From 01cdc8bcac8840fa64264ed8ddfec0e9a37fd029 Mon Sep 17 00:00:00 2001 From: Sagar Thakrar <18622288+thakrarsagar@users.noreply.github.com> Date: Thu, 15 Oct 2026 17:00:06 +0530 Subject: [PATCH 1/3] research: in-place availability census of PR2443's two-cut QQ16 observations Trace the 224 observed port arrays of PR2443's F0/B_1_2 decoding contract through the pinned 19-event QQ16 recipe with exact rational linear forms on the owner/payload-constant subspace (every "not live" entry is an exact counterexample for the routed maps). At d1 (after B_1_2) the 120 F0-cut arrays need copies; at d18 (after the terminal) all 224 do, also under scalar-multiple and same-port two-field-span relaxations. Under philippeVV's unreviewed price3 convention (pinned ceiling.py) the demand of 120 / 1688 coordinate-calls per replica exceeds the C=0 break-even (111 for any saving, 71 to beat the selected ceiling). Scoped negative result; recomputation leads L1/L2 recorded; no kappa claim. Prepared by thakrarsagar with substantial AI assistance from Claude (Anthropic, Claude Opus 5.5). Co-Authored-By: Claude Opus 5.5 --- .../CENSUS-ROWS.json | 5330 +++++++++++++++++ research/qq16-cut-retention-census/PRICE.json | 96 + research/qq16-cut-retention-census/README.md | 183 + .../qq16-cut-retention-census/RESULT.json | 449 ++ .../qq16-cut-retention-census/SOURCES.json | 42 + research/qq16-cut-retention-census/TASK.json | 78 + .../qq16-cut-retention-census/VERIFY.json | 33 + research/qq16-cut-retention-census/price.py | 114 + research/qq16-cut-retention-census/verify.py | 474 ++ 9 files changed, 6799 insertions(+) create mode 100644 research/qq16-cut-retention-census/CENSUS-ROWS.json create mode 100644 research/qq16-cut-retention-census/PRICE.json create mode 100644 research/qq16-cut-retention-census/README.md create mode 100644 research/qq16-cut-retention-census/RESULT.json create mode 100644 research/qq16-cut-retention-census/SOURCES.json create mode 100644 research/qq16-cut-retention-census/TASK.json create mode 100644 research/qq16-cut-retention-census/VERIFY.json create mode 100644 research/qq16-cut-retention-census/price.py create mode 100644 research/qq16-cut-retention-census/verify.py diff --git a/research/qq16-cut-retention-census/CENSUS-ROWS.json b/research/qq16-cut-retention-census/CENSUS-ROWS.json new file mode 100644 index 0000000000..981c614f01 --- /dev/null +++ b/research/qq16-cut-retention-census/CENSUS-ROWS.json @@ -0,0 +1,5330 @@ +[ + { + "cut_event": 0, + "d1": { + "equal_live_fields": [], + "first_overwrite_event": 1, + "same_field_unchanged": false, + "same_port_two_field_span": [], + "scalar_multiple_live_fields": [], + "untouched_by_write_sets": false + }, + "d18": { + "equal_live_fields": [], + "first_overwrite_event": 1, + "same_field_unchanged": false, + "same_port_two_field_span": [], + "scalar_multiple_live_fields": [], + "untouched_by_write_sets": false + }, + "field": "X0[0,A]", + "item": "x1_A" + }, + { + "cut_event": 0, + "d1": { + "equal_live_fields": [], + "first_overwrite_event": 1, + "same_field_unchanged": false, 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null, + "same_field_unchanged": true, + "same_port_two_field_span": [ + "X0[99,U]|Y0[99,U]" + ], + "scalar_multiple_live_fields": [ + "X0[99,U]" + ], + "untouched_by_write_sets": true + }, + "d18": { + "equal_live_fields": [], + "first_overwrite_event": 2, + "same_field_unchanged": false, + "same_port_two_field_span": [], + "scalar_multiple_live_fields": [], + "untouched_by_write_sets": false + }, + "field": "X0[99,U]", + "item": "C=x2_U" + }, + { + "cut_event": 1, + "d1": { + "equal_live_fields": [ + "X0[100,U]" + ], + "first_overwrite_event": null, + "same_field_unchanged": true, + "same_port_two_field_span": [ + "X0[100,U]|Y0[100,U]" + ], + "scalar_multiple_live_fields": [ + "X0[100,U]" + ], + "untouched_by_write_sets": true + }, + "d18": { + "equal_live_fields": [], + "first_overwrite_event": 2, + "same_field_unchanged": false, + "same_port_two_field_span": [], + "scalar_multiple_live_fields": [], + "untouched_by_write_sets": false + }, + "field": "X0[100,U]", + "item": "C=x2_U" + }, + { + "cut_event": 1, + "d1": { + "equal_live_fields": [ + "X0[101,U]" + ], + "first_overwrite_event": null, + "same_field_unchanged": true, + "same_port_two_field_span": [ + "X0[101,U]|Y0[101,U]" + ], + "scalar_multiple_live_fields": [ + "X0[101,U]" + ], + "untouched_by_write_sets": true + }, + "d18": { + "equal_live_fields": [], + "first_overwrite_event": 2, + "same_field_unchanged": false, + "same_port_two_field_span": [], + "scalar_multiple_live_fields": [], + "untouched_by_write_sets": false + }, + "field": "X0[101,U]", + "item": "C=x2_U" + }, + { + "cut_event": 1, + "d1": { + "equal_live_fields": [ + "X0[102,U]" + ], + "first_overwrite_event": null, + "same_field_unchanged": true, + "same_port_two_field_span": [ + "X0[102,U]|Y0[102,U]" + ], + "scalar_multiple_live_fields": [ + "X0[102,U]" + ], + "untouched_by_write_sets": true + }, + "d18": { + "equal_live_fields": [], + "first_overwrite_event": 2, + "same_field_unchanged": false, + "same_port_two_field_span": [], + "scalar_multiple_live_fields": [], + "untouched_by_write_sets": false + }, + "field": "X0[102,U]", + "item": "C=x2_U" + }, + { + "cut_event": 1, + "d1": { + "equal_live_fields": [ + "X0[103,U]" + ], + "first_overwrite_event": null, + "same_field_unchanged": true, + "same_port_two_field_span": [ + "X0[103,U]|Y0[103,U]" + ], + "scalar_multiple_live_fields": [ + "X0[103,U]" + ], + "untouched_by_write_sets": true + }, + "d18": { + "equal_live_fields": [], + "first_overwrite_event": 2, + "same_field_unchanged": false, + "same_port_two_field_span": [], + "scalar_multiple_live_fields": [], + "untouched_by_write_sets": false + }, + "field": "X0[103,U]", + "item": "C=x2_U" + }, + { + "cut_event": 1, + "d1": { + "equal_live_fields": [ + "X0[104,U]" + ], + "first_overwrite_event": null, + "same_field_unchanged": true, + "same_port_two_field_span": [ + "X0[104,U]|Y0[104,U]" + ], + "scalar_multiple_live_fields": [ + "X0[104,U]" + ], + "untouched_by_write_sets": true + }, + "d18": { + "equal_live_fields": [], + "first_overwrite_event": 2, + "same_field_unchanged": false, + "same_port_two_field_span": [], + "scalar_multiple_live_fields": [], + "untouched_by_write_sets": false + }, + "field": "X0[104,U]", + "item": "C=x2_U" + }, + { + "cut_event": 1, + "d1": { + "equal_live_fields": [ + "X0[105,U]" + ], + "first_overwrite_event": null, + "same_field_unchanged": true, + "same_port_two_field_span": [ + "X0[105,U]|Y0[105,U]" + ], + "scalar_multiple_live_fields": [ + "X0[105,U]" + ], + "untouched_by_write_sets": true + }, + "d18": { + "equal_live_fields": [], + "first_overwrite_event": 2, + "same_field_unchanged": false, + "same_port_two_field_span": [], + "scalar_multiple_live_fields": [], + "untouched_by_write_sets": false + }, + "field": "X0[105,U]", + "item": "C=x2_U" + }, + { + "cut_event": 1, + "d1": { + "equal_live_fields": [ + "X0[106,U]" + ], + "first_overwrite_event": null, + "same_field_unchanged": true, + "same_port_two_field_span": [ + "X0[106,U]|Y0[106,U]" + ], + "scalar_multiple_live_fields": [ + "X0[106,U]" + ], + "untouched_by_write_sets": true + }, + "d18": { + "equal_live_fields": [], + "first_overwrite_event": 2, + "same_field_unchanged": false, + "same_port_two_field_span": [], + "scalar_multiple_live_fields": [], + "untouched_by_write_sets": false + }, + "field": "X0[106,U]", + "item": "C=x2_U" + }, + { + "cut_event": 1, + "d1": { + "equal_live_fields": [ + "X0[107,U]" + ], + "first_overwrite_event": null, + "same_field_unchanged": true, + "same_port_two_field_span": [ + "X0[107,U]|Y0[107,U]" + ], + "scalar_multiple_live_fields": [ + "X0[107,U]" + ], + "untouched_by_write_sets": true + }, + "d18": { + "equal_live_fields": [], + "first_overwrite_event": 2, + "same_field_unchanged": false, + "same_port_two_field_span": [], + "scalar_multiple_live_fields": [], + "untouched_by_write_sets": false + }, + "field": "X0[107,U]", + "item": "C=x2_U" + }, + { + "cut_event": 1, + "d1": { + "equal_live_fields": [ + "X0[108,U]" + ], + "first_overwrite_event": null, + "same_field_unchanged": true, + "same_port_two_field_span": [ + "X0[108,U]|Y0[108,U]" + ], + "scalar_multiple_live_fields": [ + "X0[108,U]" + ], + "untouched_by_write_sets": true + }, + "d18": { + "equal_live_fields": [], + "first_overwrite_event": 2, + "same_field_unchanged": false, + "same_port_two_field_span": [], + "scalar_multiple_live_fields": [], + "untouched_by_write_sets": false + }, + "field": "X0[108,U]", + "item": "C=x2_U" + }, + { + "cut_event": 1, + "d1": { + "equal_live_fields": [ + "X0[109,U]" + ], + "first_overwrite_event": null, + "same_field_unchanged": true, + "same_port_two_field_span": [ + "X0[109,U]|Y0[109,U]" + ], + "scalar_multiple_live_fields": [ + "X0[109,U]" + ], + "untouched_by_write_sets": true + }, + "d18": { + "equal_live_fields": [], + "first_overwrite_event": 2, + "same_field_unchanged": false, + "same_port_two_field_span": [], + "scalar_multiple_live_fields": [], + "untouched_by_write_sets": false + }, + "field": "X0[109,U]", + "item": "C=x2_U" + } +] diff --git a/research/qq16-cut-retention-census/PRICE.json b/research/qq16-cut-retention-census/PRICE.json new file mode 100644 index 0000000000..072e56f573 --- /dev/null +++ b/research/qq16-cut-retention-census/PRICE.json @@ -0,0 +1,96 @@ +{ + "break_even": { + "C0_centre": { + "max_coordinate_calls_beating_selected": 71, + "max_coordinate_calls_positive_saving": 111 + }, + "C0_family": { + "max_coordinate_calls_beating_selected": 8, + "max_coordinate_calls_positive_saving": 12 + }, + "C64_centre": { + "max_coordinate_calls_beating_selected": 0, + "max_coordinate_calls_positive_saving": 39 + }, + "C64_family": { + "max_coordinate_calls_beating_selected": 0, + "max_coordinate_calls_positive_saving": 4 + } + }, + "coordinate_calls_per_replica": { + "d1": 120, + "d18": 1688 + }, + "copied_arrays": { + "d1": 120, + "d18_B1_cut": 104, + "d18_F0_cut": 120 + }, + "rows": [ + { + "C": 0, + "ceiling": null, + "coordinate_calls": 120, + "decode": "d1", + "kind": "centre", + "vs_selected_percent": null + }, + { + "C": 0, + "ceiling": null, + "coordinate_calls": 1688, + "decode": "d18", + "kind": "centre", + "vs_selected_percent": null + }, + { + "C": 0, + "ceiling": null, + "coordinate_calls": 120, + "decode": "d1", + "kind": "family", + "vs_selected_percent": null + }, + { + "C": 0, + "ceiling": null, + "coordinate_calls": 1688, + "decode": "d18", + "kind": "family", + "vs_selected_percent": null + }, + { + "C": 64, + "ceiling": null, + "coordinate_calls": 120, + "decode": "d1", + "kind": "centre", + "vs_selected_percent": null + }, + { + "C": 64, + "ceiling": null, + "coordinate_calls": 1688, + "decode": "d18", + "kind": "centre", + "vs_selected_percent": null + }, + { + "C": 64, + "ceiling": null, + "coordinate_calls": 120, + "decode": "d1", + "kind": "family", + "vs_selected_percent": null + }, + { + "C": 64, + "ceiling": null, + "coordinate_calls": 1688, + "decode": "d18", + "kind": "family", + "vs_selected_percent": null + } + ], + "selected_ceiling": "8450271/5000000000" +} diff --git a/research/qq16-cut-retention-census/README.md b/research/qq16-cut-retention-census/README.md new file mode 100644 index 0000000000..b29a1e1d95 --- /dev/null +++ b/research/qq16-cut-retention-census/README.md @@ -0,0 +1,183 @@ +# In-place availability of PR2443's two-cut QQ16 observations + +**Negative result (scoped screen). No kappa claim, no supplier, no controller.** +[PR2443](https://github.com/CrocSwap/integer-mult-bounds/pull/2443) (starship-s, +head `545c05e17243c962b112b91e7f84b4c1a41de7b8`) decodes all pair-0 inputs of +the conserved `F0/B_1_2` pair from 224 observed port arrays at two cuts. It +grants the retention of those arrays. This package checks which of them are +still held by a live field at a decode point of the pinned 19-event QQ16 recipe. + +| item (cut) | arrays | live at d1 (after `B_1_2`) | live at d18 (after terminal) | first overwrite event | +|---|---:|---:|---:|---| +| `x1_A` (after F0) | 8 | 0 | 0 | 1 (`B_1_2`) | +| `x1_T` (after F0) | 8 | 0 | 0 | 1 (`B_1_2`) | +| `y1_A` (after F0) | 8 | 0 | 0 | 1 (`B_1_2`) | +| `y1_T` (after F0) | 8 | 0 | 0 | 1 (`B_1_2`) | +| `x1_S` (after F0) | 88 | 0 | 0 | 1 (`B_1_2`) | +| `y2_A` (after B1) | 8 | 8 (same field) | 0 | 3 (`F2`) | +| `C=x2_U` (after B1) | 96 | 96 (same field) | 0 | 2 (bridge `1->0`); 3 (`F2`) if pairs 1-3 are zero | +| **total copies needed** | 224 | **120** | **224** | | + +"Live" means equal, as a linear map of all 896 initial port arrays, to some +field of the four bank pairs at that point. The zero entries also hold under +three relaxations. The array is not a nonzero scalar multiple of any live +field. It is not in the span of the two fields `X_(k,p)`, `Y_(k,p)` at any one +port of any pair. Neither statement changes if a cover map `M(g,delta)` is +applied (see "Model" below). The counts do not change if the terminal also +exchanges selected fields, or if pairs 1-3 start at zero. + +Per owner per replica, the contract therefore needs these retained copies: + +- **d1:** 120 copies (all F0-cut arrays), each held across one call (`B_1_2`), + so 120 coordinate-calls. +- **d18:** all 224 copies. The 120 F0-cut arrays are held for 8 calls and the + 104 B1-cut arrays for 7 calls, so 1688 coordinate-calls. + +### Comparison with the #2074 pricing (inherited, unreviewed) + +philippeVV's four-bank finding (#2074, fork `680d0997`) says that with +`C = 0` the route "pays only for in-place or single-call storage". `price.py` +re-implements the `price3.py` convention (5F+4B QQ16 profile, rank-8 child +plus 8 mass per coordinate-call for centre-like storage, 72 mass per new live +family). It uses the pinned `ceiling.py`. Before transferring anything, it +reproduces three committed values of `price3.json` exactly: the selected +ceiling and the C=0 centre rows for 62 and 64 coordinates. The results are in +[PRICE.json](PRICE.json): + +| convention | max coordinate-calls/replica with any positive saving | max still beating the selected ceiling | census demand d1 / d18 | +|---|---:|---:|---| +| C=0, centre-like copy | 111 | 71 | 120 / 1688: no saving at either | +| C=0, new live family | 12 | 8 | 120 / 1688: no saving at either | +| C=64, centre-like copy | 39 | 0 | none beats selected | +| C=64, new live family | 4 | 0 | none beats selected | + +The literal PR2443 contract needs copies at both decode points. Even the +favourable d1 point, with single-call storage, needs 120 coordinate-calls. That +is above the C=0 positive-saving break-even of 111, and above 71 for beating +the selected ceiling. **Within this convention, the literal contract fails the +stated C=0 condition.** It also exceeds #2074 Theorem B's floor of 62, which +is consistent with that theorem. This screens one contract under one inherited +price convention. It is not an impossibility theorem for QQ16 controllers. + +### Recomputation leads (not in-place availability) + +Two exact identities follow from CONSERVED-QQ16 (1) and (3). The checker also +verifies both in the model. + +- **L1.