer/witness/physical-pairs.json": "e6409fffbf5f3b1ac6434acf2e426503de3a8a18537b8fee761fc4fc931fb896", + "references/sussman/pr193-blocks.json": "4049d066f71119fa72bbc37f7db753ce1e79ae5a69aef9cd2651d618bea5c855", + "scripts/moment.py": "0c7c68122cea18503e973ccf0d244adf8fa0edab95f104393528c6c57f24863a", + "scripts/source527/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098", + "scripts/source527/moment.py": "9d465c716c6b910ff66e1453e3bf0057608a787b5f5361be93781f42cb3370f7" + }, + "module_sets": { + "pr168-v4-cut": { + "pmod": "modules/pmod_pr168_p10.json", + "qmod": "modules/qmod_pr168_p10.json", + "tmod": "modules/tmod_pr168_p10.json" + }, + "anneal": { + "pmod": "modules/pmod_p3_p10.json", + "qmod": "modules/qmod_sa1_p10.json", + "tmod": "modules/tmod_t2_p10.json" + }, + "centre": { + "centre46": true, + "pmod": "modules/pmod46_pc1_p10.json", + "qmod": "modules/qmod_sa1_p10.json", + "tmod": "modules/tmod_t2_p10.json" + } + }, + "claims": { + "pr168-v4-cut-parity": "7322/10^7", + "pr168-v4-cut-mw": "7375/10^7", + "anneal-parity": "7689/10^7", + "anneal-mw": "7737/10^7", + "centre-parity": "7747/10^7", + "centre-mw": "7795/10^7" + }, + "official": { + "pr304-mw": [ + "PR #304: re-annealed modules at p = 11, PR #233 pairs: 7635/10^7", + "7635/10000000" + ], + "pr304-parity": [ + "PR #304: re-annealed modules at p = 11, PR #193 pairs: 7586/10^7", + "7586/10000000" + ], + "pr315-centre": [ + "PR #315: centre-sharing p = 11 program, PR #233 pairs: 7727/10^7", + "7727/10000000" + ], + "pr233": [ + "the PR #233 word in the five-stage layout: 7547/10^7 (PR #256, exact bounds)", + "7547/10000000" + ] + }, + "prerequisites": { + "frontier": { + "note": "open frontier (cited, not checked here): community stacks on PR #315's p = 10 bit word, best PR #320 at kappa 7.69199e-4; the complex supplier then binding is PR #315's centre-sharing p = 11 program, 7727/10^7" + }, + "pr202": { + "commit": "8d8d67bcf69c5ea67d3a29dbc64ba588156d6e8d", + "note": "the 308 files rebuilt by references/pr233-layer/verify.py: PR #184 flow/lift (icekylinx), PR #194 v4 scripts (ikeboy), PR #168 modules (eumemic), PR #200 checker (chafreaky)", + "repository": "CrocSwap/integer-mult-bounds" + }, + "pr225": { + "note": "scripts/moment.py: exact rational moment bounds (chafreaky; adapted from eumemic/exact-dft-bounds scripts/verify_moment.py, Apache-2.0)", + "path": "research/exact-dft-transfer/scripts/moment.py", + "pr": 225, + "repository": "CrocSwap/integer-mult-bounds" + }, + "pr233": { + "author": "chafreaky (Anthropic Claude and OpenAI Codex assistance); PR #202 baseline by ikeboy et al., see NOTICE", + "commit": "109a857", + "complex_saving": "3549537/5000000000", + "path": "research/source-assisted-v4-layer", + "pr": 233, + "repository": "CrocSwap/integer-mult-bounds", + "vendored": "references/pr233-layer (baseline-pr202.tar.gz, SOURCE.json, verify.py, certificate.json, NOTICE, witness/), as vendored by PR #256" + }, + "pr256": { + "author": "chafreaky (Anthropic Claude and OpenAI Codex assistance)", + "commit": "db3f75cdc5f03f3131d48fb220f6bf1958404ff3", + "path": "research/gcert-program-233", + "pr": 256, + "pr194_certificate_sha256": "27398a0cfcbe34e5ee97360e69a2d163a417c8ae1b4fdf28ccf89a9eaf4e4cd4", + "pr233_certificate_sha256": "0c026244591a0b6737993aaac5fa8ac4a2bd27aa28e469f2567c698f57ed10a8", + "pr233_five_stage": "7547/10^7", + "repository": "CrocSwap/integer-mult-bounds", + "vendored": "gcert_emit.py, gx/gx.py, scripts/moment.py, references/pr233-layer/, references/sussman/pr193-blocks.json (byte for byte; the certificate sha256 values are of the canonical uncompressed JSON, from its certificate/expected.json)" + }, + "pr304": { + "pr": 304, + "repository": "CrocSwap/integer-mult-bounds", + "commit": "7ac169c58c96cebdb5cd490842331dff3610af62", + "path": "research/complex-module-anneal", + "author": "DreamingOfClouds (Anthropic Claude assistance)", + "claims": { + "cmod-mw": "7635/10^7", + "cmod-parity": "7586/10^7", + "pr168-v4-mw": "7522/10^7", + "pr168-v4-parity": "7469/10^7" + }, + "vendored": "aligned_word_p.py (= its aligned_word.py with --p and --centre46), paircheck.py, normalize_scatter.py, discovery/make_layer_p.py (= its discovery/make_layer.py with --p, --centre46, pairs_mw_p.py), discovery/extend_floor.py and discovery/pr233/ (byte for byte); verify.py follows its verify.py", + "note": "the p = 11 programs whose recipe this package applies at p = 10: the re-annealed modules tmod_cmod_v2.json, pmod_cmod_dropin.json and qmod_cmod.json are the parents of three of the four p = 10 modules" + }, + "pr315": { + "pr": 315, + "repository": "CrocSwap/integer-mult-bounds", + "commit": "243899975d0fbe888d5deda399060885d609e0a1", + "path": "research/five-stage-p10-banks", + "author": "DreamingOfClouds (Anthropic Claude assistance)", + "complex_supplier": "inputs/complex/gcert1-p11-cmod-centre-mw-flow.json.gz: the centre-sharing p = 11 program, 7727/10^7 (with the 10^-16 fallback 772714351296671/10^18)", + "vendored": "references/centre46_graph.diff (its inputs/complex/centre-mw/centre46_graph.diff, byte for byte: the 10-line Graph.finish patch whose effect centre46.py reproduces)" + }, + "source527": { + "repository": "CrocSwap/integer-mult-bounds", + "commit": "b07cafe23202d22d832961a04b07d48d9b245e10", + "path": "research/five-stage-source527-banks", + "author": "eumemic (OpenAI Codex assistance), PR #210 lineage; see scripts/source527/NOTICE", + "vendored": "scripts/source527/moment.py and scripts/source527/base_two_moment.py, byte for byte: the two rational moment engines with which the five-stage packages certify a coarse saving with the 10^-16 fallback envelope" + }, + "sussman": { + "commit": "f010392c", + "files": { + "tools/certificate/gcert1-p11-pr193.json.gz": "15251deb0c11e0504d7b297c9786818888a93f08b92b03c6c122784b70488633 (its block histogram and counts in references/sussman/pr193-blocks.json)", + "tools/gx/gx.py": "6f3dc8bb639933227a8dae181ec4a542e85c7276be9c9e330f49518e7b630b95 (vendored unchanged as gx/gx.py)", + "tools/gx/gxcore.py": "eb972c06fe8c322db2d9a8d9a7d05596e8f40c4ca8e5f42eb6df3c7361b5d517 (vendored unchanged as gx/gxcore.py: his Python mirror of the two Lean checks, independent of gx.py)" + }, + "licence": "Apache-2.0, Copyright 2026 Jacob Sussman", + "repository": "jacobalansussman/wht-power-saving-lean" + } + } +} diff --git a/research/complex-p10/aligned_word_p.py b/research/complex-p10/aligned_word_p.py new file mode 100644 index 0000000000..98da711519 --- /dev/null +++ b/research/complex-p10/aligned_word_p.py @@ -0,0 +1,265 @@ +#!/usr/bin/env python3 +"""aligned_word_p.py: PR #194's source-aligned complex word for given query modules and a frozen physical layer, at any +cube size p. + +PR #304's aligned_word.py with three changes: (1) --p (default 11): Graph(p) and the module sizes p, p - 1, p - 2 +replace the literals 11, 10, 9; (2) --centre46: the pair module carries a 37th root (the sum of all its inputs) that +supplies the star centre (centre46.py, the effect of PR #315's Graph.finish patch); (3) when select() chooses gauges +that the script then drops (rank other than h - 4, or unpaired), the record's gauge ledger (selected_roles, +selected_rank_histogram, remaining_internal_histogram) is corrected to the kept gauges, so that PR #200's checker can +recount it; nothing is dropped at p = 11 or on the annealed p = 10 modules, so the output is then unchanged. At +p = 11 without --centre46 it is aligned_word.py. + +This is research/source-assisted-v4/source_aligned_local_v4.py of PR #202 (ikeboy, PR #193/#194; derived from +icekylinx's research/source-assisted/decision/source_aligned_local.py, GPT-6 Astra assistance, Apache-2.0) with +its four discovery steps replaced by inputs: + * the three query modules are --tmod/--pmod/--qmod (the script hard-codes PR #168 v4's three files); they are + loaded and contract-checked by the tree's own loaders (triple_module_from, pair_module_from, all_but_one_from); + * the carrier arcs are --arcs (the script maps PR #168's frozen matching through the PR #168 v4 word); the tree's + compile_closure() checks them (one donor per use, acyclic generalized dependencies, every value span inside its + frame, exact positive-rank ledger); + * the preferred frame of every query operation is its frame in --frames (the script inherits PR #168's physical + frames). The forward closure, the clipping to the exact future cap and the minimal-frame check of every local + pair are the script's, unchanged, and the closure must return every frozen frame unchanged; + * the reuse pairs are --pairs (as the script's own --pairs option). Each pair must be an edge of the script's + candidate graph (donor ungauged and not a root, its last frame inside the recipient's gauge frame, its last + operation before the recipient's first, deadline as the script assigns it) and the list must already be a + fixed point of the script's last-late-control reordering. +Everything else, in the script's order: local configuration (G all 's', A all 'fd'), Graph.finish, merge +f8:00111100, compile_closure, select, the rank-at-most-two local phase-one prefix with its role predecessors, gauge +filtering, the target data histogram, the exact physical checks of scripts/paired_cube_physical.py (nested chains, +pair legality, spliced recount, exact numeric replay with mutations rejected) and the files written: cache/ +{graph,frames,selection,record}.json, references/paired-cube/physical/{frames,pairs}.json and +certificates/paired-cube-sinks-input.json, byte for byte in the script's encoding. Given PR #168's modules and the +script's own arcs, frames and pairs it reproduces the script's output byte for byte (verify.py checks this). + +usage: aligned_word_p.py [--p P] [--centre46] --tree TREE --tmod F --pmod F --qmod F --arcs F --frames F --pairs F --out DIR +Run with the rebuilt PR #202 tree as working directory, as the upstream scripts are; -O is refused. +""" +from collections import Counter, defaultdict +from pathlib import Path +import argparse +import json +import sys +import time + +if sys.flags.optimize: + raise SystemExit('Assertions must remain enabled: run without -O') + + +def read(p): + return json.loads(Path(p).read_text()) + + +def write(p, d): + p.parent.mkdir(parents=True, exist_ok=True) + p.write_text(json.dumps(d, separators=(',', ':')) + '\n') + + +def main(): + ap = argparse.ArgumentParser(description=__doc__, formatter_class=argparse.RawDescriptionHelpFormatter) + ap.add_argument('--tree', type=Path, required=True, help='the rebuilt PR #202 tree (its scripts/ are imported)') + ap.add_argument('--tmod', type=Path, required=True, help='disjoint-triple module (triple_module_from, p = 11)') + ap.add_argument('--pmod', type=Path, required=True, help='pair module (pair_module_from, n = 10)') + ap.add_argument('--qmod', type=Path, required=True, help='all-but-one module (all_but_one_from, n = 9)') + ap.add_argument('--arcs', type=Path, required=True, help='{"matching_arcs": [[donor node, use code], ...]}') + ap.add_argument('--frames', type=Path, required=True, help='{"frames": [[operation, frame rows], ...]}') + ap.add_argument('--pairs', type=Path, required=True, help='{"pairs": [[donor, recipient, deadline], ...]}') + ap.add_argument('--out', type=Path, required=True) + ap.add_argument('--p', type=int, default=11, help='cube size p (cp10 generalisation; 11 = the original script)') + ap.add_argument('--centre46', action='store_true', help='cp10: pair module with an extra full-sum root supplies the star centre (agent-cmod finish_centre46)') + a = ap.parse_args() + start = time.monotonic() + sys.path.insert(0, str(a.tree / 'scripts')) + from paired_cube.graph import Graph + from paired_cube.modules import triple_module_from, pair_module_from, all_but_one_from, merge_outputs + from paired_cube.closure import compile_closure + from paired_cube.gauges import select + from paired_cube.frames import basis, perp, contained + import paired_cube_physical as physical + s = a.tree / 'references/paired-cube/sources' + local = read(s / 'local_L1.json') + local['G'] = {k: 's' for k in local['G']} + local['A'] = {k: 'fd' for k in local['A']} + builder = Graph(a.p, local=local) + if a.centre46: + sys.path.insert(0, str(Path(__file__).resolve().parent)) + from centre46 import load_pmod46, finish_centre46 + g = finish_centre46(builder, triple_module_from(a.tmod, a.p), load_pmod46(a.pmod, a.p - 1), all_but_one_from(a.qmod, a.p - 2)) + else: + g = builder.finish(triple_module_from(a.tmod, a.p), pair_module_from(a.pmod, a.p - 1), all_but_one_from(a.qmod, a.p - 2)) + g = merge_outputs(g, builder, 'f8:00111100') + g['matching_frames'] = 'coordinate' + h, v = g['h'], g['v'] + newcut = v + g['counts']['local_channel_additions'] + newargs = [None] + [None if x is None else [t + 1 for t in x] for x in g['args']] + newroots = [dict(r, node=r['node'] + 1) for r in g['roots']] + # frozen carrier arcs (in place of the arcs mapped from PR #168's matching) + arcs = read(a.arcs)['matching_arcs'] + assert len({x for x, _ in arcs}) == len(arcs), 'one arc per donor' + p, w = compile_closure(g, arcs) + assert w['matching_arcs'] == arcs, 'compile_closure did not keep the frozen arcs' + p, word = select(g, p, w) + assert all(ca in (-1, 1) and cb in (-1, 1) for ca, cb in word['opcoeff']) + print(json.dumps(dict(stage='word', local=g['counts']['local_channel_additions'], arcs=len(arcs), R=p['R'], + selected=p['selected_rank_histogram'], seconds=time.monotonic() - start)), flush=True) + ops = word['ops'] + # frozen preferred frames (in place of the frames inherited from PR #168's physical layer) + frames_in = read(a.frames)['frames'] + desired = [perp(tuple(w['annihilators'][x]), h) for _, _, x in ops] + for i, F in frames_in: + desired[i] = tuple(F) + spans = [()] + [(q,) for q in g['inputs']] + for aa, bb in newargs[v + 1:]: + spans.append(basis(spans[aa] + spans[bb])) + root_frames = {} + for r, slot in zip(newroots, word['rootroles']): + root_frames[slot] = spans[r['node']] if r['kind'] == 'center' else perp(basis(g['inputs'][t] for t in r['targets']), h) + R = p['R'] + pset = set(word['phase1']) + # Both signs of a pair must occur before the center cut (source_aligned_local_v4.py, unchanged). + previous = [-1] * R + parents = [] + for i, (aa, bb, x) in enumerate(ops): + parents.append((previous[aa], previous[bb])) + previous[aa] = previous[bb] = i + if x <= newcut and len(spans[x]) <= 2: + pset.add(i) + todo = list(pset) + while todo: + i = todo.pop() + for j in parents[i]: + if j >= 0 and j not in pset: + pset.add(j) + todo.append(j) + word['phase1'] = sorted(pset) + p['phase1_operations'] = len(pset) + chron = sorted(pset) + [i for i in range(len(ops)) if i not in pset] + cap = [perp(root_frames[s], h) if s in root_frames else () for s in range(R)] + maxima = [None] * len(ops) + for i in reversed(chron): + aa, bb, x = ops[i] + A = basis(cap[aa] + cap[bb]) + maxima[i] = perp(A, h) + cap[aa] = cap[bb] = A + assert contained(spans[x], maxima[i]) + selected = [z for z in word['selected'] if z['rank'] == h - 4] + gauge = {z['role']: perp(tuple(z['annihilator']), h) for z in selected} + current = [() for _ in range(R)] + for x, slot in word['sources'].items(): + current[slot] = (g['inputs'][int(x) - 1],) + for slot, U in gauge.items(): + current[slot] = U + frames = [None] * len(ops) + minimal_pairs = query_ops = 0 + for i in chron: + aa, bb, x = ops[i] + if x <= newcut: + want = spans[x] + else: + want = desired[i] + query_ops += 1 + want = perp(basis(perp(want, h) + perp(maxima[i], h)), h) + U = basis(spans[x] + want + current[aa] + current[bb]) + assert contained(U, maxima[i]), ('Forward frame outside future cap', i) + frames[i] = current[aa] = current[bb] = U + if x <= newcut and len(spans[x]) == 2: + assert U == spans[x], ('Local pair failed its minimal physical frame', i) + minimal_pairs += 1 + for slot, U in root_frames.items(): + assert contained(current[slot], U) + bad = [i for i in range(len(ops)) if frames[i] != desired[i]] + assert not bad, ('the forward closure changes %d frozen frames, first at operation %d' % (len(bad), bad[0])) + role_ops = defaultdict(list) + for i, (aa, bb, _) in enumerate(ops): + role_ops[aa].append(i) + role_ops[bb].append(i) + pos = {i: k for k, i in enumerate(chron)} + for slot in role_ops: + role_ops[slot].sort(key=pos.