diff --git a/.github/workflows/extended-links.yml b/.github/workflows/extended-links.yml new file mode 100644 index 0000000000..c753829398 --- /dev/null +++ b/.github/workflows/extended-links.yml @@ -0,0 +1,36 @@ +name: extended-links + +on: + pull_request: + paths: + - 'research/extended-links/**' + - 'scripts/paired_cube/**' + - 'scripts/paired_cube_physical.py' + - 'scripts/paired_cube_network.py' + - 'references/paired-cube/**' + - 'certificates/paired-cube-*.json' + - '.github/workflows/extended-links.yml' + push: + paths: + - 'research/extended-links/**' + - '.github/workflows/extended-links.yml' + +jobs: + verify: + runs-on: ubuntu-latest + strategy: + matrix: + python-version: ['3.11', '3.14'] + steps: + - uses: actions/checkout@v4 + - uses: actions/setup-python@v5 + with: + python-version: ${{ matrix.python-version }} + - name: Verify the extended carrier matching + run: python3 research/extended-links/verify.py + - name: Regenerate the plan and compare + run: | + python3 research/extended-links/make_plan.py "$RUNNER_TEMP/plan" + cmp "$RUNNER_TEMP/plan/arcs.json" research/extended-links/data/arcs.json + cmp "$RUNNER_TEMP/plan/frames.json" research/extended-links/data/frames.json + cmp "$RUNNER_TEMP/plan/pairs.json" research/extended-links/data/pairs.json diff --git a/research/extended-links/NOTICE b/research/extended-links/NOTICE new file mode 100644 index 0000000000..8e11d761c8 --- /dev/null +++ b/research/extended-links/NOTICE @@ -0,0 +1,12 @@ +Extended carrier matching on #161's complex word +Copyright 2026 DaysSky. Licensed under the Apache License, Version 2.0. + +Prepared by DaysSky with Anthropic Claude assistance. + +This package imports and runs, unchanged, code from this repository by icekylinx (scripts/paired_cube/*, +scripts/paired_cube_network.py; PR #144, #130) and eumemic (scripts/paired_cube_physical.py and the module +sources; PR #161 and its lineage). cxlinks.compile_closure and verify.complex_profile are adapted from +scripts/paired_cube/frames.py and scripts/paired_cube_network.py. Their notices and licenses are retained. + +baseline-pr161.tar.gz contains 32 unmodified files of PR #161 at commit d14e291 (scripts, frozen data and +certificates), under their original licenses and notices; SOURCE.json pins each one. diff --git a/research/extended-links/PROOF.md b/research/extended-links/PROOF.md new file mode 100644 index 0000000000..2f4039587c --- /dev/null +++ b/research/extended-links/PROOF.md @@ -0,0 +1,69 @@ +# Extended carrier matching: argument and scope + +**Setting.** #161's complex word at p = 11: its signed DAG (searched triple module, annealed pair module, merged +face-2/edge-02 outputs), compiled by #144's `compile_graph`, gauged by #144's `select`, then given a physical +layer by `scripts/paired_cube_physical.py`. A carrier arc `x -> u` lets the control register of addition `x`, which +still holds one operand `y` of `x` after the gate, serve another use `u` of `y` instead of dying. Each arc removes +one role. + +**The pre-test.** `compile_graph` first gives every node the frame + + initial[x] = (intersection of the root frames reachable from x in the DAG) with unused coordinates removed + +and accepts `x -> u` only if `initial[x]` lies inside the receiving frame `initial[t]` (or the root frame), with +`t` later than `x` in the order `(dim initial, node)`. It then discards these frames and recomputes every frame as +the full backward intersection over DAG successors, arc successors and roots, and asserts that each value span +lies in its frame. The pre-test guarantees that this final assertion holds. It is not what the construction uses. + +**What the construction uses.** A physical frame must contain the span of the addresses in the value's support and +must lie inside every frame the register visits later. For an arc set A this is exactly: + +1. the graph with DAG edges and arc edges `x -> t` is acyclic, so the operations can be ordered with every arc + forward; +2. with `ann[x]` the span of the root annihilators reachable from `x` through DAG or arc edges, + `span(x)` is orthogonal to `ann[x]` for every node. + +`cxlinks.compile_closure` computes these frames, checks 1 and 2, orders the operations by (frame rank, +topological index), and then uses the repository's ledger formulas unchanged. Nothing else differs from +`compile_graph`: with #161's arcs and the repository's order it returns #161's certified record exactly, which +`verify.py` checks. + +**Why the added arcs are sound.** They satisfy 1 and 2 by construction, and this is checked independently, not by +the code that chose them. The repository's `scripts/paired_cube/verify.py` receives the graph, the frames, the +order, the arcs and the compiled word, and re-derives: + +- every DAG edge and every arc goes forward in the order; +- every frame equals the full backward intersection of its successors' frames (`Incomplete intersection`); +- every value span lies in its frame; +- the signed scalar word produces the exact matrix H, and K is its own inverse; +- the physical replay of all operations moves every role only upward, and its rank recount equals the ledger; +- the gauges are the forced intersections, on roles untouched by phase one, and the target chains ascend. + +That checker has no pre-test. It passes unchanged on the extended word. + +**Physical layer.** The layer follows #161's rules and is checked by #161's own +`scripts/paired_cube_physical.py`, unchanged: each moved operation frame contains its value span, every role chain +is nested with each hand-off spliced, each donor is ungauged, is not a root and dies before its recipient's read, +its last frame lies in the recipient's gauge, the target chains ascend in actual read order, the deficit +telescopes, and an exact aliased replay with arbitrary dirty scratch restores every slot and adds x to y. The +three negative controls are rejected. + +**Accounting.** #161's shared-core ledger is unchanged: three copies of the local, source and target children, +`2v` endpoint children, `W = 2v + R - pairs`, deficit `2v - 3 loss = 1320`. Each added arc lowers R by one. The +largest child stays 20. The role count enters #161's finite bridge and row reserve only through quantities that +decrease, and `verify.py` evaluates both with #161's functions. + +**Scope.