** F0, B1 and F2 conserve the 16 selected pair sums `X_V+Y_V=x_V+y_V`. + Nothing writes them afterwards, so they are live two-field sums at d1 and at + d18 (identity selected terminal). PR2443's last step `y_V=x1_V+y1_V-x_V` + only needs these sums. +- **L2.** At d1, `x1_U = X2_U + Y2_U - K_(1,U) ell_(1,T) x1_T`. So the 88 + `x1_S` copies could be replaced by one same-port two-field read plus an + 8-coordinate driver record. Because `B_1_2` is invertible, a decoder that may + read the whole post-B1 state of pair 0 needs no copy at d1. PR2443 excludes + `y2_U` from its reads, so that is a different contract. + +So the census prices the literal contract, not the information need. The +compressed variant is listed below as an open question. + +## Model, exactness and scope + +- **Maps:** CONSERVED-QQ16 equations (1) and (3). The checker binds them to the + packet's `F_contract`/`B_contract` strings. Pins: `R`, `K=R^T/4`, the + A/T/U96 sets and the Grams (U:48, A:4, T:4). +- **Recipe:** the literal 19-event `GLOBAL-TEMPLATE.json.gz` recipe (archive + member sha256 `a179dad8...`). Its local pairs are `0,0,0,1,1,2,2,3,3`. +- **Bridges and terminal:** semantics follow PR2346 section 1 (alephnan, head + `653520d7`). A bridge does `X_j,U += c X_i,U; Y_i,U -= c Y_j,U`. The + terminal does `(X_U,Y_U) -> (Y_U,-X_U)`; the selected terminal is identity or + the same exchange (variant). +- **Exactness:** every field is an exact rational linear form in the 896 + initial port arrays of four pairs. The executable instance is the + owner/payload-constant subspace, where every cover map + `M(g,delta)f(d,z)=f(d*g, z XOR d*delta)` is the identity. Any actual + equality, even up to a scalar or a cover map, restricts to an equality + there. So every "not live" entry is an exact counterexample for the actual + routed maps. The only "live" entries are the post-B1 arrays at d1, where no + event intervenes. The support argument proves them, and every survival claim + is checked against the symbolic write sets. +- **Consistency check:** in this model, PR2443's ordered decoder recovers all + 224 pair-0 inputs exactly, including `C=-y_U` and the two-sided `R_J` + inverse. This was implemented independently; no predecessor code is imported. +- **Not covered:** physical idle cover sweeps, terminal Y translations, + bank padding and phase adapters. These are invertible frame changes in the + inherited logical convention. They cannot make an overwritten logical value + live again. Also not covered: native read legality, read and chart-map cost, + cleanup, hosting, precision, and other contracts or schedules. + +## Negative controls (all must be rejected or change the receipt) + +1. Claiming `x1_A` survives B1 in place is rejected. +2. Dropping F2 (event 3) changes the d18 census to 216 copies. Eight arrays + are then live in place, and 104 are scalar multiples of live fields. +3. Dropping B1 (event 1) changes the d1 census to 0 copies. +4. Claiming `C=+y_U` is rejected. +5. A corrupted centre coefficient fails the Gram/source checks. +6. A wrong sign of the future logger `E_t` breaks PR2443's decoder. + +A wrong `11a -> 12a` coefficient in the backward `Y_T` output was also tried. +It does **not** break the decoder, because PR2443 never reads `y2_T`. That +mutation was therefore not used as a control. + +## Reproduce + +From the repository root (stdlib only; about 65 s and 50 s on one core): + +```sh +python3 -I -B research/qq16-cut-retention-census/verify.py +python3 -I -B research/qq16-cut-retention-census/price.py +``` + +Expected last lines: `PASS_NEGATIVE_CONTROLS 6`, `PASS_QQ16_CUT_RETENTION_CENSUS`, +then `PASS_QQ16_CUT_RETENTION_PRICE_TRANSFER`. Each script recomputes its JSON +and requires it to equal the committed [RESULT.json](RESULT.json) (receipt +`8c57f8f5...`) and [PRICE.json](PRICE.json). Per-array rows are in +[CENSUS-ROWS.json](CENSUS-ROWS.json). Registered replay: +`python3.12 scripts/research_package.py --package research/qq16-cut-retention-census`. +The checks were run with Python 3.14.4, since 3.12 was not installed locally. + +Base commit `0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2`. Input pins are in +[SOURCES.json](SOURCES.json). External, read-only pins: PR2443 `545c05e1`, +PR2346 `653520d7`, PR2174 `f79470a7`, and philippeVV `price3.py` sha256 +`1c2ca9a4...` (fork `680d0997`). + +## Open next questions + +1. **What is the smallest retained record for a final-only (d18) decode with + PR2443's read set plus legal final reads?** + - *Why it matters:* the literal contract needs 1688 coordinate-calls, while + the C=0 break-even is 71. A compressed record set must also respect + #2074 Theorem B's floor of 62. + - *First step:* replace `x1_S` by the driver record (L2) and the selected + records by the conserved sums (L1), then rerun this census. + - *Blocker:* the legal native read types for former-Y endpoints and + `X+Y` sums. +2. **Can a controller use the d1 decode point at all?** + - *Why it matters:* the demand there is only 120, and with full post-B1 + reads it is 0, since `B_1_2` is invertible. But a mid-schedule decode + must restore what it reads before F2. + - *First step:* price the CONSERVED-QQ16 inverse of B (`H_s`, `E_t`) as + reads plus restoration. + - *Blocker:* no priced read of `y2_U`/`X2_T` at the completed-X type. +3. **Which centre charge applies to QQ16, C=0 or C=64?** This is the + maintainers' open question in #2074. Under C=64 no positive retention + budget beats the selected ceiling. + +## Credit + +The observation contract and decoder are from PR2443 (starship-s). The local +maps, packet and cover semantics are from Ali Romman (PR1969, +`research/joint-query`). The bridge/terminal semantics and the 19-event +binding are from alephnan (PR2346). The two-query recovery contract is from +commdata2338 (PR2174; also PR2153, PR2376). The unread basis and 88-port +threshold are from Gareth Davidson / bitplane (PR2432). The C=64 screen and +the `y2_A` pricing are from 1337isnot1337 (PR2079, PR2197). Theorem B and the +price3 convention are from Philippe Van Velzen (#2074, fork `680d0997`). The +trace method is from Ross Richardson (PR2104). The ceiling model is +`research/complex-local-word-ceiling`. ywz65's concurrent PR2443 operator +audit is independent of this storage census. + +Prepared by thakrarsagar with substantial AI assistance from Claude +(Anthropic, Claude Opus 5.5). No independent human review is claimed. +Apache-2.0. diff --git a/research/qq16-cut-retention-census/RESULT.json b/research/qq16-cut-retention-census/RESULT.json new file mode 100644 index 0000000000..4f70b407cb --- /dev/null +++ b/research/qq16-cut-retention-census/RESULT.json @@ -0,0 +1,449 @@ +{ + "census_rows_sha256": "b30aa354b7991ab633c15e316ce641f1fb6bc96cb18c656a6cc46d312d2460b9", + "decode_points": { + "d1": "after event 1 (B_1_2)", + "d18": "after event 18 (terminal)" + }, + "leads": { + "L1_selected_pair_sums_live_at_d1_and_d18": 16, + "L2_x1_U_from_live_pair_plus_driver_record": 96 + }, + "model": "owner/payload-constant subspace (all D_s = I); exact rational linear forms in the 896 initial port arrays of four pairs; bridges and ordinary terminal per PR2346 section 1", + "negative_controls": { + "claim_C_equals_plus_y_U": "rejected", + "claim_x1_A_survives_B1": "rejected", + "corrupted_centre_coefficient": "rejected", + "drop_B1_event1": { + "changed": true, + "d1_totals": { + "copy_required": 0, + "equal_some_live_field": 224, + "in_place_same_field": 224, + "in_same_port_two_field_span": 224, + "scalar_multiple_of_live_field": 224 + } + }, + "drop_F2_event3": { + "changed": true, + "d18_totals": { + "copy_required": 