__getitem__) + recipients = sorted(gauge) + recipient_set = set(recipients) + donors = {slot for slot in range(R) if slot not in recipient_set and slot not in root_frames and slot in role_ops} + for slot in recipients: + assert role_ops[slot][0] not in pset + # frozen reuse pairs (in place of the script's matching; the script's own --pairs option) + pairs = read(a.pairs)['pairs'] + assert len({d for d, _, _ in pairs}) == len({b for _, b, _ in pairs}) == len(pairs), 'one pair per donor and recipient' + for d, b, t in pairs: + assert d in donors and b in recipient_set, ('pair outside the candidate roles', d, b) + last, first = role_ops[d][-1], role_ops[b][0] + assert contained(frames[last], gauge[b]), ('donor last frame outside the recipient gauge', d, b) + assert pos[last] < pos[first], ('donor not dead before the recipient', d, b) + assert t == (None if last in pset else first), ('deadline differs from the script\'s rule', d, b, t) + # The inherited negative replay moves its last late recipient to the phase cut (unchanged); the frozen list + # must already be in that order. + last_write = {} + for i, (aa, bb, x) in enumerate(ops): + last_write[aa] = max(last_write.get(aa, -1), pos[i]) + controls = [q for q in pairs if q[2] is not None and last_write.get(q[0], -1) >= len(pset)] + if controls: + chosen = controls[-1] + assert pairs[-1] == chosen, 'frozen pairs are not in the script\'s control order' + kept = {b for _, b, _ in pairs} + chosen = word['selected'] + word['selected'] = [z for z in selected if z['role'] in kept] + # complex-p10: keep the record's gauge ledger equal to the gauges the word keeps. select() may choose gauges of + # rank other than h - 4 (or unpaired ones); the script drops them from the selection, but its record still counts + # their births, which PR #200's complex checker (verify_fused.py) recounts and rejects. Each dropped birth is + # reversed (H[r - d] -= 1, H[r] += 1 with r the rank of the role's first frame, as select() booked it). Nothing is + # dropped at p = 11 on PR #168 v4's or PR #304's modules, nor on this package's annealed modules: the record is then + # untouched (byte for byte). Only the verifiers read these three fields. + keep_roles = {z['role'] for z in word['selected']} + dropped = [z for z in chosen if z['role'] not in keep_roles] + if dropped: + first_x = {} + for aa, bb, x in ops: + first_x.setdefault(aa, x) + first_x.setdefault(bb, x) + H = list(p['remaining_internal_histogram']) + ranks = dict(p['selected_rank_histogram']) + for z in dropped: + r, d = h - len(w['annihilators'][first_x[z['role']]]), z['rank'] + H[r - d] -= 1 + H[r] += 1 + ranks[d] -= 1 + if not ranks[d]: + del ranks[d] + p['remaining_internal_histogram'], p['selected_rank_histogram'], p['selected_roles'] = H, ranks, len(word['selected']) + moved = [[i, list(U)] for i, U in enumerate(frames) if U != perp(tuple(w['annihilators'][ops[i][2]]), h)] + assert moved == frames_in, 'frozen frames are not in the script\'s canonical form' + deadline = {b: t for _, b, t in pairs} + Y = [() for _ in range(v)] + target = Counter() + for z in sorted(word['selected'], key=lambda z: len(pset) if deadline[z['role']] is None else pos[deadline[z['role']]]): + U = gauge[z['role']] + for t in z['targets']: + assert contained(Y[t], U) + target[len(U) - len(Y[t])] += 1 + Y[t] = U + for r, slot in zip(newroots, word['rootroles']): + if r['kind'] == 'side': + U = root_frames[slot] + for t in r['targets']: + assert contained(Y[t], U) + target[len(U) - len(Y[t])] += 1 + Y[t] = U + for t in range(v): + target[h - 1 - len(Y[t])] += 1 + p['target_data_histogram'] = dict(target) + print(json.dumps(dict(stage='physical', query_ops=query_ops, moved_frames=len(moved), minimal_pair_ops=minimal_pairs, + pairs=len(pairs), gauges=len(word['selected']), seconds=time.monotonic() - start, + dropped_gauges=dict(sorted(Counter(z['rank'] for z in dropped).items())))), flush=True) + out = a.out + for name, data in [('graph.json', g), ('frames.json', w), ('selection.json', word), ('record.json', p)]: + write(out / 'cache' / name, data) + write(out / 'references/paired-cube/physical/frames.json', {'frames': moved}) + write(out / 'references/paired-cube/physical/pairs.json', {'pairs': pairs}) + result = physical.physical(g, w, word, p, moved, pairs) + write(out / 'certificates/paired-cube-sinks-input.json', result) + print(json.dumps(dict(stage='checked', R=p['R'], physical_R=result['physical_R'], arcs=len(arcs), moved_frames=len(moved), + pairs=len(pairs), seconds=time.monotonic() - start)), flush=True) + + +if __name__ == '__main__': + main() diff --git a/research/complex-p10/centre46.py b/research/complex-p10/centre46.py new file mode 100644 index 0000000000..ede0d1b210 --- /dev/null +++ b/research/complex-p10/centre46.py @@ -0,0 +1,91 @@ +"""centre46.py: the centre-sharing variant of PR #144's Graph.finish used for PR #315's complex program (the research +copy, unchanged): the pair module supplies the star centre as an extra root (sum of all its inputs) instead of +Graph.sum over the A's. load_pmod46(path, n) checks the contract (C(n,2) roots + one full-sum root). +Prepared by DreamingOfClouds with Anthropic Claude assistance; Apache-2.0. Graph.finish is icekylinx's (PR #144).""" +import json +from pathlib import Path +from itertools import combinations + + +# ---- centre-sharing variant (agent-cmod): the pair module supplies the star centre as a 46th root ------------- +def load_pmod46(path, n=10): + """Pair module JSON with 45 contract roots plus a 46th root = sum of all 45 inputs (checked).""" + from itertools import combinations as _c + d = json.loads(Path(path).read_text()) + pairs = list(_c(range(n), 2)) + assert d['input_count'] == len(pairs) and len(d['roots']) == len(pairs) + 1 + support = [] + for x, a in enumerate(d['args']): + if x < len(pairs): + assert a is None; support.append(1 << x) + else: + assert a is not None and 0 <= a[0] < x and 0 <= a[1] < x and not support[a[0]] & support[a[1]] + support.append(support[a[0]] | support[a[1]]) + for (i, j), r in zip(pairs, d['roots']): + assert support[r] == sum(1 << k for k, (a, b) in enumerate(pairs) if i not in (a, b) and j not in (a, b)) + assert support[d['roots'][-1]] == (1 << len(pairs)) - 1 + return dict(kind='pair_disjoint_centre', n=n, input_count=len(pairs), input_labels=pairs, output_labels=pairs, + args=[None if a is None else list(a) for a in d['args']], roots=list(d['roots'])) + + +def finish_centre46(G, triple, pair46, allbut): + """Graph.finish (star centre) with centre[2i+e] = the pair module (i, e)'s 46th root instead of G.sum(...).""" + from itertools import product as _prod + from fractions import Fraction + G.local_channels() + base_nodes = len(G.a) + D = dict(zip(G.cubes, G.module(triple, [G.F[I] for I in G.cubes]))) + P, Q, CEN = {}, {}, {} + for i in range(G.p): + others = [a for a in range(G.p) if a != i] + pairs = list(combinations(others, 2)) + for bit in range(2): + inputs = [G.A[tuple(sorted((i, *K))), i, bit] for K in pairs] + outs = G.module(pair46, inputs) + for K, node in zip(pairs, outs[:len(pairs)]): + P[tuple(sorted((i, *K))), i, bit] = node + CEN[i, bit] = outs[len(pairs)] + for i, j in combinations(range(G.p), 2): + others = [a for a in range(G.p) if a not in (i, j)] + for mode in range(2): + inputs = [G.G[tuple(sorted((i, j, k))), i, j, mode] for k in others] + for k, node in zip(others, G.module(allbut, inputs)): + Q[tuple(sorted((i, j, k))), i, j, mode] = node + query_nodes = len(G.a) + def emit(I, bits_list, node, numerator=1, channel=''): + G.root.append(dict(node=node, targets=[G.source[I, b] for b in bits_list], + coefficients=[f'{numerator}/2'] * len(bits_list), kind='side', channel=channel)) + for I in G.cubes: + all_bits = list(_prod(range(2), repeat=3)) + emit(I, all_bits, D[I], channel='disjoint') + for a in range(2): + emit(I, [b for b in all_bits if b[0] == a], P[I, I[0], 1 - a], channel='face0') + for a, b in _prod(range(2), repeat=2): + emit(I, [(a, b, c) for c in range(2)], P[I, I[1], 1 - b], channel='face1') + for a, b in _prod(range(2), repeat=2): + emit(I, [(a, b, c) for c in range(2)], Q[I, I[0], I[1], a ^ b], 2 * a - 1, 'edge01') + for bits in all_bits: + emit(I, [bits], P[I, I[2], 1 - bits[2]], channel='face2') + for ii, jj in [(0, 2), (1, 2)]: + for bits in all_bits: + emit(I, [bits], Q[I, I[ii], I[jj], bits[ii] ^ bits[jj]], 2 * bits[ii] - 1, f'edge{ii}{jj}') + for i in range(G.p): + for e in range(2): + G.centers.append(CEN[i, e]) + for coordinate, node in enumerate(G.centers): + coefficients = ['1/3' if coordinate in t else '-1/6' for t in G.labels] + G.root.append(dict(node=node, targets=list(range(len(G.labels))), coefficients=coefficients, kind='center', + coordinate=coordinate)) + return dict(p=G.p, h=G.h, v=len(G.labels), labels=G.labels, inputs=[sum(1 << x for x in t) for t in G.labels], + args=G.a, signs=G.signs, roots=G.root, centers=G.centers, center_kind='star', + center_scatter='1/2 sum_(i in T) S_i - 1/6 sum_i S_i', + local_K='Two 4x4 Hadamard/2 blocks on opposite cube parities, using original X destructively', + source_data_histogram={2: len(G.labels), G.h - 4: len(G.labels), 1: len(G.labels)}, + target_data_histogram={G.h - 4: len(G.labels), 1: 3 * len(G.labels)}, + counts=dict(local_channel_additions=base_nodes - len(G.labels), query_additions=query_nodes - base_nodes, + center_additions=0, center_tree_incidences=0, + signed_additions=sum(x < 0 for x in G.signs), + side_root_uses=sum(r['kind'] == 'side' for r in G.root), center_roots=len(G.centers)), + status='agent-cmod centre-sharing variant') + + diff --git a/research/complex-p10/certificate/expected.json b/research/complex-p10/certificate/expected.json new file mode 100644 index 0000000000..825fcfb658 --- /dev/null +++ b/research/complex-p10/certificate/expected.json @@ -0,0 +1,1887 @@ +{ + "anchor_centre_patch": { + "center_additions": 0, + "centres_from_pair_module": 20, + "differing_fields": [ + "status" + ], + "fields_compared": 16, + "hunks": 2, + "ordinary_pair_module_unchanged": true, + "patch_sha256": "229eea46b56d19b262d1498f489f9bca84c347e33b16553079d38c4276700280" + }, + "anchor_control_modules": { + "pmod": { + "additions": 256, + "dropped_point": [ + 4 + ], + "source": "pmod_J0_full_6.0666810e-4.json" + }, + "qmod": { + "additions": 24, + "dropped_point": [ + 1 + ], + "source": "qmod_climb3u_best.json" + }, + "tmod": { + "additions": 1220, + "dropped_point": [ + 6 + ], + "source": "tmod_TE_TD_TB3_1_1_4_full_6.0617964e-4.json" + } + }, + "anchor_pr194": { + "N": 262944, + "R": 9412, + "blocks_total": 70169, + "certificate_sha256": "27398a0cfcbe34e5ee97360e69a2d163a417c8ae1b4fdf28ccf89a9eaf4e4cd4", + "equals_pr256_certificate": true, + "equals_sussman_pr193_blocks": true, + "generic_idle_ranks_at_h22": [ + 42, + 21, + 46, + 4 + ] + }, + "anneal-mw": { + "N": 167140, + "R": 6515, + "admission": { + "formal": { + "absolute_coefficient_bound": 709038, + "base_exceeds_twice_bound": true, + "columns": [ + { + "K_and_inverse": true, + "all_aliases_and_deadline_reads": true, + "all_physical_dirty_slots_restored": true, + "direction": 1, + "dirty_columns": 9395, + "every_formal_column": true, + "source_columns": 960, + "target_columns": 960 + }, + { + "K_and_inverse": true, + "all_aliases_and_deadline_reads": true, + "all_physical_dirty_slots_restored": true, + "direction": -1, + "dirty_columns": 9395, + "every_formal_column": true, + "source_columns": 960, + "target_columns": 960 + } + ], + "packed_digit_bits": 24 + }, + "mutations": { + "early-read": "REJECTED", + "missing-read": "REJECTED" + }, + "source_sha256": { + "notes/general-clifford-frames.tex": "c9bb9655b594583c6b4bab8cb485233f1d1e588f83858cf1e4c3530cee8fed54", + "research/paired-cube-diagonal-bit-168/complex/physical.py": "01961fad4b04aaa940d2dc99c87690bc861b3861200296974c5e065ce3446659", + "research/paired-cube-diagonal-bit-168/complex/verify_fused.py": "75c3dcd80fcdbc461651fa2d2fa463e6b41a569d695fc74700d240223ef198e9", + "scripts/paired_cube/frames.py": "7d897418dbfee47de0723ea4983098a982610ccba45e1bac9000a79626d8421c", + "scripts/paired_cube_physical.py": "9c9ea1ea29e551ab6116d7c8ca09f4703ff9e2fa102032d5055327fde07ba319" + }, + "status": "PASS exact fused physical candidate, all formal source/target/dirty columns" + }, + "blocks": { + "c": { + "18": 20 + }, + "s": { + "1": 17306, + "10": 850, + "11": 69, + "12": 518, + "13": 936, + "14": 207, + "17": 515, + "2": 7618, + "3": 6173, + "4": 3392, + "5": 814, + "6": 1467, + "7": 531, + "8": 681, + "9": 482 + }, + "x": { + "1": 960, + "16": 960, + "2": 960 + }, + "y": { + "1": 2880, + "16": 960 + } + }, + "blocks_total": 48299, + "certificate_sha256": "433848305e705a22cb46cea4f5aa2c3052d3011788c3741d9b43890e375716e5", + "contract_checks": { + "all_centers_in_phase1": true, + "all_fresh_columns_equal_identity": true, + "all_target_cap_reads_in_phase2": true, + "arithmetic": "integers, endpoint scaled by 6", + "checked_source_columns": 960, + "checked_target_rows": 960, + "controls_before_original_K": true, + "original_source_V_before_all_controls": true, + "positive_target_data_histogram": { 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verified; monotone flow and zero-fresh kernel reuse DAG verified." + }, + "paircheck": { + "controls": { + "donor_frame_outside_gauge": "REJECTED (donor frame outside gauge)", + "duplicate_pair": "REJECTED (not one-to-one)", + "late_read_before_donor_death": "REJECTED (donor frame outside gauge, late chronology)", + "parity_erasable_donor": "REJECTED (erasable)", + "unpaired_gauge": "REJECTED (live external gauges)" + }, + "early": 705, + "erasable": 0, + "first_violations": [], + "gauges": 1672, + "kinds": [], + "late": 967, + "pairs": 1672, + "status": "PASS", + "violations": 0 + }, + "registers": 9041, + "scalar_denominators": { + "s": 2, + "x": 2, + "y": 6 + }, + "scalar_max_abs": { + "s": "2", + "x": "3/2", + "y": "2" + }, + "scatter": { + "changed_coefficients": 0, + "changed_gates": 0, + "flipped_coordinates": [], + "flipped_registers": [], + "gx_check1": "ACCEPTED (raw and committed program)", + "gxcore_mirror": "ACCEPTED (raw and committed program; label and scalar checks)", + "raw_certificate_sha256": "192a58ffdbe7afd29449a401830e122f8a812063dcc293a3ab263d91c84b7926", + "raw_scatter": "star" + } + }, + "prerequisites": { + "pr202": "8d8d67bcf69c5ea67d3a29dbc64ba588156d6e8d", + "pr233": { + "author": "chafreaky (Anthropic Claude and OpenAI Codex assistance); PR #202 baseline by ikeboy et al., see NOTICE", + "commit": "109a857", + "complex_saving": "3549537/5000000000", + "path": "research/source-assisted-v4-layer", + "pr": 233, + "repository": "CrocSwap/integer-mult-bounds", + "vendored": "references/pr233-layer (baseline-pr202.tar.gz, SOURCE.json, verify.py, certificate.json, NOTICE, witness/), as vendored by PR #256" + }, + "pr256": { + "author": "chafreaky (Anthropic Claude and OpenAI Codex assistance)", + "commit": "db3f75cdc5f03f3131d48fb220f6bf1958404ff3", + "path": "research/gcert-program-233", + "pr": 256, + "pr194_certificate_sha256": "27398a0cfcbe34e5ee97360e69a2d163a417c8ae1b4fdf28ccf89a9eaf4e4cd4", + "pr233_certificate_sha256": "0c026244591a0b6737993aaac5fa8ac4a2bd27aa28e469f2567c698f57ed10a8", + "pr233_five_stage": "7547/10^7", + "repository": "CrocSwap/integer-mult-bounds", + "vendored": "gcert_emit.py, gx/gx.py, scripts/moment.py, references/pr233-layer/, references/sussman/pr193-blocks.json (byte for byte; the certificate sha256 values are of the canonical uncompressed JSON, from its certificate/expected.json)" + }, + "pr304": { + "author": "DreamingOfClouds (Anthropic Claude assistance)", + "claims": { + "cmod-mw": "7635/10^7", + "cmod-parity": "7586/10^7", + "pr168-v4-mw": "7522/10^7", + "pr168-v4-parity": "7469/10^7" + }, + "commit": "7ac169c58c96cebdb5cd490842331dff3610af62", + "note": "the p = 11 programs whose recipe this package applies at p = 10: the re-annealed modules tmod_cmod_v2.json, pmod_cmod_dropin.json and qmod_cmod.json are the parents of three of the four p = 10 modules", + "path": "research/complex-module-anneal", + "pr": 304, + "repository": "CrocSwap/integer-mult-bounds", + "vendored": "aligned_word_p.py (= its aligned_word.py with --p and --centre46), paircheck.py, normalize_scatter.py, discovery/make_layer_p.py (= its discovery/make_layer.py with --p, --centre46, pairs_mw_p.py), discovery/extend_floor.py and discovery/pr233/ (byte for byte); verify.py follows its verify.py" + }, + "pr315": { + "author": "DreamingOfClouds (Anthropic Claude assistance)", + "commit": "243899975d0fbe888d5deda399060885d609e0a1", + "complex_supplier": "inputs/complex/gcert1-p11-cmod-centre-mw-flow.json.gz: the centre-sharing p = 11 program, 7727/10^7 (with the 10^-16 fallback 772714351296671/10^18)", + "path": "research/five-stage-p10-banks", + "pr": 315, + "repository": "CrocSwap/integer-mult-bounds", + "vendored": "references/centre46_graph.diff (its inputs/complex/centre-mw/centre46_graph.diff, byte for byte: the 10-line Graph.finish patch whose effect centre46.py reproduces)" + }, + "source527": { + "author": "eumemic (OpenAI Codex assistance), PR #210 lineage; see scripts/source527/NOTICE", + "commit": "b07cafe23202d22d832961a04b07d48d9b245e10", + "path": "research/five-stage-source527-banks", + "repository": "CrocSwap/integer-mult-bounds", + "vendored": "scripts/source527/moment.py and scripts/source527/base_two_moment.py, byte for byte: the two rational moment engines with which the five-stage packages certify a coarse saving with the 10^-16 fallback envelope" + }, + "sussman": { + "commit": "f010392c", + "files": { + "tools/certificate/gcert1-p11-pr193.json.gz": "15251deb0c11e0504d7b297c9786818888a93f08b92b03c6c122784b70488633 (its block histogram and counts in references/sussman/pr193-blocks.json)", + "tools/gx/gx.py": "6f3dc8bb639933227a8dae181ec4a542e85c7276be9c9e330f49518e7b630b95 (vendored unchanged as gx/gx.py)", + "tools/gx/gxcore.py": "eb972c06fe8c322db2d9a8d9a7d05596e8f40c4ca8e5f42eb6df3c7361b5d517 (vendored unchanged as gx/gxcore.py: his Python mirror of the two Lean checks, independent of gx.py)" + }, + "licence": "Apache-2.0, 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it and records the set's files in `SOURCE.json` +(`module_sets`, with `centre46` for the centre-sharing set). Delete a superseded module file from `modules/` before +`--write`. + +## Vendored harness (`pr233/`) + +PR #233's discovery files (Chafik Boukhalfa with Anthropic Claude and OpenAI Codex assistance; Apache-2.0; PR #162 +extension DaysSky et al.), unchanged, as PR #304 vendors them: `matching.py`, `physical_opt.py`, `bundles.py`, +`joint.py`, `pairs_mw.py` and their `README.md`. sha256: + + 59d1cd30e67d3511cf799140eb248e785e77aaccff7c47a22a0feef8fb6f021e matching.py + cbfd06026a44df30944781262848c88ec987ca5e80381e35ae7ad715a9db1fce physical_opt.py + 71c81bc858e62e03e2a5230c16c4c199a027c24402cdc937bd4ded60f4ee3286 bundles.py + e4857418f6e16d6fbb1815d3c4148116e35a6b9940cb57acb2b563da5621b92c joint.py + aa927718ad27bebcfa2bddeb3704d4721433c2d4e6b6e218ceb9d28a07cd6c83 pairs_mw.py + 1bd628da0afbccfd9baafc2d51cd96a51a4e46c782b783a1c16bea04fd88d98c README.md + +`extend_floor.py` is PR #304's (`extend.py` of the harness with a donor floor, two lines). `add_centre.py` is the +greedy centre-root step of the centre-sharing pair module (DreamingOfClouds with Anthropic Claude assistance, +Apache-2.0). diff --git a/research/complex-p10/discovery/add_centre.py b/research/complex-p10/discovery/add_centre.py new file mode 100644 index 0000000000..d9ee63aa2f --- /dev/null +++ b/research/complex-p10/discovery/add_centre.py @@ -0,0 +1,30 @@ +"""Append a centre root (sum of all inputs) to a pair module by a greedy disjoint cover of existing nodes. +usage: add_centre.py SRC.json DST.json (made pmod46_p1 from pmod_p1, the seed of the centre-sharing anneal) +Prepared by DreamingOfClouds with Anthropic Claude assistance (Apache-2.0).""" +import json,sys +src,dst=sys.argv[1],sys.argv[2] +d=json.load(open(src)); n=d['input_count']; args=d['args'] +sup=[] +for x,a in enumerate(args): + sup.append(1<1: + nxt=[] + for i in range(0,len(cur)-1,2): + args.append([cur[i],cur[i+1]]);nxt.append(len(args)-1) + if len(cur)%2:nxt.append(cur[-1]) + cur=nxt +d['roots']=d['roots']+[cur[0]] +d['provenance']=dict(source=src,extra_root='greedy disjoint cover centre, %d parts'%len(parts)) +json.dump(d,open(dst,'w')) +print('parts',len(parts),'additions',len(args)-n,'roots',len(d['roots'])) diff --git a/research/complex-p10/discovery/extend_floor.py b/research/complex-p10/discovery/extend_floor.py new file mode 100644 index 0000000000..b9f2bb7619 --- /dev/null +++ b/research/complex-p10/discovery/extend_floor.py @@ -0,0 +1,99 @@ +# agent-cmod copy of PR233 discovery extend.py (PR162 extension, DaysSky et al., Apache-2.0) with a donor floor. +"""PR162 generalized-carrier construction helper, DaysSky et al. Apache-2.0. +Extracted unchanged function only; no foreign producer invocation. +""" +from collections import defaultdict +from functools import lru_cache +from paired_cube.frames import basis,perp,contained +@lru_cache(maxsize=None) +def join(A,B): + if A==B or not B:return A + if not A:return B + return basis(A+B) +@lru_cache(maxsize=None) +def orthogonal(S,A):return all((s&a).bit_count()%2==0 for s in S for a in A) +def extended_arcs(g, frozen, min_donor=0): + """Greedy extension of the frozen arcs. gspan[x]: span of every value that reaches x through DAG or arc edges; + gann[x]: annihilator of the intersection of every root frame reachable from x. An arc x -> t is legal iff + gspan[x] is orthogonal to gann[t] and t does not reach x.""" + h = g['h']; inputs = g['inputs'] + args = [None] + [None if a is None else [x + 1 for x in a] for a in g['args']] + roots = [dict(r, node=r['node'] + 1) for r in g['roots']] + v, n = len(inputs), len(args) + spans = [()] * n + for i, u in enumerate(inputs): spans[i + 