** This is a finite conditional construction. Every interface #161 retains stays an assumption: the +paired source scheduling and completed-core sharing, the Clifford frame compiler, the uniform recursion and the +analytic and tape contracts. + +Not established here: + +- No optimality. The arcs are a greedy extension of #161's matching in node order, and the pairing is greedy by + first-order saving. The certified value does not depend on how either was found. +- The repository's operation order is replaced by another linear extension. The two orders give different + phase-one closures (11,302 operations here, 10,150 in #161). The gauges are selected by the repository's rule + on the new order and are checked by the repository's checker; there are 2,970 rank-18 gauges in both. +- #161's bit supplier is used as certified there and is not re-run by this package. +- #161 was closed in favour of #168 and is not on main. Its files are pinned at `d14e291` in `baseline-pr161.tar.gz`, so + this package stays valid for that commit. diff --git a/research/extended-links/README.md b/research/extended-links/README.md new file mode 100644 index 0000000000..10e5aed525 --- /dev/null +++ b/research/extended-links/README.md @@ -0,0 +1,67 @@ +# Extended carrier matching on #161's complex word + +Built on #161 (eumemic, `d14e291`). Under #161's retained interfaces this package certifies + + T(n) = O(n (log n)^(1 - kappa)), kappa = 5901881/10^10 = 5.901881e-4 + +That is +0.394% over #161 (5878747/10^10). #161 is complex-bound, so a complex-side change moves kappa directly. +Only the complex word's carrier arcs and its physical layer change. The graph, the gauges, the bit supplier, the +phase stop, the atom exponent and the assembly are #161's, unchanged. + +#161 is not on main, so the package carries the 32 files of #161 it reads as a pinned archive +(`baseline-pr161.tar.gz`, 0.3 MB), following `research/coordinated-frames-and-entrance-banks`. `baseline.py` +rebuilds them in a temporary directory after checking the archive and every file's sha256 against `SOURCE.json` +(commit `d14e291`). Set `EXTENDED_LINKS_TREE` to a full #161 checkout to use that instead. No existing file changes. + +| | carrier arcs | roles R | W per vertex | complex saving | kappa | +|---|---:|---:|---:|---:|---:| +| #161 | 6,201 | 16,011 | 15,681 | 5885669/10^10 | 5878747/10^10 | +| #161's arcs, layer rebuilt here | 6,201 | 16,011 | 15,681 | 5893384/10^10 | 5886444/10^10 | +| **this package** | **6,249** | **15,963** | **15,633** | **5908857/10^10** | **5901881/10^10** | + +## What changes + +1. **48 more carrier arcs.** `scripts/paired_cube/frames.py` accepts an arc only if the donor's coordinate-padded + maximal frame already lies inside the receiving frame. That pre-test is sufficient, not necessary. What the + construction needs, and what the repository's independent checker verifies, is weaker: the dependency graph + with the arcs is acyclic, and every value span still lies in its full backward-intersection frame. `cxlinks.py` + compiles with exactly that condition. Every arc of #161 is kept; 48 arcs that the pre-test rejects are added. +2. **The physical layer is rebuilt** for the new word with #161's own rules (frame descent, each gauged role in a + dead donor's slot, late old-value reads). The pairing here is chosen by first-order saving; on #161's own arcs + that alone is worth +0.13%. + +Further output merges (`s`, `w12`, and a pair-level merge of face 1 with edge 01) and two other all-but-one modules +were tried under this pipeline. The merges are cost-neutral and the modules are worse, so none is used. + +## Verify + + python3 research/extended-links/verify.py # stdlib only, about 15 seconds; do not use -O + +`verify.py` checks, in order: + +1. **Control.** `cxlinks.compile_closure()` with #161's arcs and the repository's operation order returns #161's + certified complex record exactly. #161's frozen physical record prices to 5885669/10^10 and 5878747/10^10. +2. **Word.** The extended arcs compile, the repository's gauge selection runs unchanged (2,970 rank-18 gauges), and + the repository's `scripts/paired_cube/verify.py` passes on the result: 1,742,400 signed scalar pairs, K, full + backward intersections, the physical replay of every frame movement, gauges and target chains. +3. **Physical layer.** The repository's `scripts/paired_cube_physical.py` passes on `data/frames.json` and + `data/pairs.json`: value spans, nested spliced role chains, pair chronology, target chains in read order, the + telescoping deficit and the exact aliased dirty-scratch replay, with its three controls rejected. +4. **Pricing.** #161's `exact_moment`, `finite_bridge` and 47-constraint assembly give the complex saving and kappa + as the largest points of the 10^-10 grid; the next points are rejected. One check of #161's code is relaxed: + the complex role count is not pinned to 16,011, it must equal `c + q - matched` and not exceed 16,011. + +`make_plan.py` regenerates the three data files byte for byte (about 20 seconds). Verification does not use it. + +[PROOF.md](PROOF.md) gives the argument and the limits. + +## Credits + +- eumemic: #161 and its lineage (#117, #131, #143, #152, #155, #157): the complex DAGs, output merging, the + physical layer and its checker, used here unchanged. +- icekylinx: #144 and #130 (paired cubes, the compiler and its independent checker, gauges, shared cores, assembly). +- an664: #128 completed-core sharing. jamesyc: #124 birth-read reuse. geckods: #153, #158 phase stop. +- Zhihao Chen and Swapnil Jain: the bit lineage behind #161's unchanged bit supplier. + +The closure-condition compile, the extended arcs and this physical layer were prepared by DaysSky, assisted with +Claude. No priority over concurrent work is claimed. diff --git a/research/extended-links/SOURCE.json b/research/extended-links/SOURCE.json new file mode 100644 index 0000000000..156fcbf100 --- /dev/null +++ b/research/extended-links/SOURCE.json @@ -0,0 +1,42 @@ +{ + "archive": "baseline-pr161.tar.gz", + "archive_sha256": "fd60f2652cc01137500f83b16393f29f3f4cbbb3a11dcba4c5ea1b5c432d2b3c", + "commit": "d14e29157bc905be1ced0776dd893d0714013f3a", + "files": { + "certificates/paired-cube-complex-input.json": "a499fe8824a8ffc212576f85e63ad3deeb8e63379c94925a4b7d0c026065146c", + "certificates/paired-cube-physical-input.json": "ec50292944fff281900961b929643da32760e1b12ff57c269724a616e230ff15", + "references/paired-cube/selected-module/SOURCE.json": "a7ea4e32112dddad4268c2a33cacbaabc6a951f32ef8d1200e3597e0eae7687c", + "references/paired-cube/selected-module/matching-arcs.json": "cbc3e1e0f332916511d775427c7f8dfa4441a8450e3f4a2ce9a30d3284bb74b3", + "references/paired-cube/sources/SOURCE.json": "93a574848569e06bc2ba0fd1be61c15c3c78415effa33bccb73ff8ceb66e2e32", + "references/paired-cube/sources/h20_g1.json.gz": "2da21138a3887b0b190b234033c08740e81e145dd0db059e8f24c45d52fa41e9", + "references/paired-cube/sources/pmod_C35_5.483127e-4.json": "55e1979722255b3b70acf0b93b3a62a1e4e603a56276b254858a5b99974f47a9", + "scripts/audit_short_guards.py": "c2c929c956e617bee739963b517b9069e0d067cfebc6820f401a4e90a1769eb1", + "scripts/certify.py": "2348d95008276c5d5764f7e028c3918e484582cd589bd4d9b82919161745e53e", + "scripts/compact_control_layer.py": "e814c9f8d84f2e5d3aa2e06c36697f27f110218addc40ff8df2801fde861ff9f", + "scripts/complex_circuit.py": "d623617f7c5cb3189580883a8ab30c0bd3832688ae3f1f0c1f881bbbbff8e0c1", + "scripts/complex_network.py": "0da395e67ac04fa213494e71012c1b19b544596d34cdce5a3b172b1fb6af5f1b", + "scripts/exclusion_circuit.py": "b253f9d7318becda1c1f3b24e2287ed44a9c27fcea00cf9d531afb950d0457a0", + "scripts/fast_gaussian.py": "11430c2df0783b933dc91080595bb7514bb052b8c7b12107e27a1ef701e31e43", + "scripts/paired_cube/__init__.py": "b5fb17c79fd41a75c0648e7a5f99076f9f42a619857d5e34e71699bf00ef0c91", + "scripts/paired_cube/frames.py": "7d897418dbfee47de0723ea4983098a982610ccba45e1bac9000a79626d8421c", + "scripts/paired_cube/gauges.py": "8a501c66e1330f054e0e11a35e9321d2deea7b51cd03ca56b6a41765e43fe061", + "scripts/paired_cube/graph.py": "c757d47997f2fa42a95c16f6e6855cf8b125216ae3335b3891e305cf1da82855", + "scripts/paired_cube/modules.py": "d64813a6a6721ebe1ad4bd3b7f807afafc86446bbe8d9cecda75cbc7ef76b9d6", + "scripts/paired_cube/verify.py": "b64f137847e4626ef70e543b1d28c1cb6c31d3e3ba4f365019a4b1c8439abf7d", + "scripts/paired_cube_network.py": "738831593efd98f200a6fd00adb12a7e1b2f46beec94c589a8970d2614f1322f", + "scripts/paired_cube_physical.py": "9c9ea1ea29e551ab6116d7c8ca09f4703ff9e2fa102032d5055327fde07ba319", + "scripts/paired_exclusion_circuit.py": "8f05f04cf06217befd6d0ee0f2d7d0c5c5eb32cfab8c9a8ca7917fd6d620b7d2", + "scripts/paired_network.py": "991223dc3c1374284c361ed017e42bf732dd971fa0bea2be2282cfb18257b3f7", + "scripts/partial_gauge_bit.py": "7d58e86061da2d73991531e9bc431589019359391adea866c61c7dd1f99ac855", + "scripts/partial_swap_network.py": "acdd81b4dea2815f8838a0c3ea8ac4968f2bc13fd7c99173473d865779096782", + "scripts/prepare_layers.py": "a6e2adc612f264b1c0e51d18ce6315de9ae5e2ae2420aa22e99a22d8bf304947", + "scripts/search_network.py": "3a4faa5037d9b8e7ca5828afac193a96b6966a8b114f14937921795b24ec4f6a", + "scripts/shared_point_circuit.py": "c9bb7a5df92d260a4e3ad532b53e26936730d7c93f7facfb0784957c1e81c8ba", + "scripts/shared_point_network.py": "a85e7f0d8c42d6a27e3846308571ca324a1824ac5c2d59e4daa5c7673c33c697", + "scripts/structured_bulk_assembly.py": "e99467e14211fba699878ed036e1e2362eb8e395dc22f9ecdcecc7fbf2cc736d", + "scripts/three_stage_cover_network.py": "7e0ad6fd1921b6905a53ce1eeaa03d3bb3a8a8bbaa0382516ea98b636f46335e" + }, + "note": "The exact files of #161 that verify.py and make_plan.py read (scripts, frozen arcs, physical layer, module sources and certificates), byte for byte from commit d14e291; reproducible with: git archive --format=tar d14e291 | gzip -n -9", + "pr": 161, + "repository": "CrocSwap/integer-mult-bounds" +} diff --git a/research/extended-links/baseline-pr161.tar.gz b/research/extended-links/baseline-pr161.tar.gz new file mode 100644 index 0000000000..c4ba28ff37 Binary files /dev/null and b/research/extended-links/baseline-pr161.tar.gz differ diff --git a/research/extended-links/baseline.py b/research/extended-links/baseline.py new file mode 100644 index 0000000000..59abc04e08 --- /dev/null +++ b/research/extended-links/baseline.py @@ -0,0 +1,52 @@ +"""The #161 files this package reads, rebuilt from a pinned archive. + +#161 (eumemic) is not on main. Its 32 files that cxlinks.py, verify.py and make_plan.py read (scripts, frozen arcs and +physical layer, module sources and certificates) are kept in baseline-pr161.tar.gz, following the convention of +research/coordinated-frames-and-entrance-banks. tree() writes them into a temporary directory after checking the +archive's sha256 and every file's sha256 against SOURCE.json, whose hashes are those of commit d14e291. Set +EXTENDED_LINKS_TREE to a full #161 checkout to use that instead. +""" +import atexit +import hashlib +import io +import json +import os +import shutil +import tarfile +import tempfile +from pathlib import Path + +HERE = Path(__file__).resolve().parent + + +def rebuild(dest): + src = json.loads((HERE / 'SOURCE.json').read_text()) + data = (HERE / src['archive']).read_bytes() + if hashlib.sha256(data).hexdigest() != src['archive_sha256']: + raise SystemExit('baseline archive differs from SOURCE.json') + with tarfile.open(fileobj=io.BytesIO(data), mode='r:gz') as archive: + members = [x for x in archive.getmembers() if x.isfile()] + if sorted(x.name for x in members) != sorted(src['files']): + raise SystemExit('baseline archive lists other files than SOURCE.json') + for x in members: + part = Path(x.name) + if part.is_absolute() or '..' in part.parts: + raise SystemExit('unsafe path in baseline archive: ' + x.name) + handle = archive.extractfile(x) + if handle is None: + raise SystemExit('unreadable member in baseline archive: ' + x.name) + body = handle.read() + if hashlib.sha256(body).hexdigest() != src['files'][x.name]: + raise SystemExit('baseline file differs from SOURCE.json: ' + x.name) + (dest / part).parent.mkdir(parents=True, exist_ok=True) + (dest / part).write_bytes(body) + return src['commit'] + + +def tree(): + if os.environ.get('EXTENDED_LINKS_TREE'): + return Path(os.environ['EXTENDED_LINKS_TREE']).resolve() + dest = Path(tempfile.mkdtemp(prefix='extended-links-pr161-')) + atexit.register(shutil.rmtree, dest, True) + rebuild(dest) + return dest.resolve() diff --git a/research/extended-links/cxlinks.py b/research/extended-links/cxlinks.py new file mode 