216, + "equal_some_live_field": 8, + "in_place_same_field": 8, + "in_same_port_two_field_span": 104, + "scalar_multiple_of_live_field": 104 + } + }, + "wrong_E_t_sign_breaks_decoder": "rejected" + }, + "per_item": { + "C=x2_U": { + "arrays": 96, + "d1": { + "copy_required": 0, + "equal_some_live_field": 96, + "first_overwrite_events": [], + "in_place_same_field": 96, + "in_same_port_two_field_span": 96, + "scalar_multiple_of_live_field": 96 + }, + "d18": { + "copy_required": 96, + "equal_some_live_field": 0, + "first_overwrite_events": [ + 2 + ], + "in_place_same_field": 0, + "in_same_port_two_field_span": 0, + "scalar_multiple_of_live_field": 0 + } + }, + "x1_A": { + "arrays": 8, + "d1": { + "copy_required": 8, + "equal_some_live_field": 0, + "first_overwrite_events": [ + 1 + ], + "in_place_same_field": 0, + "in_same_port_two_field_span": 0, + "scalar_multiple_of_live_field": 0 + }, + "d18": { + "copy_required": 8, + "equal_some_live_field": 0, + "first_overwrite_events": [ + 1 + ], + "in_place_same_field": 0, + "in_same_port_two_field_span": 0, + "scalar_multiple_of_live_field": 0 + } + }, + "x1_S": { + "arrays": 88, + "d1": { + "copy_required": 88, + "equal_some_live_field": 0, + "first_overwrite_events": [ + 1 + ], + "in_place_same_field": 0, + "in_same_port_two_field_span": 0, + "scalar_multiple_of_live_field": 0 + }, + "d18": { + "copy_required": 88, + "equal_some_live_field": 0, + "first_overwrite_events": [ + 1 + ], + "in_place_same_field": 0, + "in_same_port_two_field_span": 0, + "scalar_multiple_of_live_field": 0 + } + }, + "x1_T": { + "arrays": 8, + "d1": { + "copy_required": 8, + "equal_some_live_field": 0, + "first_overwrite_events": [ + 1 + ], + "in_place_same_field": 0, + "in_same_port_two_field_span": 0, + "scalar_multiple_of_live_field": 0 + }, + "d18": { + "copy_required": 8, + "equal_some_live_field": 0, + "first_overwrite_events": [ + 1 + ], + "in_place_same_field": 0, + "in_same_port_two_field_span": 0, + "scalar_multiple_of_live_field": 0 + } + }, + "y1_A": { + "arrays": 8, + "d1": { + "copy_required": 8, + "equal_some_live_field": 0, + "first_overwrite_events": [ + 1 + ], + "in_place_same_field": 0, + "in_same_port_two_field_span": 0, + "scalar_multiple_of_live_field": 0 + }, + "d18": { + "copy_required": 8, + "equal_some_live_field": 0, + "first_overwrite_events": [ + 1 + ], + "in_place_same_field": 0, + "in_same_port_two_field_span": 0, + "scalar_multiple_of_live_field": 0 + } + }, + "y1_T": { + "arrays": 8, + "d1": { + "copy_required": 8, + "equal_some_live_field": 0, + "first_overwrite_events": [ + 1 + ], + "in_place_same_field": 0, + "in_same_port_two_field_span": 0, + "scalar_multiple_of_live_field": 0 + }, + "d18": { + "copy_required": 8, + "equal_some_live_field": 0, + "first_overwrite_events": [ + 1 + ], + "in_place_same_field": 0, + "in_same_port_two_field_span": 0, + "scalar_multiple_of_live_field": 0 + } + }, + "y2_A": { + "arrays": 8, + "d1": { + "copy_required": 0, + "equal_some_live_field": 8, + "first_overwrite_events": [], + "in_place_same_field": 8, + "in_same_port_two_field_span": 8, + "scalar_multiple_of_live_field": 8 + }, + "d18": { + "copy_required": 8, + "equal_some_live_field": 0, + "first_overwrite_events": [ + 3 + ], + "in_place_same_field": 0, + "in_same_port_two_field_span": 0, + "scalar_multiple_of_live_field": 0 + } + } + }, + "pins": { + "research/community-frontier1042-audit/selected-replay.tar.gz": "22c3f4dce4b897a1d423d1388801933e288b6a6b1906cb15e1b16a5eb68db754", + "research/community-frontier1042-audit/selected-replay.tar.gz::t16/global/base/split-centres/GLOBAL-TEMPLATE.json.gz": "a179dad87651aba340a5a8ddbcd86a8e757cad87b8a1f8bad48106fbecd38518", + "research/joint-query/certificate.json.gz": "a5ed85fac5ebf3c091482a113ab0d351eb5a7892fe2841a35e16017ec1ff49f7" + }, + "receipt_sha256": "8c57f8f5b137d5abb0cd0fcef9504721f85a36560299246732daa7e6a801cb6d", + "status": "PASS_QQ16_CUT_RETENTION_CENSUS", + "totals": { + "d1": { + "copy_required": 120, + "equal_some_live_field": 104, + "in_place_same_field": 104, + "in_same_port_two_field_span": 104, + "scalar_multiple_of_live_field": 104 + }, + "d18": { + "copy_required": 224, + "equal_some_live_field": 0, + "in_place_same_field": 0, + "in_same_port_two_field_span": 0, + "scalar_multiple_of_live_field": 0 + } + }, + "variants": { + "pairs_1_to_3_initially_zero": { + "d1": { + "copy_required": 120, + "equal_some_live_field": 104, + "in_place_same_field": 104, + "in_same_port_two_field_span": 104, + "scalar_multiple_of_live_field": 104 + }, + "d18": { + "copy_required": 224, + "equal_some_live_field": 0, + "in_place_same_field": 0, + "in_same_port_two_field_span": 0, + "scalar_multiple_of_live_field": 0 + } + }, + "terminal_also_exchanges_selected": { + "d1": { + "copy_required": 120, + "equal_some_live_field": 104, + "in_place_same_field": 104, + "in_same_port_two_field_span": 104, + "scalar_multiple_of_live_field": 104 + }, + "d18": { + "copy_required": 224, + "equal_some_live_field": 0, + "in_place_same_field": 0, + "in_same_port_two_field_span": 0, + "scalar_multiple_of_live_field": 0 + } + } + }, + "write_sets": [ + { + "event": 0, + "fields_written": 224, + "kind": "local", + "pair_or_bridge": 0, + "writes_pair0": [ + "XA", + "XT", + "XU", + "YA", + "YT", + "YU" + ] + }, + { + "event": 1, + "fields_written": 224, + "kind": "local", + "pair_or_bridge": 0, + "writes_pair0": [ + "XA", + "XT", + "XU", + "YA", + "YT", + "YU" + ] + }, + { + "event": 2, + "fields_written": 192, + "kind": "bridge", + "pair_or_bridge": [ + 1, + 0 + ], + "writes_pair0": [ + "XU" + ] + }, + { + "event": 3, + "fields_written": 224, + "kind": "local", + "pair_or_bridge": 0, + "writes_pair0": [ + "XA", + "XT", + "XU", + "YA", + "YT", + "YU" + ] + }, + { + "event": 4, + "fields_written": 192, + "kind": "bridge", + "pair_or_bridge": [ + 1, + 0 + ], + "writes_pair0": [ + "XU" + ] + }, + { + "event": 5, + "fields_written": 224, + "kind": "local", + "pair_or_bridge": 1, + "writes_pair0": [] + }, + { + "event": 6, + "fields_written": 192, + "kind": "bridge", + "pair_or_bridge": [ + 2, + 1 + ], + "writes_pair0": [] + }, + { + "event": 7, + "fields_written": 224, + "kind": "local", + "pair_or_bridge": 1, + "writes_pair0": [] + }, + { + "event": 8, + "fields_written": 192, + "kind": "bridge", + "pair_or_bridge": [ + 2, + 1 + ], + "writes_pair0": [] + }, + { + "event": 9, + "fields_written": 224, + "kind": "local", + "pair_or_bridge": 2, + "writes_pair0": [] + }, + { + "event": 10, + "fields_written": 192, + "kind": "bridge", + "pair_or_bridge": [ + 3, + 2 + ], + "writes_pair0": [] + }, + { + "event": 11, + "fields_written": 224, + "kind": "local", + "pair_or_bridge": 2, + "writes_pair0": [] + }, + { + "event": 12, + "fields_written": 192, + "kind": "bridge", + "pair_or_bridge": [ + 3, + 2 + ], + "writes_pair0": [] + }, + { + "event": 13, + "fields_written": 224, + "kind": "local", + "pair_or_bridge": 3, + "writes_pair0": [] + }, + { + "event": 14, + "fields_written": 224, + "kind": "local", + "pair_or_bridge": 3, + "writes_pair0": [] + }, + { + "event": 15, + "fields_written": 192, + "kind": "bridge", + "pair_or_bridge": [ + 2, + 3 + ], + "writes_pair0": [] + }, + { + "event": 16, + "fields_written": 192, + "kind": "bridge", + "pair_or_bridge": [ + 1, + 2 + ], + "writes_pair0": [] + }, + { + "event": 17, + "fields_written": 192, + "kind": "bridge", + "pair_or_bridge": [ + 0, + 1 + ], + "writes_pair0": [ + "YU" + ] + }, + { + "event": 18, + "fields_written": 768, + "kind": "terminal", + "pair_or_bridge": [ + null, + null + ], + "writes_pair0": [ + "XU", + "YU" + ] + } + ] +} diff --git a/research/qq16-cut-retention-census/SOURCES.json b/research/qq16-cut-retention-census/SOURCES.json new file mode 100644 index 0000000000..49ba699e4f --- /dev/null +++ b/research/qq16-cut-retention-census/SOURCES.json @@ -0,0 +1,42 @@ +{ + "schema_version": 1, + "base_commit": "0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "ae6a99f28aa468649eb66a361e764d769363bf11", + "sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "e8870e5917057d59b730eb14721a778639eca050", + "sha256": "d46eb6d5b3e279428753d770653663fbdf1063e55c255ea073d768f344927ef7" + }, + { + "path": "research/community-frontier1042-audit/selected-replay.tar.gz", + "usage": "input", + "git_blob": "6f4dc6fe7631d8aacf8081fcaecf32197181685b", + "sha256": "22c3f4dce4b897a1d423d1388801933e288b6a6b1906cb15e1b16a5eb68db754" + }, + { + "path": "research/joint-query/certificate.json.gz", + "usage": "input", + "git_blob": "c6e876d8b48d768214deee265ade428f8983b566", + "sha256": "a5ed85fac5ebf3c091482a113ab0d351eb5a7892fe2841a35e16017ec1ff49f7" + }, + { + "path": "research/complex-local-word-ceiling/ceiling.py", + "usage": "input", + "git_blob": "6c0f54527d879396f689523bfde19928a9b6157c", + "sha256": "86a1432870b3b21d8454106ec9162fddc0471472d9214c590a1420f2426cedfc" + }, + { + "path": "research/joint-query/evidence/CONSERVED-QQ16.md", + "usage": "provenance", + "git_blob": "4639583c1be02c2fb60ed8a8072c9969ef1569ce", + "sha256": "60f0de3a7205ba5046b5ae7ffa8bf2b1ea42ea46b498face0a77966b59e7f3fb" + } + ] +} diff --git a/research/qq16-cut-retention-census/TASK.json b/research/qq16-cut-retention-census/TASK.json new file mode 100644 index 0000000000..ceb6a558f8 --- /dev/null +++ b/research/qq16-cut-retention-census/TASK.json @@ -0,0 +1,78 @@ +{ + "schema_version": 1, + "task_id": "joint-query-controller", + "priority_revision": 4, + "base_commit": "0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2", + "original_card": { + "id": "joint-query-controller", + "question": "Can one explicitly changed QQ16 interface recover the missing chart query and close a two-call controller within a favorable full budget?", + "starting_points": [ + "research/joint-query/README.md", + "research/joint-query/evidence/QQ16-SELECTED-WITNESS.md", + "research/joint-query/evidence/JOINT-QUERY-TRANSFER.md", + "docs/research/community-efficient1000-review.md" + ], + "methods": [ + "Add one explicitly priced ordinary-to-selected observation and derive the ordered two-call map and inverse.", + "Change the first local pair or retained state, then test the existing lost-observation witness and price all new operations." + ], + "acceptance_gate": "Name the changed premise of the fixed F0/B1 observation obstruction. Show exactly which query is recovered, legal native reads and restoration, and a full favorable budget including cover maps, helpers and endpoints. Local inverse identities alone do not close the global controller.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read the fixed-first-pair QQ16 witness before designing a controller. The checked #1969 local words do not evade that witness or supply global placement.", + "scope": "Source-bound orientation only. Read the named package and review before relying on its local evidence; this command is not its replay or supplier admission." + }, + "first_experiment": "Apply the existing witness to one proposed extra observation or changed first pair. If it still loses the required record, stop. Otherwise derive one ordered two-call identity and charge the added read, chart maps and restoration before extending to more stages.", + "bottleneck_link": "The native local words exist; retained query information and its physical access are the missing link to a composed recursive interface.", + "allowed_variations": [ + "One paid query, one changed first pair, or one precisely specified affine helper state.", + "A counterexample or lower bound for that exact proposed repair." + ], + "scope_change_triggers": [ + "Retaining the fixed first pair and ordinary schedule while allowing only homogeneous selected-only control, already excluded by the witness.", + "Treating cover-map counts as zero-cost physical address operations." + ], + "overlap_terms": [ + "QQ16", + "joint-query", + "changing-chart controller", + "selected observation", + "1969" + ] + }, + "scope_status": "refined", + "actual_scope": "In-place availability census of PR2443's (545c05e1) 224 observed port arrays for the unchanged conserved F0/B_1_2 pair, traced through the pinned 19-event QQ16 recipe to two decode points (after B_1_2 and after the terminal), with exact copy counts per owner per replica and their transfer to philippeVV's C=0/C=64 price convention.", + "scope_change_reason": "PR2443 open questions 1-2 ask whether a controller can retain its two-cut records and at what price. The generic C=64 screen is already recorded (#2074/PR2079, PR2197) and #2074 Theorem B gives a 62-coordinate floor; the remaining premise for the C=0 case is whether the contract's arrays are available in place or need copies, and for how many calls. This card answers only that storage term; it does not price reads, chart maps, the minor inverse or cleanup.", + "bottleneck_link": "Retained query information and its physical access are the missing link to a composed QQ16 interface. This census shows the PR2443 contract's records are not in place at either decode point, so they must be copied or recomputed; recomputation is left open.", + "budget_minutes": 60, + "stop_rule": "Stop once the census of all 224 arrays at both decode points is exact and checked; if at least one array per owner must be retained across calls, record that the literal PR2443 contract fails the stated C=0 condition (scoped screen, not an impossibility theorem). Hard stop 2026-10-15T12:07:20Z.", + "outcome": "negative-result", + "evidence": "verify.py: exact rational linear-form census (896 variables) on the owner/payload-constant subspace of the conserved maps; PR2443 decoder reproduced; 6 negative controls; RESULT.json and CENSUS-ROWS.json. price.py: transfer of the copy counts to philippeVV's price3 convention with pinned ceiling.py; PRICE.json.", + "author": "thakrarsagar", + "ai_assistance": "Substantial AI assistance from Claude (Anthropic, Claude Opus 5.5): derivation, checker implementation and write-up. No independent human or proof-assistant review is claimed.", + "open_questions": [ + { + "question": "What is the minimum number of coordinates per owner per replica that must be retained (copied or kept as query records) so that PR2443's read set, plus legal reads of the final live state, recovers pair-0 inputs at the end of the 19-event schedule?", + "why_it_matters": "The literal contract needs 1688 coordinate-calls per replica at d18, against a C=0 break-even of 71 (centre-like price). Any compressed record set must still respect #2074 Theorem B's floor of 62; whether one fits below 71 is open.", + "first_step": "Replace the 88 x1_S arrays by the 8-coordinate driver record a1=ell_(1,T)x1_T (identity L2) and the selected arrays by the conserved pair sums (L1); recompute the coordinate-calls with the same census code.", + "blocked_by": "Legal native read types for X2_U+Y2_U and the final former-Y endpoints; which reads PR2443's contract excludes on purpose." + }, + { + "question": "Is the d1 decode point (immediately after B_1_2) usable by a controller that must continue with F2..F8?", + "why_it_matters": "At d1 the copy demand is only 120 coordinate-calls, and B1 is invertible, so with a full post-B1 read no copy is needed; but a mid-schedule decode