1] = (u,) + for x in range(v + 1, n): spans[x] = basis(spans[args[x][0]] + spans[args[x][1]]) + rann = [perp(spans[r['node']], h) if r.get('kind', 'side') == 'center' else basis(inputs[t] for t in r['targets']) + for r in roots] + active = set(range(1, v + 1)); todo = [r['node'] for r in roots] + while todo: + x = todo.pop() + if x in active: continue + active.add(x) + if args[x]: todo.extend(args[x]) + succ = [set() for _ in args]; pred = [set() for _ in args]; direct = [[] for _ in args] + uses = defaultdict(list) + for x in sorted(active): + if args[x]: + for j, y in enumerate(args[x]): succ[y].add(x); pred[x].add(y); uses[y].append(2 * x + j) + for j, r in enumerate(roots): direct[r['node']].extend(rann[j]); uses[r['node']].append((1 << 31) | j) + gann = [None] * n; gspan = list(spans) + for x in sorted(active, reverse=True): gann[x] = basis(direct[x] + [z for y in succ[x] for z in gann[y]]) + plain = list(gann) # DAG-only intersections, for the candidate screen + ancestors = {} + def above(x): + if x not in ancestors: + seen = set(); stack = [x] + while stack: + y = stack.pop() + if args[y]: + for z in args[y]: + if z not in seen: seen.add(z); stack.append(z) + ancestors[x] = seen + return ancestors[x] + arcs = {}; used = set() + def value(code): return roots[code & 0x7fffffff]['node'] if code >> 31 else args[code // 2][code & 1] + def add(x, code, check): + t = None if code >> 31 else code // 2 + At = rann[code & 0x7fffffff] if t is None else gann[t] + if check: + if not orthogonal(gspan[x], At): return False + if t is not None: + stack = [t]; seen = {t} + while stack: + y = stack.pop() + if y == x: return False + for z in succ[y]: + if z not in seen: seen.add(z); stack.append(z) + arcs[x] = code; used.add(code) + work = [(x, At)] + while work: + y, extra = work.pop(); new = join(gann[y], extra) + if new == gann[y]: continue + gann[y] = new + for z in pred[y]: work.append((z, new)) + if t is not None: + succ[x].add(t); pred[t].add(x); work = [(t, gspan[x])] + while work: + y, extra = work.pop(); new = join(gspan[y], extra) + if new == gspan[y]: continue + gspan[y] = new + for z in succ[y]: work.append((z, new)) + return True + for x, code in frozen: assert add(x, code, True), ('frozen arc rejected', x, code) + for x in sorted(active): + if x < min_donor: continue + if not args[x]: continue + for j, y in enumerate(args[x]): + other = args[x][1 - j] + for code in uses[y]: + if code == 2 * x + j or x in arcs or code in used: continue + if code >> 31: screen = rann[code & 0x7fffffff] + else: + t = code // 2 + if t < x and t in above(x): continue + screen = plain[t] + if not orthogonal(spans[other], screen): continue + if sum(1 for u in uses[value(code)] if u not in used) <= 1: continue # every value keeps a free use + add(x, code, True) + return sorted([x, code] for x, code in arcs.items()) diff --git a/research/complex-p10/discovery/make_layer_p.py b/research/complex-p10/discovery/make_layer_p.py new file mode 100644 index 0000000000..747db04c56 --- /dev/null +++ b/research/complex-p10/discovery/make_layer_p.py @@ -0,0 +1,318 @@ +#!/usr/bin/env python3 +"""make_layer_p.py: discovery of a frozen physical layer for three query modules at cube size p (NOT run by verify.py). + +PR #304's discovery/make_layer.py with the cube size as a parameter (Graph(p), triple module at p, pair module at +p - 1, all-but-one module at p - 2 instead of the literals 11, 10, 9), the centre-sharing graph as an option +(--centre46: the pair module's 37th root is the star centre, centre46.py), the maximum-weight pairing with the gauge +rank f = h - 4 (pairs_mw_p.py; PR #233's pairs_mw.py hard-codes f = 18, which is h - 4 only at h = 22) and +aligned_word_p.py for the kernel-pair step. Nothing else changed. + +verify.py never searches: it reads layers// and checks it. This script is how those files were found, kept for +provenance and for re-pinning after a module changes. Recipe (the same for the control and the results): + 1. the source-aligned graph of PR #194's pipeline with the given modules (aligned_word.py's construction); + 2. fresh carrier arcs: the deterministic Hopcroft-Karp carrier matching of PR #200/#233's discovery harness + (pr233/matching.py, ordering 'reverse'), arcs of local donors dropped (as the mapped arcs of PR #193/#194 drop + them), then PR #162's greedy extension restricted to query donors (extend_floor.py); + 3. compile_closure + select, then PR #200's operation-frame descent on that word (pr233/physical_opt.py single + endpoint moves, bundles.py equal-frame components, joint.py adjacent components; up to three cycles); + 4. source_aligned_local_v4.py's forward closure with the descended frames as preferred frames (clipped to the + future cap; local operations keep their literal spans); + 5. reuse pairs, two recipes on the same frames: 'parity' = source_aligned_local_v4.py --avoid-parity-erasure (PR + #193's minimum-weight full matching avoiding PR #184's parity erasures), 'mw' = PR #200/#233's maximum-weight + late compensated pairing (pairs_mw_p.py = pr233/pairs_mw.py with f = h - 4) with harness.descend's + last-late-pair order; + 6. kernel pairs: PR #184's complex_frame_flow.py --witness --purify-source-donors --recycle-kernels on the + aligned tree written by aligned_word_p.py (its own maximum matching), frozen as found. +Writes layers//{matching-arcs,physical-frames,physical-pairs-parity,physical-pairs-mw,kernel-pairs-parity, +kernel-pairs-mw}.json and, for a set of package modules, records the module files used in SOURCE.json's +module_sets (a module given outside modules/ is first copied there). Then run verify.py --write (re-pins +SOURCE.json, sets the claims, regenerates the certificates) and verify.py. + +usage: python3 -B discovery/make_layer_p.py --set anneal [--p 10] [--tmod F] [--pmod F] [--qmod F] [--centre46] +A module not given (and --centre46 when not given) defaults to the set's current entry in SOURCE.json. Needs +numpy/scipy as verify.py; about two minutes at p = 10. Floating-point scores choose the frames and pairs; nothing +here is a proof. +Adapted from PR #304 (DreamingOfClouds with Anthropic Claude assistance, Apache-2.0) by DreamingOfClouds with +Anthropic Claude assistance (Apache-2.0). +""" +import argparse +import bisect +import importlib.util +import json +import subprocess +import sys +import tempfile +import time +from collections import defaultdict +from pathlib import Path + +if sys.flags.optimize: + raise SystemExit('Assertions must remain enabled: run without -O') +sys.dont_write_bytecode = True +HERE = Path(__file__).resolve().parent +PKG = HERE.parent +KINDS = ('tmod', 'pmod', 'qmod') +DESCRIPTIONS = dict( + arcs='Frozen carrier arcs of the source-aligned word (discovery/make_layer.py step 2): deterministic HK carrier ' + 'matching (PR200/233 harness, ordering reverse) on query donors plus PR162 extension; checked by compile_closure.', + frames='Frozen operation frames (source_aligned_local_v4.py canonical form: operations whose frame differs from the ' + 'closure frame), from PR200 descent on the aligned word and the script\'s forward closure.', + parity='Frozen reuse pairs [donor, recipient, deadline]: PR193 recipe (source_aligned_local_v4.py ' + '--avoid-parity-erasure minimum-weight full matching), in the script\'s control order.', + mw='Frozen reuse pairs [donor, recipient, deadline]: PR200/233 maximum-weight late compensated pairing ' + '(pairs_mw.py) with the last late pair moved to the phase cut.', + kernel='Frozen kernel pairs of the frame flow on this layer (complex_frame_flow.py --witness --recycle-kernels).') + + +def dump(path, data): + path.parent.mkdir(parents=True, exist_ok=True) + path.write_text(json.dumps(data, separators=(',', ':')) + '\n') + + +def log(msg, t0=time.monotonic()): + print('[%6.1fs] %s' % (time.monotonic() - t0, msg), flush=True) + + +def rebuild_tree(dest): + spec = importlib.util.spec_from_file_location('pr233_layer_verify', PKG / 'references/pr233-layer/verify.py') + mod = importlib.util.module_from_spec(spec) + spec.loader.exec_module(mod) + mod.rebuild(dest) + return dest + + +def main(): + ap = argparse.ArgumentParser(description=__doc__, formatter_class=argparse.RawDescriptionHelpFormatter) + ap.add_argument('--set', required=True, help='layer name: writes layers//') + ap.add_argument('--p', type=int, default=10, help='cube size (PR #304: 11)') + ap.add_argument('--centre46', action='store_true', default=None, + help='centre-sharing graph: the pair module supplies the star centre as an extra root (centre46.py)') + ap.add_argument('--tmod', type=Path); ap.add_argument('--pmod', type=Path); ap.add_argument('--qmod', type=Path) + ap.add_argument('--tree', type=Path, help='an already rebuilt PR #202 tree (default: rebuild into a temporary directory)') + ap.add_argument('--out', type=Path, help='output directory (default: layers/)') + a = ap.parse_args() + out = (a.out or PKG / 'layers' / a.set).resolve() + source = json.loads((PKG / 'SOURCE.json').read_text()) + current = source['module_sets'].get(a.set, {}) + centre = bool(current.get('centre46', False) if a.centre46 is None else a.centre46) + P = a.p + with tempfile.TemporaryDirectory(prefix='make-layer-') as d: + root = a.tree.resolve() if a.tree else rebuild_tree(Path(d).resolve()) + src = root / 'references/paired-cube/sources' + mods, record = {}, {} + for k in KINDS: + given = getattr(a, k) + if given is None: + rel = current[k] + mods[k] = root / rel[5:] if rel.startswith('tree:') else PKG / rel + record[k] = rel + continue + given = given.resolve() + if (PKG / 'modules') not in given.parents: + dest = PKG / 'modules' / given.name + assert not dest.exists() or dest.read_bytes() == given.read_bytes(), 'a different module file exists: %s' % dest + dest.write_bytes(given.read_bytes()) + log('copied %s into modules/' % given.name) + given = dest + mods[k] = given + record[k] = given.relative_to(PKG).as_posix() + sys.path.insert(0, str(root / 'scripts')) + sys.path.insert(0, str(HERE / 'pr233')) + sys.path.insert(0, str(HERE)) + from paired_cube.graph import Graph + from paired_cube.modules import triple_module_from, pair_module_from, all_but_one_from, merge_outputs + from paired_cube.closure import compile_closure + from paired_cube.gauges import select + from paired_cube.frames import basis, perp, contained + from matching import carrier_matching + from extend_floor import extended_arcs + import physical_opt + import bundles + import joint + from pairs_mw_p import pairs_maxweight # PR #233's pairs_mw.py with f = h - 4 + import numpy as np + from scipy.sparse import csr_matrix + from scipy.sparse.csgraph import min_weight_full_bipartite_matching + # 1. graph (aligned_word.py / source_aligned_local_v4.py construction) + local = json.loads((src / 'local_L1.json').read_text()) + local['G'] = {k: 's' for k in local['G']} + local['A'] = {k: 'fd' for k in local['A']} + builder = Graph(P, local=local) + if centre: + sys.path.insert(0, str(PKG)) + from centre46 import load_pmod46, finish_centre46 + g = finish_centre46(builder, triple_module_from(mods['tmod'], P), load_pmod46(mods['pmod'], P - 1), all_but_one_from(mods['qmod'], P - 2)) + else: + g = builder.finish(triple_module_from(mods['tmod'], P), pair_module_from(mods['pmod'], P - 1), all_but_one_from(mods['qmod'], P - 2)) + g = merge_outputs(g, builder, 'f8:00111100') + g['matching_frames'] = 'coordinate' + h, v = g['h'], g['v'] + newcut = v + g['counts']['local_channel_additions'] + # 2. fresh arcs + arcs, stats = carrier_matching(g, 'reverse') + arcs = [x for x in arcs if x[0] > newcut] + arcs = extended_arcs(g, arcs, min_donor=newcut + 1) + assert all(x[0] > newcut for x in arcs) + log('arcs: %d (HK matched %d of %d donors)' % (len(arcs), stats['matched'], stats['donors'])) + # 3. descent on the aligned word + base, w = compile_closure(g, arcs) + row, word = select(g, base, w) + o = physical_opt.Physical(g, w, word, row) + for k in range(3): + r1 = o.descend(6); r2 = bundles.descend(o, 3); r3 = joint.descend(o, 3, 'forward', k) + if not any(x['changed'] for x in r1) and not any(x['moved_components'] for x in r2) and not any(x['moved'] for x in r3): + break + dframes = o.frames + log('descent done') + # 4. forward closure (source_aligned_local_v4.py, preferred frames = descended frames) + p, w = compile_closure(g, arcs) + p, word = select(g, p, w) + ops = word['ops'] + assert len(ops) == len(dframes) + newargs = [None] + [None if x is None else [t + 1 for t in x] for x in g['args']] + newroots = [dict(r, node=r['node'] + 1) for r in g['roots']] + spans = [()] + [(q,) for q in g['inputs']] + for aa, bb in newargs[v + 1:]: + spans.append(basis(spans[aa] + spans[bb])) + root_frames = {} + for r, slot in zip(newroots, word['rootroles']): + root_frames[slot] = spans[r['node']] if r['kind'] == 'center' else perp(basis(g['inputs'][t] for t in r['targets']), h) + R = p['R'] + pset = set(word['phase1']) + previous = [-1] * R + parents = [] + for i, (aa, bb, x) in enumerate(ops): + parents.append((previous[aa], previous[bb])) + previous[aa] = previous[bb] = i + if x <= newcut and len(spans[x]) <= 2: + pset.add(i) + todo = list(pset) + while todo: + i = todo.pop() + for j in parents[i]: + if j >= 0 and j not in pset: + pset.add(j) + todo.append(j) + word['phase1'] = sorted(pset) + p['phase1_operations'] = len(pset) + chron = sorted(pset) + [i for i in range(len(ops)) if i not in pset] + cap = [perp(root_frames[s], h) if s in root_frames else () for s in range(R)] + maxima = [None] * len(ops) + for i in reversed(chron): + aa, bb, x = ops[i] + A = basis(cap[aa] + cap[bb]) + maxima[i] = perp(A, h) + cap[aa] = cap[bb] = A + selected = [z for z in word['selected'] if z['rank'] == h - 4] + gauge = {z['role']: perp(tuple(z['annihilator']), h) for z in selected} + current = [() for _ in range(R)] + for x, slot in word['sources'].items(): + current[slot] = (g['inputs'][int(x) - 1],) + for slot, U in gauge.items(): + current[slot] = U + frames = [None] * len(ops) + for i in chron: + aa, bb, x = ops[i] + want = spans[x] if x <= newcut else perp(basis(perp(tuple(dframes[i]), h) + perp(maxima[i], h)), h) + U = basis(spans[x] + want + current[aa] + current[bb]) + assert contained(U, maxima[i]), ('Forward frame outside future cap', i) + frames[i] = current[aa] = current[bb] = U + moved = [[i, list(U)] for i, U in enumerate(frames) if U != perp(tuple(w['annihilators'][ops[i][2]]), h)] + log('frames: %d of %d operations moved from their closure frames' % (len(moved), len(ops))) + # 5. pairs + role_ops = defaultdict(list) + for i, (aa, bb, _) in enumerate(ops): + role_ops[aa].append(i) + role_ops[bb].append(i) + pos = {i: k for k, i in enumerate(chron)} + for slot in role_ops: + role_ops[slot].sort(key=pos.__getitem__) + last_write = {} + for i, (aa, bb, x) in enumerate(ops): + last_write[aa] = max(last_write.get(aa, -1), pos[i]) + + def control_order(pairs): + controls = [q for q in pairs if q[2] is not None and last_write.get(q[0], -1) >= len(pset)] + if controls: + chosen = controls[-1] + pairs.remove(chosen) + pairs.append(chosen) + return pairs + recipients = sorted(gauge) + recipient_set = set(recipients) + donors = [slot for slot in range(R) if slot not in recipient_set and slot not in root_frames and slot in role_ops] + groups = defaultdict(list) + for j, slot in enumerate(recipients): + groups[gauge[slot]].append((pos[role_ops[slot][0]], j)) + group_data = [] + for U, ls in groups.items(): + ls.sort() + group_data.append((U, [x for x, _ in ls], [j for _, j in ls])) + cache, indices, indptr = {}, [], [0] + for slot in donors: + last = role_ops[slot][-1] + U = frames[last] + eligible = cache.get(U) + if eligible is None: + eligible = cache[U] = [(ps, js) for V, ps, js in group_data if contained(U, V)] + for ps, js in eligible: + indices.extend(js[bisect.bisect_right(ps, pos[last]):]) + indptr.append(len(indices)) + parity = [] + for cube in range(v // 8): + for bit in range(2): + parity.append(basis(tuple(g['inputs'][8 * cube + j] for j in range(8) if j.bit_count() % 2 == bit))) + erasable = {} + + def weight(slot, j): + key = (frames[role_ops[slot][-1]], gauge[recipients[j]]) + if key not in erasable: + U, V = key + erasable[key] = len(U) <= 3 and any(contained(U, S) and contained(S, V) for S in parity) + return 2.0 if erasable[key] else 1.0 + weights = np.array([weight(slot, indices[k]) for r, slot in enumerate(donors) for k in range(indptr[r], indptr[r + 1])]) + wmatrix = csr_matrix((weights, np.array(indices, dtype=np.int32), np.array(indptr, dtype=np.int32)), shape=(len(donors), len(recipients))) + rows, cols = min_weight_full_bipartite_matching(wmatrix.T.tocsr()) + matched = np.full(len(donors), -1) + matched[cols] = rows + pairs_parity = control_order([[slot, recipients[j], None if role_ops[slot][-1] in pset else role_ops[recipients[j]][0]] + for slot, j in zip(donors, matched) if j >= 0]) + o = physical_opt.Physical(g, w, dict(word, selected=selected), p) + for i, U in enumerate(frames): + o.frames[i] = tuple(U) + pairs_mw, mwstats = pairs_maxweight(o) + good = [k for k, (dd, b, t) in enumerate(pairs_mw) if t is not None and any(i not in o.phase and o.ops[i][0] == dd for i in o.role_ops[dd])] + if good: + pairs_mw.append(pairs_mw.pop(good[-1])) + log('pairs: parity %d, mw %d (of %d gauges)' % (len(pairs_parity), len(pairs_mw), len(recipients))) + dump(out / 'matching-arcs.json', dict(description=DESCRIPTIONS['arcs'], matching_arcs=arcs)) + dump(out / 'physical-frames.json', dict(description=DESCRIPTIONS['frames'], frames=moved)) + dump(out / 'physical-pairs-parity.json', dict(description=DESCRIPTIONS['parity'], pairs=pairs_parity)) + dump(out / 'physical-pairs-mw.json', dict(description=DESCRIPTIONS['mw'], pairs=pairs_mw)) + # 6. kernel pairs: aligned tree with aligned_word.py, flow with its own kernel matching + for recipe in ('parity', 'mw'): + tree = Path(d) / ('tree-' + recipe) + for cmd in ([PKG / 'aligned_word_p.py', '--p', P, *(['--centre46'] if centre else []), '--tree', root, + '--tmod', mods['tmod'], '--pmod', mods['pmod'], '--qmod', mods['qmod'], + '--arcs', out / 'matching-arcs.json', '--frames', out / 'physical-frames.json', + '--pairs', out / ('physical-pairs-%s.json' % recipe), '--out', tree], + [root / 'research/source-assisted/decision/complex_frame_flow.py', '--tree', tree, '--cache', tree / 'cache', + '--out', tree / 'flow.json', '--witness', '--purify-source-donors', '--recycle-kernels']): + r = subprocess.run([sys.executable, '-B', *map(str, cmd)], cwd=root, capture_output=True, text=True) + if r.returncode: + raise SystemExit('FAILED: %s\n%s%s' % (cmd[0], r.stdout[-3000:], r.stderr[-3000:])) + kernel = json.loads((tree / 'flow.witness.json').read_text())['kernel_pairs'] + flow = json.loads((tree / 'flow.json').read_text()) + dump(out / ('kernel-pairs-%s.json' % recipe), dict(description=DESCRIPTIONS['kernel'], kernel_pairs=kernel)) + log('%s: flow new_R %d, kernel reuses %d, numerical three-stage root %.7e' % (recipe, flow['new_R'], len(kernel), flow['numerical_local_root'])) + log('wrote %s' % out) + if centre: + record['centre46'] = True + if out == (PKG / 