100644 index 0000000000..b508b86ab4 --- /dev/null +++ b/research/extended-links/cxlinks.py @@ -0,0 +1,197 @@ +"""Complex word of #161 with an extended carrier matching. + +Stdlib only. The graph, the gauge selection, the independent word checker and the physical-layer checker are the +repository's own (scripts/paired_cube/*, scripts/paired_cube_physical.py); this file only replaces the *compile* step. + +scripts/paired_cube/frames.py accepts a carrier arc x -> u only when x's coordinate-padded maximal frame already lies +inside the receiving frame. That test is sufficient, not necessary. compile_closure() below accepts any arc set for +which the full backward intersection over DAG successors, arc successors and roots still contains every value span, +and whose generalized dependency graph is acyclic. Those are the conditions scripts/paired_cube/verify.py checks +independently (order, 'Incomplete intersection', span containment, replay of every frame movement). +With #161's frozen arcs and the repository's own operation order it returns #161's certified record exactly. +""" +import gzip +import hashlib +import heapq +import json +import sys +from collections import Counter +from pathlib import Path + +HERE = Path(__file__).resolve().parent +sys.path.insert(0, str(HERE)) +from baseline import tree # noqa: E402 + +ROOT = tree() # #161's pinned files (see baseline.py) +sys.path.insert(0, str(ROOT / 'scripts')) +from paired_cube.graph import Graph # noqa: E402 +from paired_cube.modules import all_but_one, restricted_triples_from, pair_module_from, merge_outputs # noqa: E402 +from paired_cube.frames import basis, perp, contained # noqa: E402 +from paired_cube.gauges import select # noqa: E402 +from paired_cube.verify import verify # noqa: E402 + +DIAGNOSTICS = ('numerical_complex_root', 'status', 'gauge_selection', 'gauge_cost_rejections', 'gauge_trial_saving') + + +def graph(): + """#161's signed paired-cube DAG, rebuilt exactly as scripts/paired_cube_producer.py does and bound to its pin.""" + src = ROOT / 'references/paired-cube/sources' + for name, digest in json.loads((src / 'SOURCE.json').read_text())['files'].items(): + assert hashlib.sha256((src / name).read_bytes()).hexdigest() == digest, name + builder = Graph(11) + g = builder.finish(restricted_triples_from(src / 'h20_g1.json.gz', [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 16]), + pair_module_from(src / 'pmod_C35_5.483127e-4.json', 10), all_but_one(9)) + g = merge_outputs(g, builder, 'w02') + g['matching_frames'] = 'coordinate' + binding = {k: g[k] for k in ('inputs', 'labels', 'args', 'signs', 'roots', 'centers')} + pin = json.loads((ROOT / 'references/paired-cube/selected-module/SOURCE.json').read_text()) + assert hashlib.sha256(json.dumps(binding, separators=(',', ':')).encode()).hexdigest() == pin['graph_sha256'] + return g + + +def compile_closure(g, arcs, repository_order=False): + """compile_graph() of scripts/paired_cube/frames.py for an arbitrary legal arc list [[donor node, use code], ...]. + + Frames are the full backward intersections (as in the repository) and the positive-rank ledger is the + repository's. The operation order is (frame rank, generalized topological index); with repository_order it is + the repository's own key (dimension of the coordinate-padded frame, node), which is a linear extension only for + arcs that pass the repository's pre-test. Raises AssertionError if the arc set is cyclic, if the order is not a + linear extension, or if a value span leaves its frame.""" + g = dict(g) + g['args'] = [None] + [None if a is None else [x + 1 for x in a] for a in g['args']] + g['roots'] = [dict(r, node=r['node'] + 1) for r in g['roots']] + h, inputs, args, roots = g['h'], g['inputs'], g['args'], g['roots'] + v, n, q = len(inputs), len(args), len(roots) + spans = [()] * n + for i, u in enumerate(inputs): spans[i + 1] = (u,) + for x in range(v + 1, n): + a, b = args[x] + assert 0 < a < x and 0 < b < x + spans[x] = basis(spans[a] + spans[b]) + rframe, rann, Y, targetH, ell = [], [], [() for _ in inputs], Counter(), 0 + for r in roots: + x = r['node'] + if r.get('kind', 'side') == 'center': + U = spans[x]; A = perp(U, h); ell += len(U) + else: + A = basis(inputs[t] for t in r['targets']); U = perp(A, h) + for t in r['targets']: + assert contained(Y[t], U), ('target retreat', t) + targetH[len(U) - len(Y[t])] += 1; Y[t] = U + assert contained(spans[x], U), ('root physical incompatibility', x) + rframe.append(U); rann.append(A) + for t in range(v): + cap = perp((inputs[t],), h) + assert contained(Y[t], cap) + targetH[h - 1 - len(Y[t])] += 1 + 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]) + arcs = dict(arcs) + def use_node(code): return None if code >> 31 else code // 2 + def use_value(code): return roots[code & 0x7fffffff]['node'] if code >> 31 else args[code // 2][code & 1] + succ, direct, indeg = [[] for _ in args], [[] for _ in args], [0] * n + for x in sorted(active): + if args[x]: + for y in args[x]: succ[y].append(x); indeg[x] += 1 + for j, r in enumerate(roots): direct[r['node']].extend(rann[j]) + assert len(set(arcs.values())) == len(arcs), 'one donor per use' + for x, code in arcs.items(): + assert args[x] and use_value(code) in args[x] and code not in (2 * x, 2 * x + 1), 'a donor carries one of its own operands' + t = use_node(code) + if t is None: direct[x].extend(rann[code & 0x7fffffff]) + else: succ[x].append(t); indeg[t] += 1 + heap = [x for x in sorted(active) if indeg[x] == 0]; heapq.heapify(heap); topo = [] + while heap: + x = heapq.heappop(heap); topo.append(x) + for y in succ[x]: + indeg[y] -= 1 + if indeg[y] == 0: heapq.heappush(heap, y) + assert len(topo) == len(active), 'the generalized dependency graph is acyclic' + ann, rank = [None] * n, [0] * n + for x in reversed(topo): + ann[x] = basis(direct[x] + [z for y in succ[x] for z in ann[y]]); rank[x] = h - len(ann[x]) + assert contained(spans[x], perp(ann[x], h)), ('value span outside its frame', x) + index = {x: i for i, x in enumerate(topo)} + if repository_order: + dag = [[] for _ in args]; constraint = [[] for _ in args]; padded = {} + for x in sorted(active): + if args[x]: + for y in args[x]: dag[y].append(x) + for j, r in enumerate(roots): constraint[r['node']].extend(rann[j]) + pre = [None] * n + for x in