must restore the state it reads.", + "first_step": "Write the restoration and read cost of a mid-schedule decode at d1 using the CONSERVED-QQ16 inverse of B (H_s, E_t).", + "blocked_by": "No priced native read of y2_U / X2_T at the completed-X type; restoration accounting." + }, + { + "question": "Which centre charge applies to QQ16, C=0 or C=64?", + "why_it_matters": "Under C=64 even a free controller gains at most +0.28%; under C=0 the census break-even is 71 coordinate-calls.", + "first_step": "Maintainer decision on the #2074 question.", + "blocked_by": "Maintainer review of the coverage-law convention." + } + ] +} diff --git a/research/qq16-cut-retention-census/VERIFY.json b/research/qq16-cut-retention-census/VERIFY.json new file mode 100644 index 0000000000..7f3c30936b --- /dev/null +++ b/research/qq16-cut-retention-census/VERIFY.json @@ -0,0 +1,33 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/community-frontier1042-audit/selected-replay.tar.gz", + "research/complex-local-word-ceiling/ceiling.py", + "research/joint-query/certificate.json.gz" + ], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 300, + "checks": "Source pins, Grams, K=R^T/4, packet F/B contract strings, the pinned 19-event recipe; PR2443 decoder recovers all 224 pair-0 inputs in the constant-subspace model; exact census of the 224 observed arrays at d1 (after B_1_2) and d18 (after the terminal); two variants; recomputation-lead identities; six negative controls; recomputed RESULT.json must equal the committed file." + }, + { + "argv": [ + "{python}", + "-I", + "-B", + "{package}/price.py" + ], + "timeout_seconds": 300, + "checks": "Transfers the census copy counts to philippeVV's unreviewed C=0/C=64 price3 convention with the pinned ceiling.py; recomputed PRICE.json must equal the committed file." + } + ] +} diff --git a/research/qq16-cut-retention-census/price.py b/research/qq16-cut-retention-census/price.py new file mode 100644 index 0000000000..a72f4f0423 --- /dev/null +++ b/research/qq16-cut-retention-census/price.py @@ -0,0 +1,114 @@ +#!/usr/bin/env python3 +"""Map the retention census onto philippeVV's C=0 / C=64 pricing convention. + +This is a convention transfer, not a new cost model. The convention is +Philippe Van Velzen's `price3.py` (fork commit 680d0997, four-bank/, read on +2026-10-15; sha256 1c2ca9a4f89d7851dee6b765119f1f84f1227e30ec23f3e169aa327d2cc7f1f7), +re-implemented here in a few lines against the pinned repository +`research/complex-local-word-ceiling/ceiling.py`. Its prices are unreviewed: + +* per-call local profile MIX = (5 F + 4 B)/9 with the QQ16 F and B profiles; +* base centre charge C (0 or 64); +* a retained coordinate held for L live calls costs, per coordinate-call, + either one rank-8 child plus 8 units of total mass ("centre") or 72 units + of total mass paid by ideal idle children ("family"); coordinate-calls are + per nine-call replica, so the per-call increment is coords * L / 9. + +`None` means ceiling.ceiling raises ValueError, i.e. the relaxation has no +positive saving (no admissible ceiling). Each retained port array counts as +one coordinate per owner per replica, the unit of #2074 Theorem B. + +Apache-2.0. Prepared by thakrarsagar with substantial AI assistance from +Claude (Anthropic, Claude Opus 5.5). +""" +from fractions import Fraction as Q +from hashlib import sha256 +from pathlib import Path +import json +import sys + +ROOT = Path(__file__).resolve().parents[2] +CEILING = ROOT / "research/complex-local-word-ceiling/ceiling.py" +CEILING_PIN = "86a1432870b3b21d8454106ec9162fddc0471472d9214c590a1420f2426cedfc" +if sha256(CEILING.read_bytes()).hexdigest() != CEILING_PIN: + raise SystemExit("ceiling.py pin mismatch") +sys.path.insert(0, str(CEILING.parent)) +import ceiling as C # noqa: E402 + +M, FAM, ST, GRID = 73, 896, 9, Q(1, 10 ** 10) +SEL = {1: 2412, 2: 418, 3: 432, 4: 142, 5: 82, 8: 8} +B = {1: 2436, 2: 418, 3: 432, 4: 142, 5: 82} +F = {1: 2420, 2: 418, 3: 432, 4: 142, 5: 82} +MIX = {r: Q(5 * F[r] + 4 * B[r], 9) for r in B} + + +def cap(profile, centre): + try: + return C.ceiling(profile, M, FAM, ST, centre, grid=GRID)[1] + except ValueError: + return None + + +def priced(base, coordinate_calls, kind): + n = Q(coordinate_calls, 9) + p, c = dict(MIX), Q(base) + if kind == "centre": + p[8] = p.get(8, 0) + n + c += 8 * n + else: + c += 72 * n + return cap(p, c) + + +def largest(base, kind, beats): + """Largest integer coordinate-calls per replica whose ceiling exists and beats `beats`.""" + ok = lambda x: (lambda a: a is not None and a > beats)(priced(base, x, kind)) + if not ok(0): + return None + lo, hi = 0, 1 + while ok(hi): + lo, hi = hi, 2 * hi + while hi - lo > 1: + mid = (lo + hi) // 2 + lo, hi = (mid, hi) if ok(mid) else (lo, mid) + return lo + + +def main(): + res = json.loads((Path(__file__).resolve().parent / "RESULT.json").read_text()) + pi = res["per_item"] + f0 = sum(pi[k]["d18"]["copy_required"] for k in ("x1_A", "x1_T", "y1_A", "y1_T", "x1_S")) + b1 = sum(pi[k]["d18"]["copy_required"] for k in ("y2_A", "C=x2_U")) + d1 = sum(pi[k]["d1"]["copy_required"] for k in pi) + # live calls held: F0 cut -> d1 spans B1 (1 call); F0 cut -> d18 spans B1,F2,...,F8 (8 calls); + # B1 cut -> d18 spans F2,...,F8 (7 calls). Bridges and the terminal are not calls. + demand = {"d1": d1 * 1, "d18": f0 * 8 + b1 * 7} + sel = cap(SEL, 64) + # Convention reproduction: two rows of philippeVV's committed price3.json (fork 680d0997). + if (str(sel), str(priced(0, 62, "centre")), str(priced(0, 64, "centre"))) != ( + "8450271/5000000000", "5267381/2500000000", "5056523/2500000000"): + raise SystemExit("price3 convention not reproduced") + out = {"selected_ceiling": str(sel), "copied_arrays": {"d1": d1, "d18_F0_cut": f0, "d18_B1_cut": b1}, + "coordinate_calls_per_replica": demand, "rows": [], "break_even": {}} + for base in (0, 64): + for kind in ("centre", "family"): + for name, x in sorted(demand.items()): + a = priced(base, x, kind) + out["rows"].append({"C": base, "kind": kind, "decode": name, "coordinate_calls": x, + "ceiling": None if a is None else str(a), + "vs_selected_percent": None if a is None else "%+.4f" % (float(a / sel - 1) * 100)}) + out["break_even"]["C%d_%s" % (base, kind)] = { + "max_coordinate_calls_positive_saving": largest(base, kind, Q(0)), + "max_coordinate_calls_beating_selected": largest(base, kind, sel)} + return out + + +if __name__ == "__main__": + out = main() + here = Path(__file__).resolve().parent / "PRICE.json" + if "--write" in sys.argv: + here.write_text(json.dumps(out, indent=1, sort_keys=True) + "\n") + elif json.loads(here.read_text()) != out: + raise SystemExit("PRICE.json mismatch") + print(json.dumps(out, indent=1)) + print("PASS_QQ16_CUT_RETENTION_PRICE_TRANSFER") diff --git a/research/qq16-cut-retention-census/verify.py b/research/qq16-cut-retention-census/verify.py new file mode 100644 index 0000000000..3f0dac506f --- /dev/null +++ b/research/qq16-cut-retention-census/verify.py @@ -0,0 +1,474 @@ +#!