'layers' / a.set).resolve() and source['module_sets'].get(a.set) != record: + source['module_sets'][a.set] = dict(sorted(record.items())) + (PKG / 'SOURCE.json').write_text(json.dumps(source, indent=1) + '\n') + log('recorded the modules of %s in SOURCE.json: %s; now run verify.py --write, then verify.py' % (a.set, record)) + + +if __name__ == '__main__': + main() diff --git a/research/complex-p10/discovery/pairs_mw_p.py b/research/complex-p10/discovery/pairs_mw_p.py new file mode 100644 index 0000000000..0a96000bf5 --- /dev/null +++ b/research/complex-p10/discovery/pairs_mw_p.py @@ -0,0 +1,47 @@ +# pairs_mw_p.py: PR #233's discovery/pairs_mw.py (Chafik Boukhalfa with Anthropic Claude and OpenAI Codex +# assistance, Apache-2.0; vendored unchanged in pr233/pairs_mw.py) with ONE line changed: the gauge rank f in the +# donor weight is h - 4 (the rank of the selected gauges) instead of the literal 18, which equals h - 4 only at +# h = 22. At h = 18 the literal makes every weight 0 (no pairs); see README.md. Identical to pairs_mw.py at h = 22. +# Change by DreamingOfClouds with Anthropic Claude assistance (Apache-2.0). +"""Maximum-weight donor pairing for gauged recipients (weights depend on the donor only, so the +transversal-matroid greedy with augmenting paths is optimal). Explicit legality: donor ungauged non-root with ops, +last frame contained in the recipient gauge, donor dead before the recipient's first operation (or in phase one).""" +from collections import defaultdict +import sys +from paired_cube.frames import contained +def pairs_maxweight(o): + sys.setrecursionlimit(100000) + donors=[s for s in range(o.R) if s not in o.gauge and s not in o.roots and o.role_ops[s]] + recipients=sorted(o.gauge,key=lambda b:(o.position[o.role_ops[b][0]],b));rindex={b:i for i,b in enumerate(recipients)} + rtime=[o.position[o.role_ops[b][0]] for b in recipients] + byframe=defaultdict(list) + for s in donors:byframe[o.frames[o.role_ops[s][-1]]].append(s) + groups={} + adj=defaultdict(list) # donor -> recipient indices + for b in recipients: + F=o.gauge[b] + if F not in groups:groups[F]=[s for D,ss in byframe.items() if contained(D,F) for s in ss] + t=rtime[rindex[b]] + for s in groups[F]: + if o.position[o.role_ops[s][-1]]=dd else -1e9 + order=sorted(adj,key=lambda s:(-weight(s),o.position[o.role_ops[s][-1]],s)) + mr=[-1]*len(recipients);md={} + def dfs(s,seen): + for r in adj[s]: + if r in seen:continue + seen.add(r) + if mr[r]<0 or dfs(mr[r],seen):mr[r]=s;md[s]=r;return True + return False + for s in order: + if weight(s)<=0:break + dfs(s,set()) + result=[] + for r,s in enumerate(mr): + if s>=0: + b=recipients[r];first=o.role_ops[b][0] + result.append([s,b,None if o.role_ops[s][-1] in o.phase else first]) + stats=dict(donors=len(donors),recipients=len(recipients),edges=sum(map(len,adj.values())),matched=len(result),total_weight=sum(weight(s) for s,_,_ in result)) + return result,stats diff --git a/research/complex-p10/discovery/pr233/README.md b/research/complex-p10/discovery/pr233/README.md new file mode 100644 index 0000000000..339adb1c76 --- /dev/null +++ b/research/complex-p10/discovery/pr233/README.md @@ -0,0 +1,18 @@ +# Discovery (not run by verify.py) + +The physical layer of the certified package is PR #168's operation frames with PR #200's late compensated reuse +pairing (`physical_opt.py:pairs`, the maximum-weight pairing of `pairs_mw.py` (transversal-matroid greedy with augmenting paths, donor weight the gain heuristic of PR #200)). `flow_frames.py` runs `harness.descend` on the source-aligned cache of +PR #194's pipeline with all frame moves frozen (`DESCENT_LIGHT_ROUNDS=1 DESCENT_FREEZE_FRAC=1.0 --light +--seed-frames`), recomputes the pairs and prices the layer with PR #184's `complex_frame_flow.py`: + + SA_TREE= SA_PY= DESCENT_LIGHT_ROUNDS=1 DESCENT_FREEZE_FRAC=1.0 \ + python3 -B flow_frames.py --aligned --seed-frames --light --mw 1 --keep out/ + +Float flow roots: PR #168's pairing 7.00918e-4; PR #200's default pairing (donors ordered by the gain heuristic) +7.09765e-4; donors ordered by widest end frame with recipients in reverse chronology (`PAIR_ORDER=wide +PAIR_RECIPIENTS=reverse`) 7.09882e-4; the maximum-weight pairing (`--mw 1`, `pairs_mw.py`, every donor-weight variant +tried) 7.09907e-4, the certified layer; random donor orders 6.4e-4 to 6.6e-4. With frames also descended: full cycle +7.08613e-4, one light round 7.0950e-4, 98% of operations frozen 7.09767e-4; a screen over every single endpoint move +on top of PR #168's frames (`flow_moves.py`) finds no improving move, so the frames are left untouched. The matching +itself is PR #168's frozen carrier matching (`matching.py`, `extend.py` are needed only to import `harness`). +Prepared by Chafik Boukhalfa with Anthropic Claude and OpenAI Codex assistance; Apache-2.0. diff --git a/research/complex-p10/discovery/pr233/bundles.py b/research/complex-p10/discovery/pr233/bundles.py new file mode 100644 index 0000000000..2035223567 --- /dev/null +++ b/research/complex-p10/discovery/pr233/bundles.py @@ -0,0 +1,50 @@ +"""Connected equal-frame endpoint moves, motivated by PR164/168 bundle descent. + +Own explicit boundary implementation: all source spans, incoming and outgoing +role frames are recomputed before a move. No physical legality is inferred from +an optimization score; the independent physical verifier remains mandatory. +""" +from collections import defaultdict +from physical_opt import join,meet +from paired_cube.frames import contained + +def descend(o,rounds=4): + report=[] + for rnd in range(rounds): + n=len(o.ops);parent=list(range(n)) + def root(i): + while parent[i]!=i:parent[i]=parent[parent[i]];i=parent[i] + return i + def union(i,j): + a,b=root(i),root(j) + if a!=b:parent[max(a,b)]=min(a,b) + for i in range(n): + for j in o.prev[i]: + if j is not None and o.frames[i]==o.frames[j]:union(i,j) + groups=defaultdict(list) + for i in range(n):groups[root(i)].append(i) + groups=[l for l in groups.values() if len(l)>1];groups.sort(key=lambda l:min(l),reverse=not rnd%2) + moved=changed=0;gain=0.;big=0 + for ids in groups: + inside=set(ids);F=o.frames[ids[0]];assert all(o.frames[i]==F for i in ids) + L=();U=o.full;previous=[];after=[] + for i in ids: + a,b,x=o.ops[i];L=join(L,o.spans[x]) + for role,j in zip((a,b),o.prev[i]): + if j not in inside: + A=o.frames[j] if j is not None else o.start[role];previous.append(A);L=join(L,A) + for role,j in zip((a,b),o.next[i]): + if j not in inside: + A=o.frames[j] if j is not None else o.end[role];after.append(A);U=meet(U,A,o.h) + assert contained(L,F) and contained(F,U) + def score(A): + d=len(A);return sum(o.phi[d-len(P)] for P in previous)+sum(o.phi[len(N)-d] for N in after) + old=score(F);candidate=min((L,U),key=score);delta=old-score(candidate) + if delta>1e-7: + for i in ids:o.frames[i]=candidate + moved+=1;changed+=len(ids);gain+=delta;big=max(big,len(ids)) + rec=dict(round=rnd,components=len(groups),moved_components=moved,changed_operations=changed,numerical_excess_gain=gain,largest_moved_component=big);report.append(rec);print('bundles',rec,flush=True) + if not moved:break + for i in range(n): + P,N=o.neighbors(i);assert contained(o.spans[o.ops[i][2]],o.frames[i]);assert all(contained(F,o.frames[i]) for F in P);assert all(contained(o.frames[i],F) for F in N) + return report diff --git a/research/complex-p10/discovery/pr233/joint.py b/research/complex-p10/discovery/pr233/joint.py new file mode 100644 index 0000000000..a67d18034d --- /dev/null +++ b/research/complex-p10/discovery/pr233/joint.py @@ -0,0 +1,67 @@ +"""Joint collapse of adjacent operation-frame components. + +All incoming/outgoing chains and actual value supports bound each common +frame. Old internal rank increments are charged once per role edge. A move +must reduce the full boundary-plus-internal numerical objective. Floating +scores select a witness only; admission requires the independent exact audit. +""" +from collections import defaultdict +import random,time +from physical_opt import join,meet +from paired_cube.frames import contained + +def components(o): + n=len(o.ops);parent=list(range(n)) + def root(i): + while parent[i]!=i:parent[i]=parent[parent[i]];i=parent[i] + return i + for i in range(n): + for j in o.prev[i]: + if j is not None and o.frames[i]==o.frames[j]: + a,b=root(i),root(j) + if a!=b:parent[max(a,b)]=min(a,b) + groups=defaultdict(list) + for i in range(n):groups[root(i)].append(i) + adjacent=set() + for i in range(n): + for j in o.prev[i]: + if j is not None and root(i)!=root(j):adjacent.add(tuple(sorted((root(i),root(j))))) + return groups,sorted(adjacent) + +def descend(o,rounds=5,order='forward',seed=0): + result=[];rng=random.Random(seed) + for rnd in range(rounds): + t=time.monotonic();groups,adjacent=components(o) + if order=='random':rng.shuffle(adjacent) + elif (order=='reverse')^(rnd%2==1):adjacent.reverse() + tried=feasible=moved=changed=largest=0;gain=0. + for a,b in adjacent: + ids=groups[a]+groups[b];inside=set(ids);tried+=1 + # Each original component remains uniform even after overlapping moves. + assert all(o.frames[i]==o.frames[a] for i in groups[a]) + assert all(o.frames[i]==o.frames[b] for i in groups[b]) + L=();U=o.full;previous=[];after=[];old=0. + for i in ids: + x,y,node=o.ops[i];F=o.frames[i];L=join(L,o.spans[node]) + for role,j in zip((x,y),o.prev[i]): + P=o.frames[j] if j is not None else o.start[role] + assert contained(P,F);old+=o.phi[len(F)-len(P)] + if j not in inside:previous.append(P);L=join(L,P) + for role,j in zip((x,y),o.next[i]): + if j not in inside: + N=o.frames[j] if j is not None else o.end[role] + assert contained(F,N);after.append(N);U=meet(U,N,o.h);old+=o.phi[len(N)-len(F)] + if not contained(L,U):continue + feasible+=1 + def score(F): + d=len(F);return sum(o.phi[d-len(P)] for P in previous)+sum(o.phi[len(N)-d] for N in after) + best=min((L,U),key=lambda F:(score(F),len(F),F));delta=old-score(best) + if delta>1e-7: + for i in ids:o.frames[i]=best + moved+=1;changed+=len(ids);gain+=delta;largest=max(largest,len(ids)) + row=dict(round=rnd,groups=len(groups),tried=tried,feasible=feasible,moved=moved,changed=changed,largest=largest,numerical_excess_gain=gain,seconds=time.monotonic()-t) + print('joint',row,flush=True);result.append(row) + if not moved:break + for i in range(len(o.ops)): + P,N=o.neighbors(i);assert contained(o.spans[o.ops[i][2]],o.frames[i]);assert all(contained(F,o.frames[i]) for F in P);assert all(contained(o.frames[i],F) for F in N) + return result diff --git a/research/complex-p10/discovery/pr233/matching.py b/research/complex-p10/discovery/pr233/matching.py new file mode 100644 index 0000000000..e84e348556 --- /dev/null +++ b/research/complex-p10/discovery/pr233/matching.py @@ -0,0 +1,131 @@ +"""Own explicit legal-edge Hopcroft-Karp witness; from our r13 search.""" +from collections import deque +import sys +from paired_cube.frames import basis,perp,contained +def carrier_matching(g,ordering='node'): + """Exact legal edge list, then deterministic Hopcroft--Karp matching. + + Frame and chronological predicates are the retained compiler's predicates; + the resulting explicit arcs are checked anew by compile_graph. + """ + h=g['h'];v=g['v'];args=[None]+[None if a is None else [y+1 for y in a] for a in g['args']] + roots=[dict(r,node=r['node']+1) for r in g['roots']];n=len(args) + spans=[()]*n + for i,u in enumerate(g['inputs']):spans[i+1]=(u,) + for x in range(v+1,n):spans[x]=basis(spans[args[x][0]]+spans[args[x][1]]) + rann=[];rframe=[] + for r in roots: + if r['kind']=='center':U=spans[r['node']];A=perp(U,h) + else:A=basis(g['inputs'][t] for t in r['targets']);U=perp(A,h) + rann.append(A);rframe.append(U) + active=set(range(1,v+1));todo=[r['node'] for r in roots] + while todo: + x=todo.pop() + if x in active:continue + active.add(x);todo.extend(args[x] or []) + initial=spans + if g['matching_frames'] in ('maximal','coordinate'): + initial=[()]*n;ann=[None]*n;successors=[[] for _ in args];constraints=[[] for _ in args] + for x in sorted(active): + for y in args[x] or []:successors[y].append(x) + for j,r in enumerate(roots):constraints[r['node']].extend(rann[j]) + for x in sorted(active,reverse=True): + ann[x]=basis(constraints[x]+[z for y in successors[x] for z in ann[y]]) + initial[x]=perp(ann[x],h) + if g['matching_frames']=='coordinate': + cover=0 + for u in spans[x]:cover|=u + initial[x]=perp(ann[x]+tuple(1<>j&1),h) + assert contained(spans[x],initial[x]) + order=sorted(active,key=lambda x:(len(initial[x]),x));position={x:i for i,x in enumerate(order)} + uses=[[] for _ in args];uf=[];ut=[];uc=[] + for x in order: + for j,y in enumerate(args[x] or []):uses[y].append(len(uc));uf.append(initial[x]);ut.append(x);uc.append(2*x+j) + for j,r in enumerate(roots):uses[r['node']].append(len(uc));uf.append(rframe[j]);ut.append(n+j);uc.append((1<<31)|j) + donors=[x for x in order if args[x]] + if ordering=='reverse':donors.reverse() + elif ordering=='narrow':donors.sort(key=lambda x:(len(initial[x]),x)) + elif ordering=='wide':donors.sort(key=lambda x:(-len(initial[x]),x)) + elif ordering=='node':donors.sort() + elif ordering.startswith('random:'): + import random + rnd=random.Random(int(ordering.split(':',1)[1]));rnd.shuffle(donors) + adjacency=[] + for x in donors: + row=[u for y in args[x] for u in uses[y] if (ut[u]>=n or position[ut[u]]>position[x]) and contained(initial[x],uf[u])] + if ordering.startswith('late'): # prefer the latest use in the chronology (root uses last), then the largest growth + row.sort(key=lambda u:(-(position[ut[u]] if ut[u]=0] + stats=dict(donors=L,uses=len(uc),edges=sum(map(len,adjacency)),matched=len(arcs),augment_rounds=iterations) + if ordering.startswith('frozen:'): + import json as _j + given=_j.loads(open(ordering.split(':',1)[1]).read());pos_of={uc[u]:u for u in range(len(uc))} + growth=0;seen=0 + for x,code in given: + u=pos_of.get(code) + if u is None:continue + seen+=1;growth+=len(uf[u])-len(initial[x]) + stats.update(frozen_arcs=len(given),frozen_seen=seen,frozen_growth=growth,hk_growth=int(sum(len(uf[v2])-len(initial[donors[i]]) for i,v2 in enumerate(ml) if v2>=0))) + import os as _os + if _os.environ.get('MATCH_FEATURES'): + chosen={x:pos_of[c] for x,c in given if c in pos_of};hk={donors[i]:v2 for i,v2 in enumerate(ml) if v2>=0} + rec=[] + for i,x in enumerate(donors): + cands=[dict(u=u,growth=len(uf[u])-len(initial[x]),udim=len(uf[u]),root=int(ut[u]>=n),gap=(position[ut[u]]-position[x]) if ut[u]1 and parts[1]=='max' else 1 + noise=None + if len(parts)>2: + import random as _r;noise=_r.Random(int(parts[2])) + rows=[i for i,v2 in enumerate(ml) if v2>=0];rid={i:k for k,i in enumerate(rows)} + data=[];ri=[];ci=[] + for i in rows: + x=donors[i] + for u in adjacency[i]: + growth=len(uf[u])-len(initial[x]);ri.append(rid[i]);ci.append(u);data.append(1+sign*growth+(0 if sign>0 else 30)+(noise.random()*float(parts[3]) if noise else 0.0)) + M=csr_matrix((np.array(data,dtype=float),(np.array(ri),np.array(ci))),shape=(len(rows),len(uc))) + r_ind,c_ind=min_weight_full_bipartite_matching(M) + arcs=[[donors[rows[r]],uc[c]] for r,c in zip(r_ind,c_ind)] + stats.update(matched=len(arcs),total_growth=int(sum(len(uf[c])-len(initial[donors[rows[r]]]) for r,c in zip(r_ind,c_ind))),mincost=True) + hk_growth=int(sum(len(uf[v2])-len(initial[donors[i]]) for i,v2 in enumerate(ml) if v2>=0));stats['hk_growth']=hk_growth + return arcs,stats + diff --git a/research/complex-p10/discovery/pr233/pairs_mw.py b/research/complex-p10/discovery/pr233/pairs_mw.py new file mode 100644 index 0000000000..7e0db9777e --- /dev/null +++ b/research/complex-p10/discovery/pr233/pairs_mw.py @@ -0,0 +1,42 @@ +"""Maximum-weight donor pairing for gauged recipients (weights depend on the donor only, so the +transversal-matroid greedy with augmenting paths is optimal). Explicit legality: donor ungauged non-root with ops, +last frame contained in the recipient gauge, donor dead before the recipient's first operation (or in phase one).""" +from collections import defaultdict +import sys +from paired_cube.frames import contained +def pairs_maxweight(o): + sys.setrecursionlimit(100000) + donors=[s for s in range(o.R) if s not in o.gauge and s not in o.roots and o.role_ops[s]] + recipients=sorted(o.gauge,key=lambda b:(o.position[o.role_ops[b][0]],b));rindex={b:i for i,b in enumerate(recipients)} + rtime=[o.position[o.role_ops[b][0]] for b in recipients] + byframe=defaultdict(list) + for s in donors:byframe[o.frames[o.role_ops[s][-1]]].append(s) + groups={} + adj=defaultdict(list) # donor -> recipient indices + for b in recipients: + F=o.gauge[b] + if F not in groups:groups[F]=[s for D,ss in byframe.items() if contained(D,F) for s in ss] + t=rtime[rindex[b]] + for s in groups[F]: + if o.position[o.role_ops[s][-1]]=dd else -1e9 + order=sorted(adj,key=lambda s:(-weight(s),o.position[o.role_ops[s][-1]],s)) + mr=[-1]*len(recipients);md={} + def dfs(s,seen): + for r in adj[s]: + if r in seen:continue + seen.add(r) + if mr[r]<0 or dfs(mr[r],seen):mr[r]=s;md[s]=r;return True + return False + for s in order: + if weight(s)<=0:break + dfs(s,set()) + result=[] + for r,s in enumerate(mr): + if s>=0: + b=recipients[r];first=o.role_ops[b][0] + result.append([s,b,None if o.role_ops[s][-1] in o.phase else first]) + stats=dict(donors=len(donors),recipients=len(recipients),edges=sum(map(len,adj.values())),matched=len(result),total_weight=sum(weight(s) for s,_,_ in result)) + return result,stats diff --git a/research/complex-p10/discovery/pr233/physical_opt.py b/research/complex-p10/discovery/pr233/physical_opt.py new file mode 100644 index 0000000000..a2e8e7d053 --- /dev/null +++ b/research/complex-p10/discovery/pr233/physical_opt.py @@ -0,0 +1,127 @@ +#!/usr/bin/env python3 +"""New deterministic exact frame endpoints and legal late handoff discovery. + +Chafik Boukhalfa with OpenAI Codex assistance. Apache-2.0. +Builds on PR144 binary frame/word contract and PR157 physical reuse theorem. +Numerical excess weights only select witnesses; exact containment, histogram +and scalar checks must be independently replayed on the selected candidate. +""" +from collections import defaultdict,deque,Counter +from functools import lru_cache +import math +from paired_cube.frames import basis,perp,contained + +@lru_cache(maxsize=300000) +def join(A,B): + if contained(A,B):return B + if contained(B,A):return A + return basis(A+B) +@lru_cache(maxsize=300000) +def meet(A,B,h): + if contained(A,B):return A + if contained(B,A):return B + return perp(join(perp(A,h),perp(B,h)),h) + +class Physical: + def __init__(self,g,w,word,row): + self.g,self.w,self.word,self.row=g,w,word,row;self.h=g['h'];self.R=row['R'];self.v=g['v'];h=self.h + self.full=basis(1<1e-10 or abs(delta)<=1e-10 and len(best)=0: + b=recipients[j];first=self.role_ops[b][0] + result.append([d,b,None if self.role_ops[d][-1] in self.phase else first]) + return result,dict(donors=len(donors),recipients=L,edges=sum(map(len,adj)),matched=len(result),gauge_frames=len(groups),donor_frames=len(byframe)) + + def changed(self):return [[i,F] for i,F in enumerate(self.frames) if F!