sorted(active, reverse=True): + pre[x] = basis(constraint[x] + [z for y in dag[x] for z in pre[y]]) + cover = g.get('side_padding_mask', 0) + for u in spans[x]: cover |= u + padded[x] = perp(pre[x] + tuple(1 << j for j in range(h) if not cover >> j & 1), h) + order = sorted(active, key=lambda x: (len(padded[x]), x)) + else: + order = sorted(active, key=lambda x: (rank[x], index[x])) + position = {x: i for i, x in enumerate(order)} + for x in order: + for y in succ[x]: assert position[y] > position[x] + uses = [[] for _ in args] + for x in order: + if args[x]: + for j, y in enumerate(args[x]): uses[y].append(2 * x + j) + for j, r in enumerate(roots): uses[r['node']].append((1 << 31) | j) + donors = [x for x in order if args[x]] + H = Counter() + for x in order: + r, degree = rank[x], len(uses[x]); assert degree > 0, ('unused input', x) + H[r] += degree - 1 + if args[x]: + H[h - r] += 1 + for y in args[x]: + assert contained(ann[x], ann[y]) + H[r - rank[y]] += 1 + else: H[1] += 1; H[r - 1] += 1 + for j, rt in enumerate(roots): + x = rt['node']; r = rank[x]; top = len(rframe[j]); assert r <= top + if rt.get('kind', 'side') == 'center': + assert r == top + H[r] += 1; H[h - r] += 1 + else: H[top - r] += 1; H[h - top] += 1 + for x, code in arcs.items(): + value, t = use_value(code), use_node(code); rv, rd = rank[value], rank[x] + top = rank[t] if t is not None else len(rframe[code & 0x7fffffff]) + assert top >= rd >= rv + H[h - rd] -= 1; H[rv] -= 1; H[top - rv] -= 1; H[top - rd] += 1 + assert min(H.values()) >= 0 + R = len(donors) + q - len(arcs) + mass = sum(r * c for r, c in H.items()); assert mass == h * R + ell, (mass, h * R + ell) + source = Counter({int(r): c for r, c in g['source_data_histogram'].items()}) + assert sum(r * c for r, c in source.items()) == v * (h - 1) + m, W = 3 * h, 2 * v + R + children = Counter({r: 3 * c for r, c in H.items() if r}) + children.update({r: 3 * c for r, c in source.items() if r}) + children.update({r: 3 * c for r, c in targetH.items() if r}) + children[2] += 2 * v + cmass = sum(r * c for r, c in children.items()); deficit = W * m - cmass + assert deficit == 2 * v - 3 * ell + profile = dict(h=h, v=v, R=R, q=q, c=len(donors), matched=len(arcs), loss=ell, selected_roles=0, + selected_rank_histogram={}, remaining_internal_histogram=[H[r] for r in range(h + 1)], + source_data_histogram=dict(source), target_data_histogram=dict(targetH), copied_centers_already=True, + m=m, W_per_vertex=W, rank_per_vertex=cmass, deficit_per_vertex=deficit, + child_histogram=dict(children), matching_frames='coordinate') + witness = dict(matching_arcs=[[x, c] for x, c in arcs.items()], annihilators=ann, order=order) + return profile, witness + + +def word(g, arcs, repository_order=False): + """(baseline, witness, record, word): compile_closure, then the repository's own gauge selection.""" + baseline, witness = compile_closure(g, arcs, repository_order) + record, w = select(g, baseline, witness) + record = json.loads(json.dumps(record)) + for key in DIAGNOSTICS: record.pop(key, None) + return baseline, witness, record, w + + +def load(name): + path = HERE / 'data' / name + with (gzip.open(path, 'rt') if path.suffix == '.gz' else open(path)) as f: + return json.load(f) diff --git a/research/extended-links/data/arcs.json b/research/extended-links/data/arcs.json new file mode 100644 index 0000000000..b80be88ddd --- /dev/null +++ b/research/extended-links/data/arcs.json @@ -0,0 +1 @@ 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diff --git a/research/extended-links/data/pairs.json b/research/extended-links/data/pairs.json new file mode 100644 index 0000000000..4a2787ed4d --- /dev/null +++ b/research/extended-links/data/pairs.json @@ -0,0 +1 @@ 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diff --git a/research/extended-links/data/physical.json b/research/extended-links/data/physical.json new file mode 100644 index 0000000000..f69d89530f --- /dev/null +++ b/research/extended-links/data/physical.json @@ -0,0 +1,86 @@ +{ + "R": 15963, + "W_per_vertex": 15633, + "changed_operation_frames": 8298, + "checks": { + "donor_frames_inside_gauges": true, + "pair_chronology": true, + "role_chains_nested": true, + "target_chains_nested_in_read_order": true, + "telescoping_deficit": true, + "value_spans_inside_frames": true + }, + "child_histogram": { + "1": 81561, + "10": 3021, + "11": 624, + "12": 1521, + "13": 2619, + "14": 1296, + "15": 3339, + "16": 2664, + "17": 1518, + "18": 7920, + "19": 3036, + "2": 53475, + "20": 6006, + "3": 21705, + "4": 11409, + "5": 14175, + "6": 4944, + "7": 4053, + "8": 4644, + "9": 2082 + }, + "deficit_per_vertex": 1320, + "h": 22, + "late_pairs": 2970, + "local_histogram": { + "1": 21907, + "10": 1007, + "11": 208, + "12": 507, + "13": 873, + "14": 432, + "15": 1113, + "16": 888, + "17": 506, + "19": 1012, + "2": 15625, + "20": 2002, + "3": 7235, + "4": 3803, + "5": 4725, + "6": 1648, + "7": 1351, + "8": 1548, + "9": 694 + }, + "loss": 440, + "m": 66, + "pairs": 2970, + "physical_R": 12993, + "physical_gauge_histogram": {}, + "rank_per_vertex": 1030458, + "scalar_replay": { + "modulus": "2^61-1", + "rejected_controls": [ + "flipped_signed_operation", + "late_read_before_donor_death", + "omitted_recipient_read" + ], + "seeds_restored_and_y_plus_x": true, + "slots": 12993 + }, + "source_data_histogram": { + "1": 1320, + "18": 1320, + "2": 1320 + }, + "target_data_histogram": { + "0": 8250, + "1": 3960, + "18": 1320 + }, + "v": 1320 +} diff --git a/research/extended-links/expected.json b/research/extended-links/expected.json new file mode 100644 index 0000000000..a87e2b9dd8 --- /dev/null +++ b/research/extended-links/expected.json @@ -0,0 +1 @@ +{"complex": "5908857/10000000000", "kappa": "5901881/10000000000", "binding": "complex"} diff --git a/research/extended-links/make_plan.py b/research/extended-links/make_plan.py new file mode 100644 index 0000000000..456d2c30d9 --- /dev/null +++ b/research/extended-links/make_plan.py @@ -0,0 +1,292 @@ +#!