/usr/bin/env python3 +"""In-place availability census of PR2443's two-cut QQ16 observation contract. + +For each of the 224 port arrays observed by PR2443 (starship-s, head +545c05e1) this checker decides whether its value is still held, unchanged, by +some live logical field at two decode points of the pinned 19-event QQ16 +recipe: (d1) immediately after B_1_2 and (d18) after the final terminal. + +Model. Fields are logical port arrays of four bank pairs (X/Y, 112 ports). +The local maps are the conserved F_s / B_(s,t) maps of +research/joint-query/evidence/CONSERVED-QQ16.md, equations (1) and (3) (also +the packet's F_contract/B_contract strings); the bridge and ordinary-terminal +semantics are those stated in PR2346 section 1. Every value is tracked +exactly as a rational linear form in all 896 initial port arrays. The +executable instance is the owner- and payload-constant subspace, on which +every actual cover route D_s acts as the identity. Consequences: + +* an inequality found here is an exact counterexample for the actual + routed maps (an actual equality would restrict to equality here); +* a survival claim is accepted only with the symbolic support argument + "no event in (cut, decode point] writes this field". + +New code: Apache-2.0. Prepared by thakrarsagar with substantial AI +assistance from Claude (Anthropic, Claude Opus 5.5). No predecessor +executable is imported. +""" +from fractions import Fraction as Q +from hashlib import sha256 +from io import BytesIO +from pathlib import Path +import gzip +import json +import random +import sys +import tarfile + +ROOT = Path(__file__).resolve().parents[2] +PACKET = "research/joint-query/certificate.json.gz" +ARCHIVE = "research/community-frontier1042-audit/selected-replay.tar.gz" +PINS = { + PACKET: "a5ed85fac5ebf3c091482a113ab0d351eb5a7892fe2841a35e16017ec1ff49f7", + ARCHIVE: "22c3f4dce4b897a1d423d1388801933e288b6a6b1906cb15e1b16a5eb68db754", +} +TEMPLATE = "t16/global/base/split-centres/GLOBAL-TEMPLATE.json.gz" +TEMPLATE_PIN = "a179dad87651aba340a5a8ddbcd86a8e757cad87b8a1f8bad48106fbecd38518" +A = (0, 7, 20, 27, 36, 46, 57, 111) +T = (21, 37, 47, 76, 81, 87, 92, 110) +U = tuple(p for p in range(112) if p not in A + T) +J = (1, 2, 3, 4, 5, 6, 8, 12) +S = tuple(p for p in U if p not in J) +NP, NF = 4, 4 * 224 # bank pairs, port arrays +DECODE = (1, 18) # event indices of the two decode points +ITEMS = ("x1_A", "x1_T", "y1_A", "y1_T", "x1_S", "y2_A", "C=x2_U") + + +class Fail(Exception): + pass + + +def need(ok, message): + if not ok: + raise Fail(message) + + +def fid(pair, side, port): + """Field / variable index; side 0 is X, side 1 is Y.""" + return pair * 224 + side * 112 + port + + +def fname(i): + pair, rest = divmod(i, 224) + side, port = divmod(rest, 112) + block = "A" if port in A else "T" if port in T else "U" + return "%s%d[%d,%s]" % ("XY"[side], pair, port, block) + + +# ---------------------------------------------------------------- forms +def lin(*terms): + out = {} + for c, f in terms: + if c: + for k, v in f.items(): + out[k] = out.get(k, 0) + c * v + return {k: v for k, v in out.items() if v} + + +def key(f): + return tuple(sorted(f.items())) + + +def normal_key(f): + """Key of the line spanned by f (first coefficient scaled to one).""" + if not f: + return () + items = sorted(f.items()) + lead = items[0][1] + return tuple((k, v / lead) for k, v in items) + + +# ---------------------------------------------------------------- sources +def load_sources(R_mutation=False): + raw = {} + for name, pin in PINS.items(): + data = (ROOT / name).read_bytes() + need(sha256(data).hexdigest() == pin, "source pin " + name) + raw[name] = data + packet = json.loads(gzip.decompress(raw[PACKET])) + with tarfile.open(fileobj=BytesIO(raw[ARCHIVE]), mode="r:gz") as tar: + found = [m for m in tar.getmembers() if m.name == TEMPLATE] + need(len(found) == 1 and found[0].isfile(), "one template member") + data = tar.extractfile(found[0]).read() + need(sha256(data).hexdigest() == TEMPLATE_PIN, "template member pin") + recipe = json.loads(gzip.decompress(data))["recipe"] + R = [[Q(row.get(str(p), "0")) for p in range(112)] for row in packet["R_rows"]] + K = [[Q(row.get(str(i), "0")) for i in range(8)] for row in packet["K_rows"]] + if R_mutation: + R[0][U[0]] += 1 + need((tuple(packet["A_ports"]), tuple(packet["T_ports"]), tuple(packet["U_ports"])) == (A, T, U), + "port partition") + for ports, g in ((U, 48), (A, 4), (T, 4)): + need(all(sum(R[i][p] * R[j][p] for p in ports) == g * (i == j) + for i in range(8) for j in range(8)), "Gram identity") + need(all(K[p][i] == R[i][p] / 4 for p in range(112) for i in range(8)), "K = R^T/4") + need(packet["F_contract"].startswith("f=R_s x. X_U=x_U-K_s,U f; X_A=P_s,A ell_s,T x; X_T=P_s,T f."), + "packet forward contract") + need(packet["B_contract"].startswith("u=E_t y; a=ell_s,T x; b=R_s u. Y_A=u_A; Y_U=y_U+K_s,U a; " + "Y_T=u_T-P_s,T(b+11a). X_U=x_U-y_U; X_A=x_A+y_A-u_A; X_T=P_s,T(b+12a)."), + "packet backward contract") + need(len(recipe) == 19, "19-event recipe") + need([e["pair"] for e in recipe if e["kind"] == "local"] == [0, 0, 0, 1, 1, 2, 2, 3, 3], "local pairs") + need(all(e["reverse"] == bool(e["stage"] % 2) for e in recipe if e["kind"] == "local"), "orientations") + need(recipe[-1] == {"kind": "terminal", "pairs": 4}, "terminal") + return R, recipe, {PACKET: PINS[PACKET], ARCHIVE: PINS[ARCHIVE], ARCHIVE + "::" + TEMPLATE: TEMPLATE_PIN} + + +# ---------------------------------------------------------------- maps +class Model: + """Constant-subspace realisation of the conserved maps (all D_s = I).""" + + bad_backward = False + + def __init__(self, R): + self.R = R + + def query(self, x, ports): # R_ports x_ports : 8 forms + return [lin(*((self.R[i][p], x[p]) for p in ports)) for i in range(8)] + + def sect(self, q, ports): # P_V q = R_V^T q / 4 on V (also K restricted to V) + return {p: lin(*((self.R[i][p] / 4, q[i]) for i in range(8))) for p in ports} + + def forward(self, x, y): + f = self.query(x, range(112)) + k = self.sect(f, U) + nx = {p: lin((1, x[p]), (-1, k[p])) for p in U} + nx.update(self.sect(self.query(x, T), A)) # X_A = P_A ell_T x + nx.update(self.sect(f, T)) # X_T = P_T f + ny = {p: lin((1, y[p]), (1, nx[p])) for p in U} + for p in A + T: # conserved selected sums + ny[p] = lin((1, x[p]), (1, y[p]), (-1, nx[p])) + return nx, ny + + def backward(self, x, y): + # u = E_t y = y + P_A (B_t y_U + ell_T y_T): only the A block changes. + c = [lin((1, g), (1, h)) for g, h in zip(self.query(y, U), self.query(y, T))] + corr = self.sect(c, A) + u = dict(y) + sign = -1 if self.bad_backward else 1 + for p in A: + u[p] = lin((1, y[p]), (sign, corr[p])) + a = self.query(x, T) + b = self.query(u, range(112)) + ka = self.sect(a, U) + ny, nx = {}, {} + for p in U: + ny[p] = lin((1, y[p]), (1, ka[p])) + nx[p] = lin((1, x[p]), (-1, y[p])) + for p in A: + ny[p] = u[p] + nx[p] = lin((1, x[p]), (1, y[p]), (-1, u[p])) + t11 = self.sect([lin((1, bi), (11, ai)) for bi, ai in zip(b, a)], T) + t12 = self.sect([lin((1, bi), (12, ai)) for bi, ai in zip(b, a)], T) + for p in T: + ny[p] = lin((1, u[p]), (-1, t11[p])) + nx[p] = t12[p] + return nx, ny + + +def run(R, recipe, terminal_selected="identity", drop=None, zero_other_pairs=False, model=Model): + """Return the 19 post-event states (lists of 896 forms) and symbolic write sets.""" + m = model(R) + state = [{i: Q(1)} if (i < 224 or not zero_other_pairs) else {} for i in range(NF)] + states, writes = [], [] + for index, e in enumerate(recipe): + new = list(state) + written = set() + if index != drop: + if e["kind"] == "local": + k = e["pair"] + x = {p: state[fid(k, 0, p)] for p in range(112)} + y = {p: state[fid(k, 1, p)] for p in range(112)} + nx, ny = m.backward(x, y) if e["reverse"] else m.forward(x, y) + for p in range(112): + new[fid(k, 0, p)], new[fid(k, 1, p)] = nx[p], ny[p] + written = {fid(k, s, p) for s in (0, 1) for p in range(112)} + elif e["kind"] == "bridge": + i, j, c = e["src"], e["dst"], e["coefficient"] + for p in U: # X_j,U += c X_i,U ; Y_i,U -= c Y_j,U (PR2346 section 1) + new[fid(j, 0, p)] = lin((1, state[fid(j, 0, p)]), (c, state[fid(i, 0, p)])) + new[fid(i, 1, p)] = lin((1, state[fid(i, 