=self.original[i]] diff --git a/research/complex-p10/gcert_emit.py b/research/complex-p10/gcert_emit.py new file mode 100644 index 0000000000..fd5d56f651 --- /dev/null +++ b/research/complex-p10/gcert_emit.py @@ -0,0 +1,318 @@ +#!/usr/bin/env python3 +"""gcert_emit.py: lower a source-aligned complex flow to Jacob Sussman's certificate format gcert/1. + +Inputs (all produced by the integer-mult-bounds tool chain of PR #184 / #194 on an aligned tree): + --cache the aligned tree's cache (graph.json, selection.json) + --flow flow.json (complex_frame_flow.py --witness) + --witness flow.witness.json (same run) + --lift lift.certificate.json.gz (exact_complex_flow_lift.py: local invertible completions as elementary gates) +Output: a gcert/1 JSON(.gz) as read by wht-power-saving-lean/tools/gx/gx.py (check1) and gxgen.py. + +Registers: x_j = j (sources, start at the port line), y_t = v+t (targets, start at frame 0, end at port^perp), +slots 2v.. (one per physical flow coordinate: v source copies + births; kernel reuse continues a slot). +Every node of the flow DAG (phase, frame) becomes, at its frame: the source copies (x -> slot), the reads +(slot -> targets, or a retained total for the scatter), then the lift's elementary gates. A 'swap' relabels +positions, a 'scale' changes the unit of a slot (wanted = lam * stored, as gxconv.py), an 'add' is one 'out' +gate. After phase 2: the paired-cube K blocks (1 - J/2) on each parity class of a cube, the direct reads of the +mixed sources into their antipodal targets at the target cap frames, and the inverse K blocks at the full frame. +""" +import argparse, gzip, json, heapq, sys, time +from collections import Counter, defaultdict +from fractions import Fraction as F + + +def load(p): + p = str(p) + if p.endswith('.gz'): + return json.loads(gzip.decompress(open(p, 'rb').read())) + return json.load(open(p)) + + +def rref(rows): + piv = {} + for x in rows: + for k in sorted(piv, reverse=True): + if x >> k & 1: + x ^= piv[k] + if x: + k = x.bit_length() - 1 + for kk in list(piv): + if piv[kk] >> k & 1: + piv[kk] ^= x + piv[k] = x + return tuple(piv[k] for k in sorted(piv, reverse=True)) + + +def perp(rows, h): + """basis of the orthogonal complement (standard dot product mod 2) of span(rows)""" + B = rref(rows) + piv = [b.bit_length() - 1 for b in B] + free = [k for k in range(h) if k not in piv] + out = [] + for k in free: + u = 1 << k + for b in B: + if b >> k & 1: + u |= 1 << (b.bit_length() - 1) + out.append(u) + return rref(out) + + +def enc(x): + x = F(x) + return [x.numerator, x.denominator] + + +def main(): + ap = argparse.ArgumentParser(description=__doc__) + ap.add_argument('--cache', required=True) + ap.add_argument('--flow', required=True) + ap.add_argument('--witness', required=True) + ap.add_argument('--lift', required=True) + ap.add_argument('--out', required=True) + ap.add_argument('--name', default='flow word') + a = ap.parse_args() + t0 = time.time() + g = load(a.cache + '/graph.json'); word = load(a.cache + '/selection.json') + prof = load(a.flow); wit = load(a.witness); lift = load(a.lift) + h, v = g['h'], g['v'] + ports = g['inputs'] + assert ports == wit['original_source_ports'] + nodes, edges, vectors = wit['nodes'], wit['edges'], wit['vectors'] + maps, order = lift['maps'], lift['topological_order'] + assert len(maps) == len(nodes) == len(order) + roots = g['roots'] + # ---- frames + frames = [(), tuple(1 << i for i in range(h - 1, -1, -1))] + fid = {frames[0]: 0, frames[1]: 1} + + def frame(rows): + key = rref(rows) + if key not in fid: + fid[key] = len(frames); frames.append(key) + return fid[key] + xstart = [frame((q,)) for q in ports] + caps = [frame(perp((q,), h)) for q in ports] + # ---- signed side rows of the deferred roles (as contract_v4.validate) + ops, coeff = word['ops'], word['opcoeff'] + Rw = max(max(x, y) for x, y, _ in ops) + 1 + selected = {s['role']: s for s in word['selected']} + side = [dict() for _ in range(Rw)] + for r, s in zip(roots, word['rootroles']): + if r['kind'] != 'center': + side[s] = {t: (1 if c == '1/2' else -1) for t, c in zip(r['targets'], r['coefficients'])} + + def add_scaled(dst, src, c): + for k, x in src.items(): + y = dst.get(k, 0) + c * x + if y: + dst[k] = y + else: + dst.pop(k, None) + for (x, y, _), (ca, cb) in zip(reversed(ops), reversed(coeff)): + add_scaled(side[y], side[x], cb) + if ca != 1: + side[x] = {j: ca * c for j, c in side[x].items()} + for s, z in selected.items(): + assert set(side[s]) == set(z['targets']) + + def responses(rd): + if rd['kind'] == 'side': + r = roots[rd['ref']] + return {t: F(1, 2) if c == '1/2' else F(-1, 2) for t, c in zip(r['targets'], r['coefficients'])} + assert rd['kind'] == 'deferred' + return {t: F(-c, 2) for t, c in side[rd['ref']].items()} + # ---- edge coordinates: (target node, input position) -> (source node, output position) + by_frame = {(n['frame'][0], tuple(n['frame'][1])): i for i, n in enumerate(nodes)} + out_off, in_off = Counter(), Counter() + coord_in = {} + for e in edges: + i = by_frame[(e['source'][0], tuple(e['source'][1]))]; j = by_frame[(e['target'][0], tuple(e['target'][1]))] + for k in range(len(e['basis'])): + coord_in[j, in_off[j] + k] = (i, out_off[i] + k) + out_off[i] += len(e['basis']); in_off[j] += len(e['basis']) + kernel_birth = {} + for i, aa, j, bb in wit['kernel_pairs']: + kernel_birth[j, bb] = (i, aa) + # ---- emission + A, B, ret = [], [], [] + nslot = 0 + lam = {} + + def new_slot(): + nonlocal nslot + s = 2 * v + nslot; nslot += 1; lam[s] = F(1) + return s + slot_out, kernel_slot = {}, {} + center_lam = {} + stats = Counter() + phase_of_node = {} + for i in order: + node, mp = nodes[i], maps[i] + ph, U = node['frame'] + f = frame(tuple(U)) + gates = A if ph == 1 else B + n, t, b, d, r = node['n'], node['t'], node['new_dirty'], node['d'], node['r'] + N = n + b + assert mp['size'] == N and not mp['source_erase'] and not mp['source_inject'], 'source controls not supported yet' + pos = [None] * N + nin = in_off[i] + g0_node = len(gates) + for p in range(n): + if p < nin: + pos[p] = slot_out[coord_in[i, p]] + else: # original source copy at its port line + row = vectors[node['inputs'][p]] + assert len(row) == 1 and row[0][1] == 1 and ph == 1 and f == xstart[row[0][0]] + s = new_slot(); pos[p] = s + gates.append(['out', f, row[0][0], [[s, 1, 1]], []]) + for q in range(b): + if (i, q) in kernel_birth: + s = kernel_slot[kernel_birth[i, q]]; lam[s] = F(1) + else: + s = new_slot() + pos[n + q] = s + # reads (in terms of the input positions, before the completion) + for rd, rc in zip(node['reads'], mp['read_coefficients']): + if rd['kind'] == 'center': + assert ph == 1 + k = roots[rd['ref']]['coordinate'] + val = rd['value'] + if val in node['outputs']: + assert len(rc) == 1 + center_lam[k] = (i, 'out', node['outputs'].index(val), F(rc[0][1], rc[0][2])) + else: + # the total is formed in place in one of its (retiring) input registers + assert t == 0 and not mp['inverse_gates'], ('center total neither leaves nor rests', i) + p0, n0, d0 = rc[0]; s0 = pos[p0]; c0 = F(n0, d0) * lam[s0] + for p, num, den in rc[1:]: + s = pos[p] + gates.append(['out', f, s, [[s0, *enc(F(num, den) * lam[s] / c0)]], []]) + center_lam[k] = (i, 'pos', p0, c0) + continue + assert ph == 2 + resp = responses(rd) + for p, num, den in rc: + s = pos[p] + c = F(num, den) * lam[s] + gates.append(['out', f, s, [[v + tt, *enc(c * w)] for tt, w in sorted(resp.items())], []]) + # completion gates: the lift stores the row operations taking Q to I; the registers need Q itself, + # i.e. the inverse operations in reverse order (exact_complex_flow_lift.inverse_program, 'forward'). + g0 = len(gates) + for kind, x, y, num, den in reversed(mp['inverse_gates']): + if kind == 'swap': + pos[x], pos[y] = pos[y], pos[x] + elif kind == 'scale': + assert x == y + lam[pos[x]] /= F(num, den) + else: + assert kind == 'add' and x != y + sx, sy = pos[x], pos[y] + c = -F(num, den) * lam[sy] / lam[sx] + gates.append(['out', f, sy, [[sx, *enc(c)]], []]) + # every coordinate that passes through the node is moved to its frame (the flow charges the edge): + # registers of inputs and births that no gate of this node names ride as extra registers + named = set() + for gg in gates[g0_node:]: + named.add(gg[2]); named.update(x_ for x_, _, _ in gg[3]) + if gg[0] == 'out': + named.update(gg[4]) + idle = [s_ for s_ in pos if s_ not in named] + if idle: + outs = [gg for gg in gates[g0_node:] if gg[0] == 'out'] + if outs: + outs[-1][4].extend(idle) + else: + stats['idle_nodes'] += 1 + gates.append(['out', f, idle[0], [], idle[1:]]) + for q in range(t): + slot_out[i, q] = pos[q] + for aa in range(node['retired'] - (d - r)): + kernel_slot[i, aa] = pos[t + (d - r) + aa] + # retained totals: the coordinate must survive the completion in one register + for k, z in list(center_lam.items()): + if isinstance(z, tuple) and z[0] == i: + ii, how, p, c = z + s = pos[p] + ret.append([k, s, f]); center_lam[k] = c * lam[s] if how == 'out' else c + R = nslot + assert R == prof['new_R'], (R, prof['new_R']) + ret.sort() + assert [z[0] for z in ret] == list(range(h)), 'one retained total per coordinate expected' + # ---- K blocks, direct reads, inverse K blocks + for cube in range(v // 8): + ids8 = list(range(8 * cube, 8 * cube + 8)) + for parity in range(2): + ids = [j for j in ids8 if j.bit_count() % 2 == parity] + S = frame(tuple(ports[j] for j in ids)) + assert len(frames[S]) == 3 + x1, rest = ids[0], ids[1:] + B.append(['in', S, x1, [[r_, 1, 1] for r_ in rest]]) + B.append(['out', S, x1, [[r_, -1, 2] for r_ in rest], []]) + B.append(['in', S, x1, [[r_, 1, 1] for r_ in rest]]) + for cube in range(v // 8): + ids8 = list(range(8 * cube, 8 * cube + 8)) + for j in ids8: + anti = [t for t in ids8 if (ports[t] ^ ports[j]).bit_count() == 6] + assert len(anti) == 1 + t = anti[0] + x1 = [jj for jj in ids8 if jj.bit_count() % 2 == j.bit_count() % 2][0] + B.append(['out', caps[t], j, [[v + t, -1 if j == x1 else 1, 1]], []]) + for cube in range(v // 8): + ids8 = list(range(8 * cube, 8 * cube + 8)) + for parity in range(2): + ids = [j for j in ids8 if j.bit_count() % 2 == parity] + x1, rest = ids[0], ids[1:] + B.append(['in', 1, x1, [[r_, -1, 1] for r_ in rest]]) + B.append(['out', 1, x1, [[r_, 1, 2] for r_ in rest], []]) + B.append(['in', 1, x1, [[r_, -1, 1] for r_ in rest]]) + # ---- scatter + sin, sout = F(1, 3), F(-1, 6) + if all(center_lam[k] == 1 for k in range(h)): + scat = dict(inside=[1, 3], outside=[-1, 6]) + else: + scat = dict(table=[[[k, *enc((sin if ports[t] >> k & 1 else sout) * center_lam[k])] for k in range(h)] for t in range(v)]) + nreg = 2 * v + R + start = [0] * nreg; final = [1] * nreg + for j in range(v): + start[j] = xstart[j]; final[v + j] = caps[j] + cst = sum(len(frames[f]) for _, _, f in ret) + # ---- blocks (the climb count of gx.check1) + dim = [len(f) for f in frames] + cur = list(start) + H = {'x': Counter(), 'y': Counter(), 's': Counter(), 'c': Counter()} + cls = lambda r_: 'x' if r_ < v else 'y' if r_ < 2 * v else 's' + + def climb(r_, f): + o = cur[r_] + if o != f: + assert dim[o] < dim[f], ('step not increasing', r_, o, f) + H[cls(r_)][dim[f] - dim[o]] += 1; cur[r_] = f + for ph, gates in (('A', A), ('B', B)): + if ph == 'B': + for k, s, f in ret: + assert cur[s] == f, ('retained slot moved before the cut', k, s) + H['c'][dim[f]] += 1 + for gg in gates: + regs = [gg[2]] + ([x for x, _, _ in gg[3]] + list(gg[4]) if gg[0] == 'out' else [x for x, _, _ in gg[3]] if gg[0] == 'in' else []) + for r_ in regs: + climb(r_, gg[1]) + for r_ in range(nreg): + climb(r_, final[r_]) + blocks = {k: {str(r_): n_ for r_, n_ in sorted(w.items())} for k, w in H.items()} + Nn = sum(r_ * n_ for w in H.values() for r_, n_ in w.items()) + assert Nn == R * h + 2 * v * (h - 1) + cst, (Nn, R * h + 2 * v * (h - 1) + cst) + c1 = dict(format='gcert/1', derived_from='%s (gcert_emit.py from complex_frame_flow.py witness + exact_complex_flow_lift.py completions)' % a.name, + p=g['p'], h=h, v=v, R=R, cst=cst, N=Nn, ports=ports, frames=[list(f) for f in frames], start=start, final=final, + ext=[], ret=ret, scat=scat, A=A, B=B, blocks=blocks) + data = json.dumps(c1, separators=(',', ':')).encode() + if a.out.endswith('.gz'): + open(a.out, 'wb').write(gzip.compress(data)) + else: + open(a.out, 'wb').write(data) + print(json.dumps(dict(R=R, N=Nn, cst=cst, idle_nodes=stats['idle_nodes'], gates_A=len(A), gates_B=len(B), frames=len(frames), blocks=blocks, + scatter='table' if 'table' in scat else 'star', seconds=round(time.time() - t0, 1)))) + + +if __name__ == '__main__': + main() diff --git a/research/complex-p10/gx/gx.py b/research/complex-p10/gx/gx.py new file mode 100644 index 0000000000..6d14c0a976 --- /dev/null +++ b/research/complex-p10/gx/gx.py @@ -0,0 +1,296 @@ +#!/usr/bin/python3 -I +"""gx.py. OWN code (imports nothing of port-producer, nothing outside). +(1) convert(c0): gcert/0 (port-producer's event list) -> gcert/1, the LEAN-FACING NORMAL FORM: + only the main phase (no read0 / undo / uninj: the invocation theorem derives the dirt gate and the undo + gate from the product), every gate an elementary fan-out or fan-in add, the 4x4 K block written as three + such adds plus a sign carried by one register, the star scatter as a table. +(2) check1(c1): the local decidable conditions of EXTENDED-CERT-SPEC.md on a gcert/1 file: + E0 sizes, E1 labels (nested subspaces by containment, equal frame at a gate), E2 scatter cut, + E3 shape (kinds of gates; X1; S1), E4 bracket rule S2, E5 scalar (x-content replay: hid and X3), + E6 price data (block histograms, N), E7 exterior gauges only (Q2). Raises AssertionError(": ..."). +""" +from fractions import Fraction as Fr +from collections import Counter +from math import lcm + + +def need(c, msg): + if not c: + raise AssertionError(msg) + + +def reduce(u, basis): + """basis: reduced echelon, pivot = leading bit, descending. Returns u modulo the span.""" + for b in basis: + if u >> (b.bit_length() - 1) & 1: + u ^= b + return u + + +def echelon_ok(f): + piv = [b.bit_length() - 1 for b in f] + if any(b == 0 for b in f) or piv != sorted(piv, reverse=True) or len(set(piv)) != len(piv): + return False + return all(not (b >> p & 1) for i, b in enumerate(f) for j, p in enumerate(piv) if i != j) + + +def inside(a, b): + return all(reduce(u, b) == 0 for u in a) + + +def par(x): + return bin(x).count("1") & 1 + + +KJ = [[[1, 2] if i == j else [-1, 2] for j in range(4)] for i in range(4)] + + +def convert(c0): + need(c0["format"] == "gcert/0", "input is not gcert/0") + v, h, R = c0["v"], c0["h"], c0["R"] + ev = c0["events"] + cen = [n for n, e in enumerate(ev) if e[0] == "centre"] + need(cen == list(range(cen[0], cen[0] + len(cen))), "centres are not contiguous: no single scatter cut") + A, B, ret = [], [], [] + neg = set() # x registers currently holding MINUS their value (between the two K blocks) + openq = {} + for n, e in enumerate(ev): + k = e[0] + out = A if n < cen[0] else B + if k in ("read0", "undo", "uninj"): + continue + if k == "inj": + need(e[2] not in neg, "inj reads a negated x register") + out.append(["out", e[3], e[2], [[e[1], 1, 1]], []]) + elif k == "op": + if e[3] == -1: + out.append(["neg", e[5], e[1]]) + else: + need(e[3] == 1, "op ca") + out.append(["out", e[5], e[2], [[e[1], e[4], 1]], []]) + elif k == "centre": + ret.append([e[2], e[1], e[3]]) + elif k == "gread": + hit = set(t for t, _, _ in e[3]) + out.append(["out", e[2], e[1], [[v + t, a, b] for t, a, b in e[3]], [v + t for t in e[4] if t not in hit]]) + elif k == "rread": + out.append(["out", e[2], e[1], [[v + t, a, b] for t, a, b in e[3]], []]) + elif k == "ysh": + out.append(["out", e[4], e[2], [[e[1], e[3], 1]], []]) + elif k == "yw": + out.append(["out", e[4], e[2], [[e[1], e[3][0], e[3][1]]], []]) + elif k == "kd": + out.append(["out", e[3], e[2], [[e[1], -1 if e[2] in neg else 1, 1]], []]) + elif k == "ktr": + q = tuple(e[1]) + need(e[2] == KJ, "ktr matrix is not 1 - J/2") + x1, rest = q[0], list(q[1:]) + if q not in openq: # first block: x := M x, register x1 keeps the sign + out.append(["in", e[3], x1, [[r, 1, 1] for r in rest]]) + out.append(["out", e[3], x1, [[r, -1, 2] for r in rest], []]) + out.append(["in", e[3], x1, [[r, 1, 1] for r in rest]]) + openq[q] = n + neg.add(x1) + else: # second block: the three adds undone in reverse order + out.append(["in", e[3], x1, [[r, -1, 1] for r in rest]]) + out.append(["out", e[3], x1, [[r, 1, 2] for r in rest], []]) + out.append(["in", e[3], x1, [[r, -1, 1] for r in rest]]) + del openq[q] + neg.discard(x1) + else: + raise AssertionError("unknown event kind %r" % k) + need(not openq and not neg, "a K block is not closed") + ext = sorted([z[3], z[1]] for z in c0["gauge"] if z[5]) + c1 = dict(format="gcert/1", derived_from=c0["name"] + " (gcert/0)", p=c0["p"], h=h, v=v, R=R, cst=c0["cst"], + N=c0["N"], ports=c0["ports"], frames=c0["frames"], start=c0["start"], final=c0["final"], + ext=ext, ret=sorted(ret), scat=dict(inside=c0["scat"]["inside"], outside=c0["scat"]["outside"]), + A=A, B=B, blocks=c0["blocks"]) + return c1 + + +def scat_row(c, t): + """the scatter of target t: [(k, coefficient)], from the table or from the star rule""" + sc = c["scat"] + if "table" in sc: + return [(k, Fr(a, b)) for k, a, b in sc["table"][t]] + sin, sout = Fr(*sc["inside"]), Fr(*sc["outside"]) + return [(k, sin if c["ports"][t] >> k & 1 else sout) for k in range(c["h"])] + + +def gate_regs(g): + if g[0] == "neg": + return [g[2]], [], [] + if g[0] == "out": + return [g[2]] + [t for t, _, _ in g[3]] + list(g[4]), [(t, g[2], Fr(a, b)) for t, a, b in g[3]], g[4] + if g[0] == "in": + return [g[2]] + [s for s, _, _ in g[3]], [(g[2], s, Fr(a, b)) for s, a, b in g[3]], [] + raise AssertionError("E0: unknown gate kind %r" % (g[0],)) + + +def check1(c, scalar=True, stats=None): + need(c.get("format") == "gcert/1", "E0: format") + h, v, R = c["h"], c["v"], c["R"] + nreg = 2 * v + R + ports, fr = c["ports"], [tuple(f) for f in c["frames"]] + need(len(ports) == v == len(set(ports)) and all(par(q) and 0 < q < 1 << h for q in ports), "E0: ports") + need(fr[0] == () and fr[1] == tuple(1 << i for i in range(h - 1, -1, -1)), "E0: frames 0 and 1") + need(all(echelon_ok(f) for f in fr) and len(set(fr)) == len(fr), "E0: frame table not reduced echelon / repeats") + dim = [len(f) for f in fr] + start, final = c["start"], c["final"] + need(len(start) == len(final) == nreg, "E0: start / final") + ext = {r: f for r, f in c["ext"]} + for t in range(v): + need(fr[start[t]] == (ports[t],) and final[t] == 1, "E1: x start / final") + f = fr[final[v + t]] + need(start[v + t] == 0 and len(f) == h - 1 and all(par(u & ports[t]) == 0 for u in f), "E1: y start / final") + for r in range(2 * v, nreg): + need(start[r] == ext.get(r, 0) and final[r] == 1, "E1: slot start / final") + cls = lambda r: "x" if r < v else "y" if r < 2 * v else "s" + cur = list(start) + H = {"x": Counter(), "y": Counter(), "s": Counter(), "c": Counter()} + steps = set() + + def climb(r, f, where): + o = cur[r] + if o != f: + if (o, f) not in steps: + need(dim[o] < dim[f] and inside(fr[o], fr[f]), "E1: step not nested (%s, register %d)" % (where, r)) + steps.add((o, f)) + H[cls(r)][dim[f] - dim[o]] += 