/usr/bin/env python3 +"""Regenerate data/{arcs,frames,pairs}.json: how the extended matching and its physical layer were found. + +Stdlib only, deterministic, about one minute. verify.py does not use this file: it checks the frozen plan with the +repository's own checkers, so the certified value does not depend on how the plan was found and no optimality is +claimed. + + arcs #161's frozen carrier arcs, then every further arc x -> u (x's control register keeps one of x's operands + and serves another use u of that operand) that keeps the generalized dependency graph acyclic and keeps + every value span inside its full backward-intersection frame. Candidates are tried once, in node order. + frames per-operation frame descent as in #131/#155: an operation's common frame may be any space between the + span of its two roles' previous frames (and its value span) and the intersection of their next frames. + The rank cost is concave in the frame dimension, so one of the two ends is always best. + pairs every gauged role takes the slot of a dead, ungauged, non-root donor whose last frame can be placed + inside the gauge (#124), with the old-value read immediately before the role's first operation (#143). + Greedy by first-order saving; a pair that would break an ascending target chain is dropped. +""" +import functools +import json +import math +import random +import sys +from collections import defaultdict +from pathlib import Path + +HERE = Path(__file__).resolve().parent +sys.path.insert(0, str(HERE)) +import cxlinks # noqa: E402 +from cxlinks import basis, perp, contained, ROOT # noqa: E402 + +H = 22 + + +@functools.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) + + +@functools.lru_cache(maxsize=None) +def ortho(A): return perp(A, H) + + +@functools.lru_cache(maxsize=None) +def meet(A, B): return A if A == B else ortho(basis(ortho(A) + ortho(B))) + + +@functools.lru_cache(maxsize=None) +def inside(A, B): return contained(A, B) + + +@functools.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 cost(r, m): return r * math.log(m / r) if r else 0.0 + + +# ------------------------------------------------------------------------------------------------ extended arcs +def extended_arcs(g, frozen): + """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 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()) + + +# ------------------------------------------------------------------------------------------------ physical layer +class Layer: + def __init__(self, g, witness, word, record): + self.h = h = g['h']; self.v = g['v']; self.R = record['R']; self.m = 3 * h + self.full = basis(1 << i for i in range(h)) + args = [None] + [None if a is None else (a[0] + 1, a[1] + 1) for a in g['args']]; inputs = g['inputs'] + roots = [dict(r, node=r['node'] + 1) for r in g['roots']] + ann = witness['annihilators']; self.ops = ops = [tuple(o) for o in word['ops']] + phase1 = sorted(word['phase1']); self.pset = pset = set(phase1) + rest = [i for i in range(len(ops)) if i not in pset] + self.position = {i: k for k, i in enumerate(phase1 + rest)} + sources = {int(x): s for x, s in word['sources'].items()} + spans = [()] * len(args) + for x in range(1, len(args)): + spans[x] = (inputs[x - 1],) if args[x] is None else basis(spans[args[x][0]] + spans[args[x][1]]) + self.spans = spans + self.default = [ortho(tuple(ann[x])) for _, _, x in ops]; self.frames = list(self.default) + self.start = [()] * self.R + for x, s in sources.items(): self.start[s] = (inputs[x - 1],) + self.gauge = {} + for z in word['selected']: + self.gauge[z['role']] = ortho(tuple(z['annihilator'])); self.start[z['role']] = self.gauge[z['role']] + self.selected = word['selected'] + self.rootframe = {} + for r, s in zip(roots, word['rootroles']): + self.rootframe[s] = spans[r['node']] if r['kind'] == 'center' else ortho(basis(inputs[t] for t in r['targets'])) + self.role_ops = defaultdict(list) + for i, (a, b, _) in enumerate(ops): self.role_ops[a].append(i); self.role_ops[b].append(i) + self.idx = {(s, i): k for s, l in self.role_ops.items() for k, i in enumerate(l)} + self.first = {s: l[0] for s, l in self.role_ops.items()}; self.last = {s: l[-1] for s, l in self.role_ops.items()} + self.pairs = []; self.donors = {} + + def set_pairs(self, pairs): self.pairs = list(pairs); self.donors = dict(pairs) + + def prev(self, s, i): + k = self.idx[s, i] + return self.frames[self.role_ops[s][k - 1]] if k else self.start[s] + + def next(self, s, i): + l = self.role_ops[s]; k = self.idx[s, i] + if k + 1 < len(l): return self.frames[l[k + 1]] + if s in self.rootframe: return self.rootframe[s] + if s in self.donors: return self.gauge[self.donors[s]] + return self.full + + def local(self, i, F): + a, b, _ = self.ops[i]; d = len(F) + return sum(cost(d - len(self.prev(s, i)), self.m) + cost(len(self.next(s, i)) - d, self.m) for s in (a, b)) + + def descend(self, seed=1, passes=10): + rng = random.Random(seed) + for _ in range(passes): + order = list(range(len(self.ops))); rng.shuffle(order); moved = 0 + for i in order: + a, b, x = self.ops[i] + low = join(join(self.prev(a, i), self.prev(b, i)), self.spans[x]); high = meet(self.next(a, i), self.next(b, i)) + cur = self.frames[i] + if low == high: + if cur != low: self.frames[i] = low; moved += 1 + continue + cl, ch = self.local(i, low), self.local(i, high) + if min(cl, ch) < self.local(i, cur) - 1e-9: self.frames[i] = low if cl < ch - 1e-9 else high; moved += 1 + if not moved: break + + def pair(self): + """Greedy pairing by first-order saving; returns (pairs, fitted last frames).""" + m = self.m; by_gauge = defaultdict(list) + for b, sigma in self.gauge.items(): by_gauge[sigma].append(b) + for sigma in by_gauge: by_gauge[sigma].sort(key=lambda b: self.position[self.first[b]]) + edges = [] + for a in range(self.R): + if a in self.gauge or a in self.rootframe or a not in self.last: continue + i = self.last[a]; aa, bb, x = self.ops[i]; other = bb if aa == a else aa + low = join(join(self.prev(a, i), self.prev(other, i)), self.spans[x]) + cap = self.next(other, i); current = self.local(i, self.frames[i]) + for sigma in by_gauge: + if len(low) > len(sigma) or not inside(low, sigma): continue + best = None + for F in (low, meet(cap, sigma)): + d = len(F) + c = (cost(d - len(self.prev(a, i)), m) + cost(len(sigma) - d, m) + + cost(d - len(self.prev(other, i)), m) + cost(len(cap) - d, m)) + if best is None or c < best[0]: best = (c, F) + saving = current + cost(3 * len(sigma), m) / 3.0 - best[0] + if saving > 1e-9: edges.append((saving, a, sigma, best[1])) + edges.sort(key=lambda e: -e[0]) + taken = set(); free = {sigma: list(bs) for sigma, bs in by_gauge.items()}; pairs = []; fit = {} + for _, a, sigma, F in edges: + if a in taken or not free[sigma]: continue + death = self.position[self.last[a]] + later = [b for b in free[sigma] if self.position[self.first[b]] > death] + if not later: continue + b = later[0]; free[sigma].remove(b); taken.add(a); pairs.append((a, b)); fit[a] = F + return pairs, fit + + def chain_safe(self, pairs): + """Drop recipients whose late read would break an ascending target chain.""" + cut = len(self.pset); pairs = list(pairs) + while True: + late = {b for _, b in pairs} + when = {z['role']: ((self.position[self.first[z['role']]] if z['role'] in late else cut), k) + for k, z in enumerate(reversed(self.selected))} + current = [self.full] * self.v; bad = set() + for z in sorted(self.selected, key=lambda z: when[z['role']]): + A = tuple(z['annihilator']) + if all(inside(A, current[t]) for t in z['targets']): + for t in z['targets']: current[t] = A + else: bad.add(z['role']) + bad &= late + if not bad: return pairs + pairs = [(a, b) for a, b in pairs if b not in bad] + + def build(self, rounds=3): + self.descend() + for _ in range(rounds): + self.set_pairs([]) + pairs, fit = self.pair(); pairs = self.chain_safe(pairs); self.set_pairs(pairs) + for a, _ in pairs: self.frames[self.last[a]] = fit[a] + self.descend() + + def export(self): + frames = [[i, list(F)] for i, F in enumerate(self.frames) if F != self.default[i]] + # scripts/paired_cube_physical.py re-reads the LAST late recipient at the phase cut as a negative control, + # so the last pair must have a donor that dies after the cut + order = sorted(self.pairs, key=lambda ab: (self.last[ab[0]] not in self.pset, self.position[self.last[ab[0]]])) + return frames, [[a, b, self.first[b]] for a, b in order] + + +def dump(path, obj): path.write_text(json.dumps(obj, separators=(',', ':')) + '\n') + + +def main(): + out = Path(sys.argv[1]) if len(sys.argv) > 1 else HERE / 'data' + out.mkdir(parents=True, exist_ok=True) + g = cxlinks.graph() + frozen = json.loads((ROOT / 'references/paired-cube/selected-module/matching-arcs.json').read_text()) + arcs = extended_arcs(g, [tuple(a) for a in frozen]) + baseline, witness, record, word = cxlinks.word(g, arcs) + layer = Layer(g, witness, word, record); layer.build() + frames, pairs = layer.export() + dump(out / 'arcs.json', arcs); dump(out / 'frames.json', dict(frames=frames)); dump(out / 'pairs.json', dict(pairs=pairs)) + print('arcs %d (frozen %d), moved operation frames %d, pairs %d -> %s' % (len(arcs), len(frozen), len(frames), len(pairs), out)) + + +if __name__ == '__main__': + main() diff --git a/research/extended-links/verify.py b/research/extended-links/verify.py new file mode 100644 index 0000000000..61b66b0a6c --- /dev/null +++ b/research/extended-links/verify.py @@ -0,0 +1,166 @@ +#!/usr/bin/env python3 +"""Verify the extended carrier matching on #161's complex word (Python stdlib only; about one minute; no -O). + + 1. Control. cxlinks.compile_closure() with #161's own frozen arcs and the repository's operation order returns + #161's certified complex record exactly, and #161's frozen physical record prices to #161's complex saving + 5885669/10^10 and kappa 5878747/10^10 with the functions used below. + 2. The frozen arcs data/arcs.json contain every arc of #161. compile_closure() accepts them (acyclic, order a + linear extension, every value span inside its full backward-intersection frame), the repository's gauge + selection runs unchanged, and the repository's independent checker scripts/paired_cube/verify.py passes on the + resulting word: signed scalar identity, K, full backward intersections, physical replay of every frame + movement, gauges and target chains. + 3. The repository's physical-layer checker scripts/paired_cube_physical.py passes on data/frames.json and + data/pairs.json: value spans, nested spliced role chains, pair chronology, target chains in read order, the + telescoping deficit and the exact aliased dirty-scratch replay with its three rejected controls. Its result + equals data/physical.json. + 4. #161's assembly (scripts/paired_cube_network.py: exact_moment, finite_bridge, the 47-constraint assembly) on + the new physical record, with #161's bit supplier, phase stop and atom exponent unchanged: the complex saving + and kappa are the largest points of the 10^-10 grid that pass, and the next points are rejected. +#161 is not on main: its files are rebuilt from the pinned archive baseline-pr161.tar.gz (baseline.py). +Usage: python3 research/extended-links/verify.py +""" +import json +import sys +import time +from collections import Counter +from fractions import Fraction as Q +from math import prod +from pathlib import Path + +if sys.flags.optimize: + raise SystemExit('Assertions must remain enabled: run without -O') + +HERE = Path(__file__).resolve().parent +sys.path.insert(0, str(HERE)) +T0 = time.time() +GRID = 10**10 + + +def log(*a): print('[%4.0fs]' % (time.time() - T0), *a, flush=True) + + +def complex_profile(pcn, row, phys, pinned): + """pcn.shared_profile(row, True) and pcn.physical_profile(phys, row), line for line, with one change: the role + count is not pinned to #161's 16011; it must equal c + q - matched and not exceed 16011 (pinned: exactly it).""" + require = pcn.require + h, v, R, ell = (row[k] for k in ('h', 'v', 'R', 'loss')) + m, W, H = 3 * h, 2 * v + R, Counter() + selected = {int(r): n for r, n in row['selected_rank_histogram'].items()} + require(sum(selected.values()) == row['selected_roles'], 'Selected gauge count') + for r, n in selected.items(): + require(0 < r < h and n > 0, 'Proper local gauges') + H[3 * r] += n + require((h, v, ell) == (22, 1320, 440) and (R == 16011 if pinned else 0 < R <= 16011), 'Paired-cube local dimensions') + require(R == row['c'] + row['q'] - row['matched'], 'Compatible carrier roles') + require(selected == {18: 2970}, 'Selected rank18 gauges') + for r, n in enumerate(row['remaining_internal_histogram']): H[r] += 3 * n + for name in ('source_data_histogram', 'target_data_histogram'): + for r, n in row[name].items(): H[int(r)] += 3 * n + H[2] += 2 * v + H = pcn.clean(H) + require(all(0 < r < m and n > 0 for r, n in H.items()), 'Proper shared-core children') + mass = sum(r * n for r, n in H.items()) + require(H == pcn.clean(row['child_histogram']), 'Saved complete child