1 + cur[r] = f + okind = {("x", "s"), ("s", "s"), ("s", "y"), ("x", "y"), ("x", "x"), ("y", "y")} + ysum, piv, ytg = Counter(), set(), set() + inc = 0 + for ph, gates in (("A", c["A"]), ("B", c["B"])): + if ph == "B": # ---- E2: the scatter cut + need(sorted(k for k, _, _ in c["ret"]) == list(range(len(c["ret"]))), "E2: retained totals numbered 0..") + if "table" in c["scat"]: + need(len(c["scat"]["table"]) == v and all(0 <= k < len(c["ret"]) for row in c["scat"]["table"] for k, _, _ in row), + "E2: scatter table") + else: + need(len(c["ret"]) == h, "E2: one retained total per coordinate (star rule)") + for k, s, f in c["ret"]: + need(cls(s) == "s" and cur[s] == f, "E2: retained slot %d is not at its frame" % s) + H["c"][dim[f]] += 1 + need(all(cur[v + t] == 0 for t in range(v)), "E2: a y role left frame 0 before the scatter") + for i, g in enumerate(gates): + regs, pairs, _ = gate_regs(g) + need(all(0 <= r < nreg for r in regs) and len(set(regs)) == len(regs), "E3: registers of gate %s%d" % (ph, i)) + inc += len(regs) + for r in regs: + climb(r, g[1], "%s%d" % (ph, i)) + for t, s, co in pairs: + kd = (cls(s), cls(t)) + need(kd in okind, "E3: gate kind %s -> %s (gate %s%d)" % (kd + (ph, i))) + need(ph == "B" or kd in {("x", "s"), ("s", "s")}, "E3: bank gate before the scatter (gate A%d)" % i) + if kd == ("y", "y"): + ysum[s, t] += co + piv.add(s) + ytg.add(t) + need(ph == "B" or all(cls(r) != "y" for r in regs), "E2: y role named in phase A") + for r in range(nreg): + climb(r, final[r], "final") + need(not (piv & ytg), "E4: a pivot is the target of a gate reading y") + need(all(x == 0 for x in ysum.values()), "E4: y-reads of a (pivot, target) pair do not cancel") + Hs = {k: {str(r): n for r, n in sorted(w.items())} for k, w in H.items()} + need(Hs == c["blocks"], "E6: block histograms") + N = sum(r * n for w in H.values() for r, n in w.items()) + tails = sum(dim[f] for f in ext.values()) + need(N == c["N"] and N + tails == R * h + 2 * v * (h - 1) + c["cst"], "E6: N") + if stats is not None: + stats.update(steps=len(steps), incidences=inc, blocks=sum(sum(w.values()) for w in H.values()), + step_work=sum(dim[a] * dim[b] for a, b in steps), ysh_pairs=len(ysum)) + if scalar: + scal(c, stats) + q2(c) + return True + + +def scal(c, stats=None): + """E5: exact replay of the x-content of every register through A, scatter, B.""" + h, v, R = c["h"], c["v"], c["R"] + nreg = 2 * v + R + reg = [({r: Fr(1)} if r < v else {}) for r in range(nreg)] + den = {"x": 1, "y": 1, "s": 1} + mx = {"x": Fr(0), "y": Fr(0), "s": Fr(0)} + cls = lambda r: "x" if r < v else "y" if r < 2 * v else "s" + + def axpy(t, src, co): + d = reg[t] + for k, u in src.items(): + w = d.get(k, 0) + co * u + if w: + d[k] = w + kk = cls(t) + if w.denominator != 1: + den[kk] = lcm(den[kk], w.denominator) + if abs(w) > mx[kk]: + mx[kk] = abs(w) + else: + d.pop(k, None) + + def run(gates): + for g in gates: + if g[0] == "neg": + reg[g[2]] = {k: -u for k, u in reg[g[2]].items()} + elif g[0] == "out": + src = dict(reg[g[2]]) + for t, a, b in g[3]: + axpy(t, src, Fr(a, b)) + else: + for s, a, b in g[3]: + axpy(g[2], reg[s], Fr(a, b)) + run(c["A"]) + tot = {k: dict(reg[s]) for k, s, _ in c["ret"]} + for t in range(v): + for k, co in scat_row(c, t): + axpy(v + t, tot[k], co) + run(c["B"]) + need(all(reg[t] == {t: 1} for t in range(v)), "E5: an x role is not restored (X3)") + need(all(reg[v + t] == {t: 1} for t in range(v)), "E5: a target does not receive exactly its source (hid)") + if stats is not None: + stats.update(den=dict(den), maxabs={k: str(x) for k, x in mx.items()}, + gates_A=len(c["A"]), gates_B=len(c["B"])) + + +def q2(c): + """E7 (only for files with exterior gauges, rule (2)): for every slot q that starts off the zero frame, the + column of q in the y rows of the product is zero (its dirt is removed in line, the derived dirt gate at + frame 0 does not touch it). Replay with the gauged slots as variables, x = 0.""" + h, v, R = c["h"], c["v"], c["R"] + ext = [r for r, _ in c["ext"]] + if not ext: + return True + reg = [dict() for _ in range(2 * v + R)] + for r in ext: + reg[r] = {r: Fr(1)} + + def axpy(t, src, co): + d = reg[t] + for k, u in src.items(): + w = d.get(k, 0) + co * u + if w: + d[k] = w + else: + d.pop(k, None) + + def run(gates): + for g in gates: + if g[0] == "neg": + reg[g[2]] = {k: -u for k, u in reg[g[2]].items()} + elif g[0] == "out": + src = dict(reg[g[2]]) + for t, a, b in g[3]: + axpy(t, src, Fr(a, b)) + else: + for s, a, b in g[3]: + axpy(g[2], reg[s], Fr(a, b)) + run(c["A"]) + tot = {k: dict(reg[s]) for k, s, _ in c["ret"]} + for t in range(v): + for k, co in scat_row(c, t): + if tot[k]: + axpy(v + t, tot[k], co) + run(c["B"]) + need(all(not reg[v + t] for t in range(v)), "E7: the dirt of an exterior-gauged slot reaches a y role (Q2)") + return True diff --git a/research/complex-p10/gx/gxcore.py b/research/complex-p10/gx/gxcore.py new file mode 100644 index 0000000000..3e3f0a3076 --- /dev/null +++ b/research/complex-p10/gx/gxcore.py @@ -0,0 +1,375 @@ +"""gxcore.py: gcert/1 JSON -> normal data D, PYTHON MIRROR of the two Lean checks +(label side: E0 frames, E1 pairs, E1/E2/E6 replay in segments; scalar side: E3 kinds, E4 bracket, E5 replay +in source batches, E7), derived data (distinct climbs, cut states, block histogram) and kernel sizes. +Own code; the reference is gx.py (check1), not imported. Python 3, standard library only.""" +import json, gzip +from collections import Counter +from math import gcd + + +class Reject(Exception): + pass + + +def need(c, msg): + if not c: + raise Reject(msg) + + +def load(path): + c = json.load(gzip.open(path, "rt") if path.endswith(".gz") else open(path)) + need(c.get("format") == "gcert/1", "E0: format is not gcert/1") + return c + + +def co(num, den): + need(den > 0, "E0: denominator") + return (num < 0, abs(num), den) + + +def normal(c): + """the Lean-facing data: gates as tuples, coefficients (neg, num, den), ret by total""" + def gate(g): + if g[0] == "out": + return ("out", g[1], g[2], [(t, co(a, b)) for t, a, b in g[3]], list(g[4])) + need(g[0] == "in", "E0: unknown gate kind %r" % (g[0],)) + return ("in", g[1], g[2], [(s, co(a, b)) for s, a, b in g[3]]) + ret = sorted(c["ret"]) + need([k for k, _, _ in ret] == list(range(len(ret))), "E2: retained totals numbered 0..") + sc = c["scat"] + scat = ("table", [[(k, co(a, b)) for k, a, b in row] for row in sc["table"]]) if "table" in sc else \ + ("star", co(*sc["inside"]), co(*sc["outside"])) + return dict(h=c["h"], v=c["v"], R=c["R"], N=c["N"], cst=c["cst"], ports=list(c["ports"]), + frames=[list(f) for f in c["frames"]], start=list(c["start"]), final=list(c["final"]), + ext=[tuple(e) for e in c.get("ext", [])], ret=[(s, f) for _, s, f in ret], scat=scat, + A=[gate(g) for g in c["A"]], B=[gate(g) for g in c["B"]], + blocks={k: {int(r): n for r, n in c["blocks"][k].items()} for k in "xysc"}) + + +def regs(g): + return [g[2]] + [t for t, _ in g[3]] + (g[4] if g[0] == "out" else []) + + +def adds(g): + """single adds (tgt, src, coef) in order""" + return [(t, g[2], k) for t, k in g[3]] if g[0] == "out" else [(g[2], s, k) for s, k in g[3]] + + +def reduce(u, basis): + for b in basis: + if u >> (b.bit_length() - 1) & 1: + u ^= b + return u + + +def echelon_ok(f): + piv = [b.bit_length() - 1 for b in f] + if any(b == 0 for b in f) or any(piv[i] <= piv[i + 1] for i in range(len(piv) - 1)): + return False + return all(not (b >> p & 1) for i, b in enumerate(f) for j, p in enumerate(piv) if i != j) + + +def par(x): + return bin(x).count("1") & 1 + + +def cls(D, r): + return "x" if r < D["v"] else "y" if r < 2 * D["v"] else "s" + + +# ---- label side ------------------------------------------------------------------------------------------ +def chk_frames(D): + """E0: ports; frame table reduced echelon, no repeats, zero first, full second""" + h, v, fr = D["h"], D["v"], D["frames"] + p = D["ports"] + need(len(p) == v == len(set(p)) and all(par(q) and 0 < q < 1 << h for q in p), "E0: ports") + need(len(fr) >= 2 and fr[0] == [] and fr[1] == [1 << i for i in range(h - 1, -1, -1)], "E0: frames 0 and 1") + need(all(echelon_ok(f) and all(b < 1 << h for b in f) for f in fr), "E0: frame table not reduced echelon") + need(len(set(map(tuple, fr))) == len(fr), "E0: frame table has repeats") + return [len(f) for f in fr] + + +def derive(D): + """distinct climbs in order of first use (NOT a check: plain replay of the frame ids)""" + cur, seen, pairs = list(D["start"]), set(), [] + + def go(r, f): + o = cur[r] + if o != f: + if (o, f) not in seen: + seen.add((o, f)) + pairs.append((o, f)) + cur[r] = f + for g in D["A"] + D["B"]: + for r in regs(g): + go(r, g[1]) + for r, f in enumerate(D["final"]): + go(r, f) + return pairs + + +def chk_pairs(D, dim, pairs): + """E1, level 2: every listed pair is a nested pair of the table; returns the mask-operation count""" + fr, n, work = D["frames"], len(D["frames"]), 0 + for a, b in pairs: + need(a < n and b < n and dim[a] < dim[b], "E1: pair (%d, %d) does not climb" % (a, b)) + need(all(reduce(u, fr[b]) == 0 for u in fr[a]), "E1: pair (%d, %d) is not nested" % (a, b)) + work += dim[a] * dim[b] + return work + + +def cut_points(D, gmax, wmax=210000): + """replay segments: each phase (A, B) is cut into k pieces of equal gate count, k = the least number with at + most `gmax` gates AND at most `wmax` work per piece on average (work = sum over gates of the dimension of the + gate's frame; measured at h = 22: about 1 ms of kernel time per unit, NOTES.md). + Cut points = gate counts in A ++ B (always 0, |A| and the end).""" + nA, nB = len(D["A"]), len(D["B"]) + cuts = [0] + for off, gs in ((0, D["A"]), (nA, D["B"])): + n = len(gs) + k = max(1, -(-n // gmax), -(-sum(len(D["frames"][g[1]]) for g in gs) // wmax)) + cuts += [off + (n * i) // k for i in range(1, k + 1)] + return sorted(set(cuts)) + + +def label_data(D, dim, cuts): + """for gx-labels (gcert-interface.md LABELS v1): ordered block ranks per replay segment, the final climbs as + gates without adds (same final frame, at most 32 registers, only registers that still climb), their ranks, + the largest number of registers named by one gate. Plain replay (the mirror has accepted the file).""" + cur, G = list(D["start"]), D["A"] + D["B"] + rs, most = [], 0 + for a, b in zip(cuts, cuts[1:]): + r = [] + for g in G[a:b]: + most = max(most, len(regs(g))) + for x in regs(g): + if cur[x] != g[1]: + r.append(dim[g[1]] - dim[cur[x]]) + cur[x] = g[1] + rs.append(r) + by = {} + for x, f in enumerate(D["final"]): + if cur[x] != f: + by.setdefault(f, []).append(x) + fins, rF = [], [] + for f in sorted(by): + for i in range(0, len(by[f]), 32): + xs = by[f][i:i + 32] + fins.append(("out", f, xs[0], [], xs[1:])) + rF += [dim[f] - dim[cur[x]] for x in xs] + return dict(rs=rs, fins=fins, rF=rF, most=max(most, 32 if fins else 0)) + + +def chk_replay(D, dim, pairs, cuts): + """E1 (labels), E2 (scatter cut), E6 (price), in the segments given by `cuts`. + Returns (states at the cuts, histogram by class, visits per segment).""" + h, v, R, fr = D["h"], D["v"], D["R"], D["frames"] + n = 2 * v + R + start, final, ext = D["start"], D["final"], dict(D["ext"]) + need(len(start) == len(final) == n, "E0: start / final") + for t in range(v): + need(fr[start[t]] == [D["ports"][t]] and final[t] == 1, "E1: x start / final") + f = fr[final[v + t]] + need(start[v + t] == 0 and len(f) == h - 1 and all(par(u & D["ports"][t]) == 0 for u in f), "E1: y start / final") + for r in range(2 * v, n): + need(start[r] == ext.get(r, 0) and final[r] == 1, "E1: slot start / final") + ok = set(pairs) + need(len(ok) == len(pairs), "E1: pair list has repeats") + cur = list(start) + H = {k: Counter() for k in "xysc"} + + def climb(r, f, where): + o = cur[r] + if o != f: + need((o, f) in ok, "E1: climb (%d, %d) is not a tested pair (%s, register %d)" % (o, f, where, r)) + H[cls(D, r)][dim[f] - dim[o]] += 1 + seg[dim[f] - dim[o]] += 1 + cur[r] = f + seg, segs = Counter(), [] + G, nA = D["A"] + D["B"], len(D["A"]) + states, visits = [], [] + need(cuts[0] == 0 and cuts[-1] == len(G) and cuts == sorted(cuts), "cut points") + for a, b in zip(cuts, cuts[1:]): + states.append(list(cur)) + vs = 0 + for i in range(a, b): + if i == nA: + scatter_cut(D, cur, dim, H, seg) + g = G[i] + rs = regs(g) + need(all(0 <= r < n for r in rs) and len(set(rs)) == len(rs), "E3: registers of gate %d" % i) + need(i >= nA or all(r < v or r >= 2 * v for r in rs), "E2: y role named in phase A (gate %d)" % i) + vs += len(rs) + for r in rs: + climb(r, g[1], "gate %d" % i) + visits.append(vs) + if b < len(G): + segs.append(seg) + seg = Counter() + if nA == len(G): + scatter_cut(D, cur, dim, H, seg) + states.append(list(cur)) + for r in range(n): + climb(r, final[r], "final") + segs.append(seg) + Hb = {k: dict(sorted(w.items())) for k, w in H.items()} + need(Hb == D["blocks"], "E6: block histogram differs from `blocks`") + N = sum(r * c for w in H.values() for r, c in w.items()) + need(N == D["N"] and N + sum(dim[f] for f in ext.values()) == R * h + 2 * v * (h - 1) + D["cst"], "E6: N") + need(sum(r * c for r, c in H["c"].items()) == D["cst"], "E6: cst") + return states, Hb, visits, [[w[r] for r in range(h + 1)] for w in segs] + + +def scatter_cut(D, cur, dim, H, seg): + v = D["v"] + if D["scat"][0] == "table": + need(len(D["scat"][1]) == v and all(k < len(D["ret"]) for row in D["scat"][1] for k, _ in row), "E2: scatter table") + else: + need(len(D["ret"]) == D["h"], "E2: one retained total per coordinate (star rule)") + for s, f in D["ret"]: + need(s >= 2 * v and cur[s] == f, "E2: retained slot %d is not at its frame" % s) + H["c"][dim[f]] += 1 + seg[dim[f]] += 1 + need(all(cur[v + t] == 0 for t in range(v)), "E2: a y role left frame 0 before the scatter") + + +# ---- scalar side ----------------------------------------------------------------------------------------- +SC = 6 # all scalar entries are kept as integers in units of 1/6 +KINDS = {("x", "s"), ("s", "s"), ("s", "y"), ("x", "y"), ("x", "x"), ("y", "y")} + + +def chk_shape(D): + """E3 kinds, E4 bracket""" + ysum, piv, ytg = Counter(), set(), set() + for ph in "AB": + for i, g in enumerate(D[ph]): + for t, s, (ng, a, b) in adds(g): + kd = (cls(D, s), cls(D, t)) + need(kd in KINDS and t != s, "E3: gate kind %s -> %s (gate %s%d)" % (kd + (ph, i))) + need(ph == "B" or kd in {("x", "s"), ("s", "s")}, "E3: bank gate before the scatter (gate A%d)" % i) + if kd == ("y", "y"): + need(SC % b == 0, "E4: denominator beyond sixths") + ysum[s, t] += (-a if ng else a) * (SC // b) + piv.add(s) + ytg.add(t) + need(not (piv & ytg), "E4: a pivot is the target of a gate reading y") + need(all(x == 0 for x in ysum.values()), "E4: y-reads of a (pivot, target) pair do not cancel") + return len(ysum) + + +def scat_row(D, t): + sc = D["scat"] + if sc[0] == "table": + return sc[1][t] + return [(k, sc[1] if D["ports"][t] >> k & 1 else sc[2]) for k in range(D["h"])] + + + +def replay(D, init, count=None): + """exact replay through A, scatter, B of sparse vectors with entries in sixths; `init` = register -> {key: 6}""" + v = D["v"] + reg = [dict(init.get(r, ())) for r in range(2 * v + D["R"])] + + def axpy(t, src, k): + ng, a, b = k + d = reg[t] + for key, u in src.items(): + w = u * a + need(w % b == 0, "E5: an entry needs a denominator beyond sixths (register %d)" % t) + w = w // b + w = d.get(key, 0) + (-w if ng else w) + if count is not None: + count[key] += 1 + if w: + d[key] = w + else: + d.pop(key, None) + + def run(gates): + for g in gates: + if g[0] == "out": + src = dict(reg[g[2]]) + for t, k in g[3]: + axpy(t, src, k) + else: + for s, k in g[3]: + axpy(g[2], reg[s], k) + run(D["A"]) + afterA = sum(len(d) for d in reg) + tot = [dict(reg[s]) for s, _ in D["ret"]] + for t in range(v): + for k, cf in scat_row(D, t): + if tot[k]: + axpy(v + t, tot[k], cf) + run(D["B"]) + return reg, afterA + + +def chk_scalar(D, batches=1): + """E5 (+ E7 when `ext` is non-empty). Returns stats: denominators and largest numerators per class in the + units of the spec (x halves, y sixths, slots integers), updates per source batch, entries after A.""" + v = D["v"] + count = Counter() + reg, afterA = replay(D, {t: {t: SC} for t in range(v)}, count) + need(all(reg[t] == {t: SC} for t in range(v)), "E5: an x role is not restored (X3)") + need(all(reg[v + t] == {t: SC} for t in range(v)), "E5: a target does not receive exactly its source (hid)") + if D["ext"]: + rg, _ = replay(D, {r: {r: SC} for r, _ in D["ext"]}) + need(all(not rg[v + t] for t in range(v)), "E7: the dirt of an exterior-gauged slot reaches a y role") + step = -(-v // batches) + per = [sum(count[k] for k in range(lo, min(lo + step, v))) for lo in range(0, v, step)] + return dict(updates=sum(count.values()), per_batch=per, afterA=afterA, + batches=[(lo, min(lo + step, v)) for lo in range(0, v, step)]) + + +def digits(D): + """largest |entry| met and denominators per class, by a second replay that watches every write (slow path + kept separate from the check): returns {class: (lcm of denominators, largest |numerator| in units 1/den)}""" + v = D["v"] + den = {"x": 1, "y": 1, "s": 1} + mx = {"x": 0, "y": 0, "s": 0} + reg = [({r: SC} if r < v else {}) for r in range(2 * v + D["R"])] + + def axpy(t, src, k): + ng, a, b = k + d, kk = reg[t], cls(D, t) + for key, u in src.items(): + w = d.get(key, 0) + (-(u * a // b) if ng else u * a // b) + if w: + d[key] = w + q = SC // gcd(w, SC) + if den[kk] % q: + den[kk] = den[kk] * q // gcd(den[kk], q) + if abs(w) > mx[kk]: + mx[kk] = abs(w) + else: + d.pop(key, None) + for g in D["A"]: + for t, s, k in adds(g): + axpy(t, reg[s], k) + tot = [dict(reg[s]) for s, _ in D["ret"]] + for t in range(v): + for k, cf in scat_row(D, t): + axpy(v + t, tot[k], cf) + for g in D["B"]: + for t, s, k in adds(g): + axpy(t, reg[s], k) + return {k: (den[k], mx[k] * den[k] // SC if (mx[k] * den[k]) % SC == 0 else "%d/6" % mx[k]) for k in "xys"} + + +def mirror(D, gmax=12000, batches=1, pairs=None, cuts=None): + """both checks; returns everything the generator and the dry run need""" + dim = chk_frames(D) + pairs = derive(D) if pairs is None else pairs + work = chk_pairs(D, dim, pairs) + cuts = cut_points(D, gmax) if cuts is None else cuts + states, H, visits, segH = chk_replay(D, dim, pairs, cuts) + ysh = chk_shape(D) + S = chk_scalar(D, batches) + hist = Counter() + for k in "xysc": + for r, n in H[k].items(): + hist[r] += n + return dict(dim=dim, pairs=pairs, pair_work=work, cuts=cuts, states=states, H=H, visits=visits, ysh=ysh, + scal=S, hist=dict(sorted(hist.items())), segH=segH, + lab=label_data(D, dim, cuts)) diff --git a/research/complex-p10/layers/anneal/kernel-pairs-mw.json b/research/complex-p10/layers/anneal/kernel-pairs-mw.json new file mode 100644 index 0000000000..b41b6c69ce --- /dev/null +++ b/research/complex-p10/layers/anneal/kernel-pairs-mw.json @@ -0,0 +1 @@ +{"description":"Frozen kernel pairs of the frame flow on this layer (complex_frame_flow.py --witness --recycle-kernels).","kernel_pairs":[]} diff --git a/research/complex-p10/layers/anneal/kernel-pairs-parity.json