histogram') + require((m, W, mass, W * m - mass) == (row['m'], row['W_per_vertex'], row['rank_per_vertex'], row['deficit_per_vertex']), + 'Saved sharing dimensions and rank') + require(W * m - mass == 2 * v - 3 * ell, 'Shared-core telescoping deficit') + require((phys['h'], phys['v'], phys['R'], phys['loss']) == (h, v, R, ell), 'Physical word dimensions') + require(phys['physical_R'] == R - phys['pairs'] and phys['W_per_vertex'] == 2 * v + phys['physical_R'], 'Physical stock') + W, H = phys['W_per_vertex'], Counter() + for name in ('local_histogram', 'source_data_histogram', 'target_data_histogram'): + for r, n in phys[name].items(): H[int(r)] += 3 * n + for d, n in phys['physical_gauge_histogram'].items(): H[3 * int(d)] += n + H[2] += 2 * v + H = pcn.clean(H) + require(H == pcn.clean(phys['child_histogram']), 'Saved physical child histogram') + require(all(0 < r < m and n > 0 for r, n in H.items()), 'Proper shared-core children') + mass = sum(r * n for r, n in H.items()) + require((m, mass, W * m - mass) == (phys['m'], phys['rank_per_vertex'], phys['deficit_per_vertex']), 'Saved physical rank') + require(W * m - mass == 2 * v - 3 * ell, 'Shared-core telescoping deficit') + return dict(m=m, local_dimension=h, W_per_vertex=W, rank_per_vertex=mass, deficit_per_vertex=W * m - mass, + child_multiplicities=H, maxchild=max(H), edge_count=sum(H.values()), physical_roles=phys['physical_R'], + reuse_pairs=phys['pairs'], late_reads=phys['late_pairs'], moved_operation_frames=phys['changed_operation_frames']) + + +def largest(ok, lo, hi): + assert ok(lo) and not ok(hi) + while hi - lo > 1: + mid = (lo + hi) // 2 + lo, hi = (mid, hi) if ok(mid) else (lo, mid) + return lo + + +def price(pcn, row, phys, pinned): + """Largest complex saving and kappa on the 10^-10 grid, with #161's bit supplier and constants unchanged.""" + p = complex_profile(pcn, row, phys, pinned) + def moment(k): + try: return pcn.exact_moment(p, Q(k, GRID)) + except (AssertionError, ValueError): return None + k = largest(lambda k: moment(k) is not None, 5 * 10**6, 7 * 10**6) + AC = Q(k, GRID); exact = moment(k) + m = p['m']; n = m // 2 + vertices = 2**(m - 1 + (n - 1)**2) * prod(2**(2 * i) - 1 for i in range(1, n)) # as pcn.complex_certificate + phase = dict(counts=p, **exact, vertices_per_stage=vertices, N=vertices * row['v'], W=vertices * p['W_per_vertex'], + total_rank=vertices * p['rank_per_vertex'], deficit=vertices * p['deficit_per_vertex'], + group_order_bits=vertices.bit_length()) + bridge = pcn.finite_bridge(phase, None, row) + bit = min(pcn.AB, (1 - pcn.PHASE_STOP) * AC - Q(1, 10**10)) + def accepts(kk): + try: pcn.assembly(bit, AC, bridge, Q(kk, GRID), beta=pcn.PHASE_STOP) + except (AssertionError, ValueError): return False + return True + kap = largest(accepts, 0, k + 1) + res = pcn.assembly(bit, AC, bridge, Q(kap, GRID), beta=pcn.PHASE_STOP) + assert len(res['strict_constraints']) == 47 and len(res['margins']) == 7 + assert all(value > 0 for value in res['strict_constraints'].values()) + return dict(complex=AC, complex_gap=exact['strict_gap'], kappa=Q(kap, GRID), binding='complex' if bit < pcn.AB else 'bit', + bit=pcn.AB, W=p['W_per_vertex'], maxchild=p['maxchild'], absorption_gap=res['absorption_gap'], + minimum_margin=res['minimum_margin'], row_degree_gap=bridge['rows']['degree_gap']) + + +def main(): + import cxlinks + ROOT = cxlinks.ROOT + import paired_cube_network as pcn + import paired_cube_physical as physical + expected = json.loads((HERE / 'expected.json').read_text()) + + g = cxlinks.graph() + frozen = json.loads((ROOT / 'references/paired-cube/selected-module/matching-arcs.json').read_text()) + certificate = json.loads((ROOT / 'certificates/paired-cube-complex-input.json').read_text()) + _, _, record0, _ = cxlinks.word(g, frozen, repository_order=True) + assert record0 == certificate, "compile_closure differs from #161's certified record on #161's arcs" + phys0 = json.loads((ROOT / 'certificates/paired-cube-physical-input.json').read_text()) + r0 = price(pcn, certificate, phys0, pinned=True) + assert (r0['complex'], r0['kappa']) == (pcn.AC, pcn.KAPPA) == (Q(5885669, GRID), Q(5878747, GRID)), r0 + log("PASS control: #161's arcs give #161's certified record exactly; its physical record prices to " + 'complex 5885669/10^10 and kappa 5878747/10^10 (next points rejected)') + + arcs = cxlinks.load('arcs.json') + assert {tuple(a) for a in frozen} <= {tuple(a) for a in arcs}, "every arc of #161 is kept" + baseline, witness, record, word = cxlinks.word(g, arcs) + checks = cxlinks.verify(g, baseline, witness, word, record) + assert all(v is True for k, v in checks.items() if k not in ('signed_scalar_pairs_checked', 'selected_roles')) + log('PASS extended word: %d arcs (%d new), R %d; repository verify() passes (%d signed scalar pairs, %d gauges)' % ( + record['matched'], record['matched'] - len(frozen), record['R'], checks['signed_scalar_pairs_checked'], checks['selected_roles'])) + + result = physical.physical(g, witness, word, record, cxlinks.load('frames.json')['frames'], cxlinks.load('pairs.json')['pairs']) + result = json.loads(json.dumps(result)) + assert result == cxlinks.load('physical.json'), 'physical record differs from data/physical.json' + log('PASS physical layer: repository checker passes; %d moved frames, %d pairs (%d late), W %d, deficit %d, ' + 'replay restored with controls %s rejected' % (result['changed_operation_frames'], result['pairs'], result['late_pairs'], + result['W_per_vertex'], result['deficit_per_vertex'], ', '.join(result['scalar_replay']['rejected_controls']))) + + r = price(pcn, record, result, pinned=False) + got = dict(complex=str(r['complex']), kappa=str(r['kappa']), binding=r['binding']) + assert got == expected, (got, expected) + log('PASS complex saving %s = %.7e (next rejected, gap %.3e); bit supplier unchanged at %.7e' % ( + r['complex'], float(r['complex']), float(r['complex_gap']), float(r['bit']))) + log('PASS kappa %s = %.7e (next %s rejected); %s side binds; 47 constraints, 7 margins; largest child %d' % ( + r['kappa'], float(r['kappa']), r['kappa'] + Q(1, GRID), r['binding'], r['maxchild'])) + log('gain over #161: complex %+.3f%%, kappa %+.3f%%' % (100 * (float(r['complex'] / r0['complex']) - 1), + 100 * (float(r['kappa'] / r0['kappa']) - 1))) + + +if __name__ == '__main__': + main()