b/research/complex-p10/layers/anneal/kernel-pairs-parity.json new file mode 100644 index 0000000000..b41b6c69ce --- /dev/null +++ b/research/complex-p10/layers/anneal/kernel-pairs-parity.json @@ -0,0 +1 @@ +{"description":"Frozen kernel pairs of the frame flow on this layer (complex_frame_flow.py --witness --recycle-kernels).","kernel_pairs":[]} diff --git a/research/complex-p10/layers/anneal/matching-arcs.json b/research/complex-p10/layers/anneal/matching-arcs.json new file mode 100644 index 0000000000..7129ad0726 --- /dev/null +++ b/research/complex-p10/layers/anneal/matching-arcs.json @@ -0,0 +1 @@ +{"description":"Frozen carrier arcs of the source-aligned word (discovery/make_layer.py step 2): deterministic HK carrier matching (PR200/233 harness, ordering reverse) on query donors plus PR162 extension; checked by compile_closure.","matching_arcs":[[5401,10970],[5402,10890],[5403,10891],[5405,10928],[5406,10860],[5407,10861],[5409,12354],[5410,12506],[5411,11515],[5412,11483],[5413,11482],[5414,12042],[5415,11832],[5416,13428],[5417,11833],[5418,11165],[5419,11164],[5420,10855],[5421,11008],[5422,12966],[5423,11535],[5424,11180],[5425,12114],[5426,12070],[5427,10998],[5430,10934],[5431,12342],[5432,12156],[5433,11437],[5434,11742],[5435,11481],[5436,13068],[5437,11007],[5438,11006],[5439,11544],[5442,13408],[5443,12960],[5444,12517],[5445,12916],[5447,12946],[5448,12246],[5450,12124],[5451,12900],[5452,12536],[5454,11434],[5455,11389],[5456,12481],[5457,13322],[5458,12009],[5459,11942],[5460,11830],[5461,13300],[5462,11594],[5464,12666],[5465,11290],[5466,11468],[5467,11516],[5469,12228],[5470,13212],[5471,11730],[5472,11646],[5473,12395],[5474,12186],[5475,11710],[5476,12768],[5477,11052],[5479,12394],[5480,11448],[5481,11503],[5483,11179],[5484,12515],[5485,12514],[5486,12104],[5487,12393],[5488,12872],[5489,12716],[5490,12626],[5491,12740],[5492,11534],[5493,12618],[5494,11688],[5495,12868],[5496,12549],[5497,12010],[5498,11924],[5499,11092],[5500,11093],[5501,11843],[5502,12312],[5503,11480],[5504,11416],[5505,10843],[5506,11545],[5509,13222],[5511,11408],[5512,11652],[5513,11653],[5514,12720],[5515,11532],[5516,12028],[5517,11936],[5518,12132],[5519,12081],[5520,11154],[5521,11155],[5522,11828],[5524,12749],[5525,11406],[5526,11240],[5527,12497],[5529,11850],[5530,11117],[5532,13282],[5534,11917],[5535,12639],[5536,12732],[5537,12998],[5538,12176],[5539,11244],[5540,12230],[5541,11252],[5542,12374],[5543,11114],[5544,11115],[5545,11139],[5546,11824],[5548,11929],[5549,11354],[5551,12429],[5552,11882],[5553,11104],[5554,12044],[5555,11886],[5556,12367],[5557,11491],[5558,12076],[5561,12984],[5562,10859],[5563,11461],[5564,11292],[5566,11874],[5568,13216],[5569,11598],[5571,12988],[5572,12422],[5574,11207],[5575,11206],[5576,11880],[5578,11776],[5581,12154],[5582,11398],[5583,11941],[5584,12350],[5585,13360],[5586,11378],[5587,12541],[5589,11610],[5590,11671],[5592,11268],[5594,12812],[5595,10856],[5596,13031],[5598,11894],[5599,12399],[5600,13004],[5601,12562],[5602,12706],[5603,12188],[5604,13170],[5605,11380],[5606,12472],[5607,11184],[5608,11616],[5610,11970],[5611,12974],[5612,12655],[5613,13102],[5614,11658],[5615,11640],[5616,11641],[5617,11245],[5618,12813],[5620,10957],[5621,12314],[5622,11734],[5623,11724],[5624,12075],[5625,12074],[5626,12088],[5627,13168],[5628,10838],[5629,12508],[5630,12107],[5631,12106],[5632,11186],[5633,12261],[5634,12702],[5636,10978],[5637,12224],[5638,11860],[5640,11980],[5641,11465],[5642,11881],[5644,12839],[5645,12693],[5646,12828],[5647,11995],[5648,12049],[5650,11722],[5651,11723],[5653,13444],[5654,11862],[5655,12026],[5656,12657],[5658,11651],[5661,12648],[5662,12936],[5663,11485],[5664,11484],[5665,12454],[5666,12417],[5667,12416],[5668,11194],[5669,11890],[5673,11931],[5674,11446],[5675,12153],[5676,11618],[5677,12232],[5679,11937],[5680,11600],[5682,13064],[5683,12598],[5684,11908],[5685,11751],[5686,13394],[5687,11958],[5688,12335],[5690,12755],[5691,11218],[5692,11312],[5693,13294],[5694,12480],[5695,11161],[5696,13104],[5697,13105],[5698,11259],[5700,13258],[5701,12181],[5702,12681],[5703,12680],[5704,12292],[5707,10959],[5709,13264],[5711,11846],[5712,11847],[5713,12283],[5716,12200],[5718,10870],[5719,11626],[5720,12800],[5721,12212],[5722,13256],[5723,13154],[5724,11948],[5726,13130],[5727,11748],[5728,12046],[5730,11632],[5731,11633],[5732,10930],[5733,11752],[5734,11872],[5735,11141],[5736,11962],[5739,10808],[5740,13058],[5741,11768],[5742,12832],[5743,11968],[5745,12012],[5746,12280],[5748,12891],[5749,12468],[5750,12345],[5751,12804],[5752,12802],[5753,12892],[5754,11147],[5755,11433],[5756,11925],[5757,10824],[5758,12484],[5759,11131],[5760,11315],[5761,11320],[5762,12016],[5763,12239],[5764,12238],[5765,12596],[5766,11034],[5767,13006],[5770,11452],[5771,12968],[5773,11105],[5774,10980],[5775,11124],[5776,12969],[5777,12464],[5780,13244],[5781,11953],[5783,13060],[5784,12475],[5787,10940],[5789,11276],[5790,11643],[5791,11802],[5792,12025],[5794,12272],[5798,12500],[5799,11094],[5800,11668],[5801,12479],[5802,11840],[5803,12590],[5804,13065],[5805,12122],[5806,10969],[5807,11352],[5808,11838],[5812,10993],[5813,11060],[5814,12125],[5817,12534],[5818,13204],[5820,12376],[5821,11861],[5822,12377],[5823,11720],[5824,11721],[5825,11630],[5826,11392],[5827,11477],[5828,12806],[5833,12030],[5834,12038],[5835,10858],[5836,12370],[5837,12972],[5839,13164],[5840,12306],[5841,12821],[5842,11372],[5843,12334],[5844,11177],[5845,11897],[5846,12538],[5847,12588],[5848,12708],[5849,13262],[5852,11866],[5853,12142],[5854,12870],[5855,12592],[5856,12262],[5858,12796],[5860,12580],[5861,11502],[5865,12661],[5866,13112],[5867,12658],[5869,11345],[5870,12450],[5871,11771],[5877,10848],[5878,11538],[5880,13270],[5881,13026],[5883,12836],[5884,12006],[5885,12494],[5886,11818]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diff --git a/research/complex-p10/layers/anneal/physical-frames.json b/research/complex-p10/layers/anneal/physical-frames.json new file mode 100644 index 0000000000..11648dd681 --- /dev/null +++ b/research/complex-p10/layers/anneal/physical-frames.json @@ -0,0 +1 @@ +{"description":"Frozen operation frames (source_aligned_local_v4.py canonical form: operations whose frame differs from the closure frame), from PR200 descent on the aligned word and the script's forward 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diff --git a/research/complex-p10/layers/anneal/physical-pairs-mw.json b/research/complex-p10/layers/anneal/physical-pairs-mw.json new file mode 100644 index 0000000000..37bb698448 --- /dev/null +++ b/research/complex-p10/layers/anneal/physical-pairs-mw.json @@ -0,0 +1 @@ +{"description":"Frozen reuse pairs [donor, recipient, deadline]: PR200/233 maximum-weight late compensated pairing (pairs_mw.py) with the last late pair moved to the phase 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diff --git a/research/complex-p10/layers/anneal/physical-pairs-parity.json b/research/complex-p10/layers/anneal/physical-pairs-parity.json new file mode 100644 index 0000000000..da5255a8a6 --- /dev/null +++ b/research/complex-p10/layers/anneal/physical-pairs-parity.json @@ -0,0 +1 @@ +{"description":"Frozen reuse pairs [donor, recipient, deadline]: PR193 recipe (source_aligned_local_v4.py --avoid-parity-erasure minimum-weight full matching), in the script's control 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diff --git a/research/complex-p10/layers/centre/kernel-pairs-mw.json b/research/complex-p10/layers/centre/kernel-pairs-mw.json new file mode 100644 index 0000000000..b41b6c69ce --- /dev/null +++ b/research/complex-p10/layers/centre/kernel-pairs-mw.json @@ -0,0 +1 @@ +{"description":"Frozen kernel pairs of the frame flow on this layer (complex_frame_flow.py --witness --recycle-kernels).","kernel_pairs":[]} diff --git a/research/complex-p10/layers/centre/kernel-pairs-parity.json b/research/complex-p10/layers/centre/kernel-pairs-parity.json new file mode 100644 index 0000000000..b41b6c69ce --- /dev/null +++ b/research/complex-p10/layers/centre/kernel-pairs-parity.json @@ -0,0 +1 @@ +{"description":"Frozen kernel pairs of the frame flow on this layer (complex_frame_flow.py --witness --recycle-kernels).","kernel_pairs":[]} diff --git a/research/complex-p10/layers/centre/matching-arcs.json b/research/complex-p10/layers/centre/matching-arcs.json new file mode 100644 index 0000000000..d54a47a0a9 --- /dev/null +++ b/research/complex-p10/layers/centre/matching-arcs.json @@ -0,0 +1 @@ +{"description":"Frozen carrier arcs of the source-aligned word (discovery/make_layer.py step 2): deterministic HK carrier matching (PR200/233 harness, ordering reverse) on query donors plus PR162 extension; checked by 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diff --git a/research/complex-p10/layers/centre/physical-frames.json b/research/complex-p10/layers/centre/physical-frames.json new file mode 100644 index 0000000000..2f91551281 --- /dev/null +++ b/research/complex-p10/layers/centre/physical-frames.json @@ -0,0 +1 @@ +{"description":"Frozen operation frames (source_aligned_local_v4.py canonical form: operations whose frame differs from the closure frame), from PR200 descent on the aligned word and the script's forward 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diff --git a/research/complex-p10/layers/centre/physical-pairs-mw.json b/research/complex-p10/layers/centre/physical-pairs-mw.json new file mode 100644 index 0000000000..d92f058a23 --- /dev/null +++ b/research/complex-p10/layers/centre/physical-pairs-mw.json @@ -0,0 +1 @@ +{"description":"Frozen reuse pairs [donor, recipient, deadline]: PR200/233 maximum-weight late compensated pairing (pairs_mw.py) with the last late pair moved to the phase 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diff --git a/research/complex-p10/layers/centre/physical-pairs-parity.json b/research/complex-p10/layers/centre/physical-pairs-parity.json new file mode 100644 index 0000000000..49604aed0d --- /dev/null +++ b/research/complex-p10/layers/centre/physical-pairs-parity.json @@ -0,0 +1 @@ +{"description":"Frozen reuse pairs [donor, recipient, deadline]: PR193 recipe (source_aligned_local_v4.py --avoid-parity-erasure minimum-weight full matching), in the script's control 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diff --git a/research/complex-p10/layers/pr168-v4-cut/kernel-pairs-mw.json b/research/complex-p10/layers/pr168-v4-cut/kernel-pairs-mw.json new file mode 100644 index 0000000000..b41b6c69ce --- /dev/null +++ b/research/complex-p10/layers/pr168-v4-cut/kernel-pairs-mw.json @@ -0,0 +1 @@ +{"description":"Frozen kernel pairs of the frame flow on this layer (complex_frame_flow.py --witness --recycle-kernels).","kernel_pairs":[]} diff --git a/research/complex-p10/layers/pr168-v4-cut/kernel-pairs-parity.json b/research/complex-p10/layers/pr168-v4-cut/kernel-pairs-parity.json new file mode 100644 index 0000000000..20277d9e6f --- /dev/null +++ b/research/complex-p10/layers/pr168-v4-cut/kernel-pairs-parity.json @@ -0,0 +1 @@ +{"description":"Frozen kernel pairs of the frame flow on this layer (complex_frame_flow.py --witness --recycle-kernels).","kernel_pairs":[[5251,0,12146,0],[5261,0,11980,0]]} diff --git a/research/complex-p10/layers/pr168-v4-cut/matching-arcs.json b/research/complex-p10/layers/pr168-v4-cut/matching-arcs.json new file mode 100644 index 0000000000..38a9ebcde5 --- /dev/null +++ b/research/complex-p10/layers/pr168-v4-cut/matching-arcs.json @@ -0,0 +1 @@ +{"description":"Frozen carrier arcs of the source-aligned word (discovery/make_layer.py step 2): deterministic HK carrier matching (PR200/233 harness, ordering reverse) on query donors plus PR162 extension; checked by 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diff --git a/research/complex-p10/layers/pr168-v4-cut/physical-frames.json b/research/complex-p10/layers/pr168-v4-cut/physical-frames.json new file mode 100644 index 0000000000..f98ecb8884 --- /dev/null +++ b/research/complex-p10/layers/pr168-v4-cut/physical-frames.json @@ -0,0 +1 @@ +{"description":"Frozen operation frames (source_aligned_local_v4.py canonical form: operations whose frame differs from the closure frame), from PR200 descent on the aligned word and the script's forward 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diff --git a/research/complex-p10/layers/pr168-v4-cut/physical-pairs-mw.json b/research/complex-p10/layers/pr168-v4-cut/physical-pairs-mw.json new file mode 100644 index 0000000000..8c549f40d8 --- /dev/null +++ b/research/complex-p10/layers/pr168-v4-cut/physical-pairs-mw.json @@ -0,0 +1 @@ +{"description":"Frozen reuse pairs [donor, recipient, deadline]: PR200/233 maximum-weight late compensated pairing (pairs_mw.py) with the last late pair moved to the phase 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diff --git a/research/complex-p10/layers/pr168-v4-cut/physical-pairs-parity.json b/research/complex-p10/layers/pr168-v4-cut/physical-pairs-parity.json new file mode 100644 index 0000000000..fad63c401e --- /dev/null +++ b/research/complex-p10/layers/pr168-v4-cut/physical-pairs-parity.json @@ -0,0 +1 @@ +{"description":"Frozen reuse pairs [donor, recipient, deadline]: PR193 recipe (source_aligned_local_v4.py --avoid-parity-erasure minimum-weight full matching), in the script's control 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diff --git a/research/complex-p10/module_cut.py b/research/complex-p10/module_cut.py new file mode 100644 index 0000000000..67ef904866 --- /dev/null +++ b/research/complex-p10/module_cut.py @@ -0,0 +1,114 @@ +#!/usr/bin/env python3 +"""module_cut.py: zero restriction of a query module to fewer points (p = 11 module files -> p = 10). + +Setting the inputs that touch the dropped points to zero turns a module for n points into a module for n - k points: +an addition with one zero operand becomes its other operand, an addition of two live operands is kept (merged with an +equal-support node if one exists), and nodes that no kept root reaches are removed. The roots of the dropped labels +are discarded. The result satisfies the smaller module's contract whenever the original satisfies its own (every +root of a kept label still sums exactly its kept disjoint inputs); the loaders of the rebuilt tree check this. +min_cut() drops the points that leave the fewest additions (ties: lexicographically first drop), the rule by which the +control modules of this package (PR #168 v4's modules cut to p = 10) were made; verify.py re-derives them byte for byte. + +Prepared by DreamingOfClouds with Anthropic Claude assistance (Apache-2.0); the cut is cp10's mkmods.py, unchanged +apart from file layout. +usage: module_cut.py KIND N_FROM K MODULE_JSON OUT_JSON (KIND tmod: N = p; pmod: N = p - 1; qmod: N = p - 2) +""" +import json +import sys +from itertools import combinations +from pathlib import Path + + +def restrict(args, inputs_image, nin, roots_old, one_based): + """generic zero restriction: inputs_image[k] = new input index or None (zero); returns (args, roots) pruned.""" + off = 1 if one_based else 0 + n_new = sum(1 for x in inputs_image if x is not None) + support = [1 << i for i in range(n_new)] + new_args = [None] * n_new + by = {s: i for i, s in enumerate(support)} + image = list(inputs_image) + for x in range(nin + off, len(args)): + a, b = args[x] + A, B = image[a - off], image[b - off] + if A is None or B is None: + image.append(A if B is None else B) + continue + assert not support[A] & support[B] + s = support[A] | support[B] + if s not in by: + by[s] = len(new_args); new_args.append([A, B]); support.append(s) + image.append(by[s]) + roots = [image[r - off] for r in roots_old] + active = set(range(n_new)); stack = list(roots) + while stack: + x = stack.pop() + if x in active: + continue + active.add(x) + if new_args[x] is not None: + stack.extend(new_args[x]) + ids = sorted(active); ren = {x: i for i, x in enumerate(ids)} + args2 = [None if new_args[x] is None else [ren[y] for y in new_args[x]] for x in ids] + return args2, [ren[x] for x in roots], support, ren, ids + + +def cut_triple(d, P, keep): + labels = list(combinations(range(P), 3)) + keep = sorted(keep); rn = {x: j for j, x in enumerate(keep)}; p2 = len(keep) + new_labels = list(combinations(range(p2), 3)); nid = {t: i for i, t in enumerate(new_labels)} + img = [nid[tuple(rn[x] for x in t)] if all(x in rn for x in t) else None for t in labels] + roots_old = [r for t, r in zip(labels, d['roots']) if all(x in rn for x in t)] + args, roots, support, ren, ids = restrict(d['args'], img, len(labels), roots_old, one_based=True) + # back to the one-based layout of triple_module_from + n = len(new_labels) + out_args = [[0, 0]] * (n + 1) + [[x + 1, y + 1] for x, y in (a for a in args[n:])] + return dict(kind='disjoint_triples', p=p2, input_labels=new_labels, target_labels=new_labels, input_count=n, + args=out_args, roots=[r + 1 for r in roots], source='cp10 zero restriction to points %s' % keep) + + +def cut_pair(d, n, keep): + pairs = list(combinations(range(n), 2)) + keep = sorted(keep); rn = {x: j for j, x in enumerate(keep)}; n2 = len(keep) + new_pairs = list(combinations(range(n2), 2)); nid = {t: i for i, t in enumerate(new_pairs)} + img = [nid[tuple(rn[x] for x in t)] if all(x in rn for x in t) else None for t in pairs] + roots_old = [r for t, r in zip(pairs, d['roots']) if all(x in rn for x in t)] + extra = d['roots'][len(pairs):] + args, roots, *_ = restrict(d['args'], img, len(pairs), roots_old + extra, one_based=False) + return dict(input_count=len(new_pairs), args=args, roots=roots, source='cp10 zero restriction to points %s' % keep) + + +def cut_q(d, n, keep): + keep = sorted(keep); rn = {x: j for j, x in enumerate(keep)} + img = [rn.get(i) for i in range(n)] + roots_old = [d['roots'][i] for i in keep] + args, roots, *_ = restrict(d['args'], img, n, roots_old, one_based=False) + return dict(input_count=len(keep), args=args, roots=roots, source='cp10 zero restriction to points %s' % keep) + + +def additions(d): + return sum(1 for a in d['args'] if a is not None and list(a) != [0, 0]) + + +CUT = dict(tmod=cut_triple, pmod=cut_pair, qmod=cut_q) + + +def min_cut(kind, d, n, k=1): + """the zero restriction to n - k points with the fewest additions (ties: lexicographically first drop)""" + cands = [] + for drop in combinations(range(n), k): + keep = [x for x in range(n) if x not in drop] + e = CUT[kind](d, n, keep) + cands.append((additions(e), drop, e)) + cands.sort(key=lambda c: (c[0], c[1])) + return cands[0] + + +def encode(d): + return (json.dumps(d, separators=(',', ':')) + '\n').encode() + + +if __name__ == '__main__': + kind, n, k, src, dst = sys.argv[1], int(sys.argv[2]), int(sys.argv[3]), Path(sys.argv[4]), Path(sys.argv[5]) + adds, drop, e = min_cut(kind, json.loads(src.read_text()), n, k) + dst.write_bytes(encode(e)) + print('%s: %d -> %d points, dropped %s, %d additions' % (kind, n, n - k, list(drop), adds)) diff --git a/research/complex-p10/modules/pmod46_pc1_p10.json b/research/complex-p10/modules/pmod46_pc1_p10.json new file mode 100644 index 0000000000..1f500511ac --- /dev/null +++ b/research/complex-p10/modules/pmod46_pc1_p10.json @@ -0,0 +1 @@ +{"input_count": 36, "args": [null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, [0, 3], [35, 36], [3, 10], [21, 38], [6, 7], [33, 34], [23, 41], [25, 35], [42, 43], [16, 17], [22, 23], [19, 46], [15, 47], [29, 34], [16, 49], [7, 14], [13, 51], [6, 52], [36, 53], [2, 39], [4, 11], [22, 56], [25, 57], [2, 9], [24, 59], [21, 60], [58, 61], [32, 33], [28, 29], [54, 64], [5, 12], [27, 66], [33, 67], [17, 32], [20, 25], [69, 70], [7, 71], [32, 70], [41, 73], [10, 65], [10, 36], [11, 12], [26, 77], [4, 5], [30, 79], [78, 80], [76, 81], [27, 82], [48, 83], [31, 35], [64, 85], [53, 86], [84, 87], [31, 33], [32, 89], [34, 90], [24, 25], [30, 46], [92, 93], [91, 94], [44, 67], [18, 23], [51, 66], [97, 98], [8, 9], 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zero restriction to points [0, 1, 2, 3, 4, 5, 7, 8, 9, 10]"} diff --git a/research/complex-p10/modules/tmod_t2_p10.json b/research/complex-p10/modules/tmod_t2_p10.json new file mode 100644 index 0000000000..7d2185c2be --- /dev/null +++ b/research/complex-p10/modules/tmod_t2_p10.json @@ -0,0 +1 @@ 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indexed by J sums input I exactly when I and J are disjoint.","source":"agent-cmod ctsa annealing of the complex compile ledger"} diff --git a/research/complex-p10/normalize_scatter.py b/research/complex-p10/normalize_scatter.py new file mode 100644 index 0000000000..4f62515895 --- /dev/null +++ b/research/complex-p10/normalize_scatter.py @@ -0,0 +1,106 @@ +#!/usr/bin/env python3 +"""normalize_scatter.py: write the scatter of a gcert/1 program as the star rule by re-signing retained totals. + +gcert_emit.py (PR #256, vendored unchanged) keeps every slot in a unit lam (wanted = lam * stored, the convention of +Sussman's gxconv.py). When the exact lift leaves a retained total k in a register whose unit lam_k is not 1, the +emitter writes the scatter as a table: row t, column k is the star coefficient (1/3 if coordinate k lies in port t, +-1/6 otherwise) times lam_k. The five-stage packages' complex code reads the star rule only. If every lam_k is +1 or +-1, flipping the sign convention of the registers with lam_k = -1 over the whole program (P -> D P D with +D = diag(+-1)) gives the same map from sources to targets with the star rule: every gate coefficient on an edge +with exactly one endpoint in a flipped register is negated, and the scatter column of a flipped total becomes the +star column. Registers, frames, gates, start and final labels, retained totals, blocks and N are unchanged; only +coefficient signs, the scatter field and the derived_from note change. A program already in star form is returned +unchanged. verify.py runs gx.check1 (and Sussman's gxcore mirror) on the result and compares it with the input. + +Prepared by DreamingOfClouds with Anthropic Claude assistance (Apache-2.0). +usage: normalize_scatter.py IN.json[.gz] OUT.json[.gz] +""" +import copy +import gzip +import json +import sys +from fractions import Fraction as Q + +if sys.flags.optimize: + raise SystemExit('Assertions must remain enabled: run without -O') +STAR = dict(inside=[1, 3], outside=[-1, 6]) + + +def star(c, t, k): + return Q(1, 3) if c['ports'][t] >> k & 1 else Q(-1, 6) + + +def units(c): + """lam_k of every retained total, read off a table scatter (None for a star scatter)""" + sc = c['scat'] + if 'table' not in sc: + assert sc == STAR, 'a star scatter must be 1/3 inside, -1/6 outside' + return None + h, v = c['h'], c['v'] + assert len(sc['table']) == v + lam = {} + for t, row in enumerate(sc['table']): + assert [k for k, _, _ in row] == list(range(h)), 'table row %d does not list the coordinates 0..h-1 in order' % t + for k, a, b in row: + q = Q(a, b) / star(c, t, k) + assert lam.setdefault(k, q) == q, 'column %d is not the star column times one unit' % k + return lam + + +def normalize(c): + lam = units(c) + if lam is None: + return c, dict(raw_scatter='star', flipped_coordinates=[], flipped_registers=[], changed_gates=0, changed_coefficients=0) + assert all(q in (1, -1) for q in lam.values()), 'units other than +-1 cannot be normalized by a sign flip: %s' % lam + v = c['v'] + ret = {k: s for k, s, _ in c['ret']} + assert sorted(ret) == list(range(c['h'])) and len(set(ret.values())) == len(ret), 'one retained total per coordinate' + flip = {ret[k] for k, q in lam.items() if q == -1} + assert all(s >= 2 * v for s in flip), 'only slots are re-signed' + c2 = copy.deepcopy(c) + gates = coefficients = 0 + for ph in ('A', 'B'): + for g in c2[ph]: + assert g[0] in ('out', 'in'), 'gate kind %r' % (g[0],) + pivot = g[2] in flip + hit = False + for term in g[3]: + if pivot != (term[0] in flip): # exactly one endpoint of this edge is re-signed + term[1] = -term[1] + coefficients += 1 + hit = True + gates += hit + c2['scat'] = dict(STAR) + c2['derived_from'] = c['derived_from'] + ' + normalize_scatter.py (registers %s re-signed; star scatter)' % sorted(flip) + return c2, dict(raw_scatter='table', flipped_coordinates=sorted(k for k, q in lam.items() if q == -1), + flipped_registers=sorted(flip), changed_gates=gates, changed_coefficients=coefficients) + + +def same_shape(a, b): + """True when two programs differ at most in coefficient signs, the scatter and derived_from""" + keys = set(a) | set(b) + for k in keys - {'A', 'B', 'scat', 'derived_from'}: + if a.get(k) != b.get(k): + return False + for ph in ('A', 'B'): + if len(a[ph]) != len(b[ph]): + return False + for g, h in zip(a[ph], b[ph]): + if g[:3] != h[:3] or g[4:] != h[4:] or len(g[3]) != len(h[3]): + return False + if any(x[0] != y[0] or x[2] != y[2] or abs(x[1]) != abs(y[1]) for x, y in zip(g[3], h[3])): + return False + return True + + +def main(): + src, dst = sys.argv[1:3] + raw = gzip.decompress(open(src, 'rb').read()) if src.endswith('.gz') else open(src, 'rb').read() + c2, report = normalize(json.loads(raw)) + data = json.dumps(c2, separators=(',', ':')).encode() + open(dst, 'wb').write(gzip.compress(data) if dst.endswith('.gz') else data) + print(json.dumps(report)) + + +if __name__ == '__main__': + main() diff --git a/research/complex-p10/paircheck.py b/research/complex-p10/paircheck.py new file mode 100644 index 0000000000..673cc0a684 --- /dev/null +++ b/research/complex-p10/paircheck.py @@ -0,0 +1,165 @@ +#!/usr/bin/env python3 +"""paircheck.py: standalone re-check of the compensated reuse pairs of a written aligned tree. + +Reads only the written word (cache/{graph,frames,selection}.json, references/paired-cube/physical/{frames,pairs}.json) +and re-verifies the pairs independently of the code that chose them and of aligned_word.py: + kinds: the donor is an ungauged, non-root role with operations; the recipient is a selected (rank h-4) gauge; + pairs are one-to-one and every selected gauge is paired (no live external gauge); + chronology: early pair (deadline None): the donor's last operation in phase 1, the recipient's first after the cut; + late pair: deadline = the recipient's first operation (phase 2), the donor's last operation strictly + before it in the executed order (phase 1, then phase 2 in index order), i.e. the donor is dead before the + recipient's old-value read; + frames: the donor's last physical frame lies inside the recipient's gauge frame; + parity: no pair is erasable by PR #184's --purify-source-donors (donor last frame of rank <= 3 inside a cube + parity 3-space inside the recipient gauge). +Five mutation controls must each be rejected for the condition they break (every violated condition is listed): +a late recipient given an unused donor still alive at its read; an unused donor with legal timing whose last frame +lies outside the gauge (frame containment alone); a duplicated pair; an unpaired gauge; an unused donor with legal +timing whose last frame is parity-erasable (erasability alone). +Prepared by DreamingOfClouds with Anthropic Claude assistance (Apache-2.0); uses the rebuilt tree's +scripts/paired_cube/frames.py only for basis/perp/containment. +usage: paircheck.py --root PR202_TREE WORD_TREE [WORD_TREE ...] (prints one JSON line per word tree)""" +import argparse +import json +import sys +from pathlib import Path + +if sys.flags.optimize: + raise SystemExit('Assertions must remain enabled: run without -O') + + +def check(tree, mutate=None): + from paired_cube.frames import basis, perp, contained + tree = Path(tree) + rd = lambda p: json.loads((tree / p).read_text()) + g, w, word = rd('cache/graph.json'), rd('cache/frames.json'), rd('cache/selection.json') + moved = rd('references/paired-cube/physical/frames.json')['frames'] + pairs = rd('references/paired-cube/physical/pairs.json')['pairs'] + h, v = g['h'], g['v'] + ops = word['ops'] + frames = [perp(tuple(w['annihilators'][x]), h) for _, _, x in ops] + for i, F in moved: + frames[i] = tuple(F) + pset = set(word['phase1']) + order = sorted(pset) + [i for i in range(len(ops)) if i not in pset] + pos = {i: k for k, i in enumerate(order)} + role_ops = {} + for i in order: + a, b, _ = ops[i] + role_ops.setdefault(a, []).append(i) + role_ops.setdefault(b, []).append(i) + gauge = {z['role']: perp(tuple(z['annihilator']), h) for z in word['selected']} + assert all(z['rank'] == h - 4 for z in word['selected']), 'non rank-(h-4) gauge kept' + roots = set(word['rootroles']) + parity = [] + for cube in range(v // 8): + for bit in range(2): + parity.append(basis(tuple(g['inputs'][8 * cube + j] for j in range(8) if j.bit_count() % 2 == bit))) + erasable_pair = lambda U, V: len(U) <= 3 and any(contained(U, S) and contained(S, V) for S in parity) + if mutate is not None: + pairs = mutate([list(p) for p in pairs], dict(frames=frames, pos=pos, role_ops=role_ops, gauge=gauge, roots=roots, + pset=pset, contained=contained, erasable=erasable_pair)) + bad = [] + donors, recips = set(), set() + late = early = erasable = 0 + for d, b, t in pairs: + if d in donors or b in recips: + bad.append(('not one-to-one', d, b)) + donors.add(d) + recips.add(b) + if d in gauge or d in roots or d not in role_ops: + bad.append(('donor kind', d)) + if b not in gauge: + bad.append(('recipient kind', b)) + continue + last, first = role_ops[d][-1], role_ops[b][0] + if t is None: + early += 1 + if not (last in pset and first not in pset): + bad.append(('early chronology', d, b)) + else: + late += 1 + if not (t == first and t not in pset and pos[last] < pos[t]): + bad.append(('late chronology', d, b, t)) + if not contained(frames[last], gauge[b]): + bad.append(('donor frame outside gauge', d, b)) + if erasable_pair(frames[last], gauge[b]): + erasable += 1 + unpaired = set(gauge) - recips + if unpaired: + bad.append(('live external gauges', len(unpaired))) + return dict(pairs=len(pairs), early=early, late=late, gauges=len(gauge), erasable=erasable, + violations=len(bad), kinds=sorted({x[0] for x in bad}), first_violations=bad[:5], + status='PASS' if not bad and not erasable else 'FAIL') + + +def controls(tree): + """five mutations; each must be rejected for the condition it breaks (all violated conditions are listed)""" + def free_donors(pairs, c): + used = {p[0] for p in pairs} + return [(d, ops[-1]) for d, ops in sorted(c['role_ops'].items()) if d not in used and d not in c['gauge'] and d not in c['roots']] + + def legal_timing(last, b, t, c): + first = c['role_ops'][b][0] + return last in c['pset'] if t is None else (t == first and c['pos'][last] < c['pos'][t]) + + def swap(pairs, c, *wants): + # replace the donor of some pair by an unused donor chosen by the first satisfiable predicate + # want(last frame, gauge, last op, recipient, deadline) + free = free_donors(pairs, c) + for want in wants: + for k, (d, b, t) in enumerate(pairs): + for d2, last in free: + if want(c['frames'][last], c['gauge'][b], last, b, t): + pairs[k] = [d2, b, t] + return pairs + raise RuntimeError('no control instance') + + def late_before_death(pairs, c): + # a late recipient gets an unused donor that is still alive at the recipient's read; a donor whose frame also + # fits the gauge is preferred (none exists on the committed words, so the frame check fires as well) + alive = lambda U, V, last, b, t: t is not None and c['pos'][last] > c['pos'][t] + return swap(pairs, c, lambda U, V, last, b, t: alive(U, V, last, b, t) and c['contained'](U, V) and not c['erasable'](U, V), + alive) + + def frame_outside(pairs, c): + # an unused donor with legal timing whose last frame is outside the recipient's gauge + return swap(pairs, c, lambda U, V, last, b, t: legal_timing(last, b, t, c) and not c['contained'](U, V)) + + def duplicate(pairs, c): + pairs.append(list(pairs[0])) + return pairs + + def drop(pairs, c): + return pairs[1:] + + def erasable(pairs, c): + # an unused donor with legal timing whose last frame (rank <= 3) lies in a cube parity 3-space inside the gauge + return swap(pairs, c, lambda U, V, last, b, t: legal_timing(last, b, t, c) and c['erasable'](U, V)) + out = {} + for name, f, intended in [('late_read_before_donor_death', late_before_death, 'late chronology'), + ('donor_frame_outside_gauge', frame_outside, 'donor frame outside gauge'), + ('duplicate_pair', duplicate, 'not one-to-one'), ('unpaired_gauge', drop, 'live external gauges'), + ('parity_erasable_donor', erasable, 'erasable')]: + try: + r = check(tree, f) + except RuntimeError as e: + out[name] = 'no instance: %s' % e + continue + found = r['kinds'] + (['erasable'] if r['erasable'] else []) + out[name] = ('REJECTED (%s)' if intended in found else 'ACCEPTED (control failed: %s)') % ', '.join(found) + return out + + +def main(): + ap = argparse.ArgumentParser(description=__doc__, formatter_class=argparse.RawDescriptionHelpFormatter) + ap.add_argument('--root', type=Path, required=True, help='the rebuilt PR #202 tree (scripts/paired_cube/frames.py)') + ap.add_argument('trees', type=Path, nargs='+') + a = ap.parse_args() + sys.path.insert(0, str(a.root / 'scripts')) + for t in a.trees: + print(json.dumps(dict(check(t), controls=controls(t))), flush=True) + + +if __name__ == '__main__': + main() diff --git a/research/complex-p10/references/centre46_graph.diff b/research/complex-p10/references/centre46_graph.diff new file mode 100644 index 0000000000..76437ab856 --- /dev/null +++ b/research/complex-p10/references/centre46_graph.diff @@ -0,0 +1,33 @@ +--- graph_orig.py 2026-10-10 03:55:31 ++++ graph.py 2026-10-10 03:55:31 +@@ -190,14 +190,18 @@ + self.local_channels() + base_nodes = len(self.a) + D = dict(zip(self.cubes, self.module(triple, [self.F[I] for I in self.cubes]))) +- P, Q = {}, {} ++ P, Q, star = {}, {}, {} + for i in range(self.p): + others = [a for a in range(self.p) if a != i] + pairs = list(combinations(others, 2)) + for bit in range(2): + inputs = [self.A[tuple(sorted((i, *K))), i, bit] for K in pairs] +- for K, node in zip(pairs, self.module(pair, inputs)): ++ outs = self.module(pair, inputs) ++ for K, node in zip(pairs, outs[:len(pairs)]): + P[tuple(sorted((i, *K))), i, bit] = node ++ if len(outs) > len(pairs): ++ # centre-sharing pair module: its extra root is the sum of all inputs = star(2i+bit) ++ star[i, bit] = outs[len(pairs)] + for i, j in combinations(range(self.p), 2): + others = [a for a in range(self.p) if a not in (i, j)] + for mode in range(2): +@@ -231,7 +235,8 @@ + # Their scatter is 1/2 sum_(i in T) S_i - 1/6 sum_i S_i. + for i in range(self.p): + for e in range(2): +- self.centers.append(self.sum(self.A[I, i, e] for I in self.cubes if i in I)) ++ self.centers.append(star[i, e] if (i, e) in star else ++ self.sum(self.A[I, i, e] for I in self.cubes if i in I)) + incidences = 0 + center_scatter = '1/2 sum_(i in T) S_i - 1/6 sum_i S_i' + else: diff --git a/research/complex-p10/references/pr233-layer/NOTICE b/research/complex-p10/references/pr233-layer/NOTICE new file mode 100644 index 0000000000..27c7d368fa --- /dev/null +++ b/research/complex-p10/references/pr233-layer/NOTICE @@ -0,0 +1,43 @@ +Prepared by Chafik Boukhalfa with substantial Anthropic Claude and OpenAI +Codex assistance. Apache-2.0. Inherited files retain their original notices +and assistance disclosures. This package claims no exclusive priority over +concurrent work and reports no new kappa. + +What this package contributes: the physical layer (operation frames and reuse +pairs) of PR #200's descent applied to the source-aligned complex word, the +admission of that layer with PR #200's checker on that word, and the +observation that PR #184's frame flow prices it at 7.0861e-4. Everything +else is retained and credited: + +- icekylinx (OpenAI GPT-6 Astra and Codex assistance): PR144 paired cubes, + signed decoder, shared-core accounting, original compiler, carrier + matching (the frozen round-nine matching reused here), chronological + gauges, PR130 generalized Clifford frames; PR184 source-assisted + construction: source-parity local factorization, frame flow with + independent dirty lifts and source controls, exact lifts, contract, + global assembly (research/source-assisted, vendored byte for byte). +- ikeboy: PR191/193/194, the rebuild of PR184's construction on the PR168 v4 + modules (research/source-assisted-v4: source_aligned_local_v4.py, + contract_v4.py, assemble.py, the parity-erasure-avoiding matching), and the + composition with PR189's/PR200's bit supplier. +- eumemic (Anthropic Claude and OpenAI Codex assistance): PR117 module + infrastructure; PR155/157 scalar modules, physical frames and reuse; + PR161 output merging; PR168 annealed modules, nested-prefix schedules, + local L1 circuit, fused outputs, bundle descent, both physical layers + (the physical layer replaced here is PR168's, used as the descent's seed), + pinned at 4a3c769e5c5430e7114c4d3e099ff34664677f17; PR131/143 frame/reuse + and late-read lineage; PR154 isolated snapshot verification. +- jamesyc / James Chang: PR124 compensated birth cuts, PR34 balanced + assembly, PR166 terminal-output accumulation. DaysSky: PR162 extended + carrier closure, PR192 frame-layout ceiling. GamingPuzzled: PR160. + gupt1156 PR148 and Abhinav Ramachandran/geckods PR158 (Hermes assistance). + jacklightChen / Zhihao Chen: PR23/29. Rohan Arun: PR100/103. an664: PR128. + Earlier lineage: Zhihao Chen PR97, Swapnil Jain, DaysSky PR150, hpst3r + PR147, SovereignSteak PR122, Aurel Prosz, dleen, Douglas Colkitt. +- Chafik Boukhalfa (Anthropic Claude and OpenAI Codex assistance): PR175 + fast checker; PR179/181/189/196/200 local circuits, operation-frame descent + (discovery/), independent complete complex admission (complex/physical.py, + verify_fused.py, vendored from PR200 at a1175449) and the PR200 bit + supplier the assembly reads; PR202 (the pinned tree, 8d8d67b). +- OpenAI: the original complex phase network of "Integer multiplication + below n log n". diff --git a/research/complex-p10/references/pr233-layer/SOURCE.json b/research/complex-p10/references/pr233-layer/SOURCE.json new file mode 100644 index 0000000000..dca4742101 --- /dev/null +++ b/research/complex-p10/references/pr233-layer/SOURCE.json @@ -0,0 +1,323 @@ +{ + "archive": "baseline-pr202.tar.gz", + "archive_sha256": 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