1, p)]), (-c, state[fid(j, 1, p)])) + written = {fid(j, 0, p) for p in U} | {fid(i, 1, p) for p in U} + else: # (X_U, Y_U) -> (Y_U, -X_U); selected ports optional + ports = range(112) if terminal_selected == "signed_exchange" else U + for k in range(NP): + for p in ports: + new[fid(k, 0, p)] = state[fid(k, 1, p)] + new[fid(k, 1, p)] = lin((-1, state[fid(k, 0, p)])) + written = {fid(k, s, p) for k in range(NP) for s in (0, 1) for p in ports} + state = new + states.append(state) + writes.append(written) + return states, writes + + +# ---------------------------------------------------------------- contract +def observations(states): + """PR2443's 224 observed arrays: (item, cut event index, field, form).""" + obs = [] + for item, side, ports in (("x1_A", 0, A), ("x1_T", 0, T), ("y1_A", 1, A), ("y1_T", 1, T), + ("x1_S", 0, S)): + obs += [(item, 0, fid(0, side, p)) for p in ports] + obs += [("y2_A", 1, fid(0, 1, p)) for p in A] + obs += [("C=x2_U", 1, fid(0, 0, p)) for p in U] + need(len(obs) == 224 and len({(c, f) for _, c, f in obs}) == 224, "224 distinct observations") + return [(item, cut, f, states[cut][f]) for item, cut, f in obs] + + +def decoder_check(R, states, model=Model): + """PR2443's ordered decoder recovers all 224 pair-0 inputs in this model.""" + m = model(R) + s0, s1 = states[0], states[1] + x1 = {p: s0[fid(0, 0, p)] for p in range(112)} + y1 = {p: s0[fid(0, 1, p)] for p in range(112)} + y2A = {p: s1[fid(0, 1, p)] for p in A} + C = {p: s1[fid(0, 0, p)] for p in U} + need(all(C[p] == {fid(0, 1, p): -1} for p in U), "C = x2_U = -y_U") + q = [lin((1, g), (-1, h)) for g, h in zip(m.query(y2A, A), m.query(y1, A))] + v = [lin((1, qi), (-1, ti), (1, ci)) for qi, ti, ci in zip(q, m.query(y1, T), m.query(C, U))] + w = [lin((1, vi), (-1, si)) for vi, si in zip(v, m.query(x1, S))] + M = [[R[i][p] for p in J] + [Q(i == r) for r in range(8)] for i in range(8)] + for c in range(8): # exact Gauss-Jordan inverse of R_J + piv = next(r for r in range(c, 8) if M[r][c]) + M[c], M[piv] = M[piv], M[c] + M[c] = [val / M[c][c] for val in M[c]] + for r in range(8): + if r != c and M[r][c]: + M[r] = [a_ - M[r][c] * b_ for a_, b_ in zip(M[r], M[c])] + inv = [row[8:] for row in M] + xJ = {p: lin(*((inv[jp][i], w[i]) for i in range(8))) for jp, p in enumerate(J)} + x1U = {p: (xJ[p] if p in J else x1[p]) for p in U} + f = m.query(x1, T) + t = m.sect(m.query(x1, A), T) + kf = m.sect(f, U) + xU = {p: lin((1, x1U[p]), (1, kf[p])) for p in U} + rest = [lin((1, fi), (-1, bi), (-1, ti)) for fi, bi, ti in zip(f, m.query(xU, U), m.query(t, T))] + xA = m.sect(rest, A) + rec = {} + for p in U: + rec[fid(0, 0, p)], rec[fid(0, 1, p)] = xU[p], lin((-1, C[p])) + for p in T: + rec[fid(0, 0, p)] = t[p] + for p in A: + rec[fid(0, 0, p)] = xA[p] + for p in A + T: + rec[fid(0, 1, p)] = lin((1, x1[p]), (1, y1[p]), (-1, rec[fid(0, 0, p)])) + need(all(rec[i] == {i: 1} for i in range(224)), "PR2443 decoder recovers all 224 pair-0 inputs") + + +def leads(R, states): + """Two symbolic identities (from CONSERVED-QQ16 (1)/(3)) checked exactly in this model. + + (L1) the selected pair sums of pair 0 are conserved by F0, B1 and F2 and untouched + afterwards (identity selected terminal): X_V + Y_V = x_V + y_V = x1_V + y1_V; + (L2) at d1, x1_U = X2_U + Y2_U - K_(1,U) ell_(1,T) x1_T (from x'_U = x_U - y_U and + y'_U = y_U + K_(s,U) a with y1_U = y_U + x1_U). + These are recomputation leads, not in-place availability of the observed arrays. + """ + m = Model(R) + x1 = {p: states[0][fid(0, 0, p)] for p in range(112)} + for d in DECODE: + need(all(lin((1, states[d][fid(0, 0, p)]), (1, states[d][fid(0, 1, p)])) == + {fid(0, 0, p): 1, fid(0, 1, p): 1} for p in A + T), "conserved selected pair sums") + ka = m.sect(m.query(x1, T), U) + need(all(lin((1, states[1][fid(0, 0, p)]), (1, states[1][fid(0, 1, p)]), (-1, ka[p])) == x1[p] for p in U), + "x1_U from the live post-B1 pair and one 8-coordinate driver record") + return {"L1_selected_pair_sums_live_at_d1_and_d18": 16, "L2_x1_U_from_live_pair_plus_driver_record": 96} + + +def det3(a, b, c): + return (a[0] * (b[1] * c[2] - b[2] * c[1]) - a[1] * (b[0] * c[2] - b[2] * c[0]) + + a[2] * (b[0] * c[1] - b[1] * c[0])) + + +def in_span2(o, f, g): + """Exact test: o lies in the rational span of forms f and g.""" + rows = [[f.get(k, Q(0)), g.get(k, Q(0)), o.get(k, Q(0))] for k in sorted(set(o) | set(f) | set(g))] + r = 0 + for c in range(2): + piv = next((i for i in range(r, len(rows)) if rows[i][c]), None) + if piv is None: + continue + rows[r], rows[piv] = rows[piv], rows[r] + rows[r] = [val / rows[r][c] for val in rows[r]] + for i in range(len(rows)): + if i != r and rows[i][c]: + fac = rows[i][c] + rows[i] = [a_ - fac * b_ for a_, b_ in zip(rows[i], rows[r])] + r += 1 + return all(not row[2] for row in rows[r:]) + + +def census(states, writes, obs, seed=20261015): + """Survival of each observation at the decode points d1 and d18.""" + rng = random.Random(seed) + pts = [[Q(rng.randint(-10**6, 10**6), rng.randint(1, 10**3)) for _ in range(NF)] for _ in range(3)] + + def ev(f): + return [sum(v * pt[k] for k, v in f.items()) for pt in pts] + + index = {} + for d in DECODE: + exact, line = {}, {} + for i, f in enumerate(states[d]): + exact.setdefault(key(f), []).append(i) + line.setdefault(normal_key(f), []).append(i) + index[d] = (exact, line, [ev(f) for f in states[d]]) + rows = [] + for item, cut, field, form in obs: + need(form, "observed array is a nonzero form") + row = {"item": item, "cut_event": cut, "field": fname(field)} + ov = ev(form) + for d in DECODE: + exact, line, vals = index[d] + st = states[d] + touched = any(field in writes[e] for e in range(cut + 1, d + 1)) + same = st[field] == form + need(same or touched, "a field outside every write set changed") + span = [] + for k in range(NP): + for p in range(112): + fx, fy = fid(k, 0, p), fid(k, 1, p) + # A nonzero 3x3 evaluation determinant certifies o outside the span. + if det3(vals[fx], vals[fy], ov) == 0 and in_span2(form, st[fx], st[fy]): + span.append(fname(fx) + "|" + fname(fy)) + first = next((e for e in range(cut + 1, d + 1) if states[e][field] != form), None) + entry = {"same_field_unchanged": same, "untouched_by_write_sets": not touched, + "first_overwrite_event": first, + "equal_live_fields": [fname(i) for i in exact.get(key(form), [])], + "scalar_multiple_live_fields": [fname(i) for i in line.get(normal_key(form), [])], + "same_port_two_field_span": span} + if not touched: # symbolic survival: no event in (cut, d] writes the field + need(same and fname(field) in entry["equal_live_fields"], "symbolic survival") + row["d%d" % d] = entry + rows.append(row) + return rows + + +def summarise(rows): + keys = ("in_place_same_field", "equal_some_live_field", "scalar_multiple_of_live_field", + "in_same_port_two_field_span", "copy_required") + table = {} + for it in ITEMS: + sel = [r for r in rows if r["item"] == it] + entry = {"arrays": len(sel)} + for d in DECODE: + es = [r["d%d" % d] for r in sel] + entry["d%d" % d] = { + "in_place_same_field": sum(e["same_field_unchanged"] for e in es), + "equal_some_live_field": sum(bool(e["equal_live_fields"]) for e in es), + "scalar_multiple_of_live_field": sum(bool(e["scalar_multiple_live_fields"]) for e in es), + "in_same_port_two_field_span": sum(bool(e["same_port_two_field_span"]) for e in es), + "copy_required": sum(not e["equal_live_fields"] for e in es), + "first_overwrite_events": sorted({e["first_overwrite_event"] for e in es + if e["first_overwrite_event"] is not None}), + } + table[it] = entry + totals = {"d%d" % d: {k: sum(table[it]["d%d" % d][k] for it in ITEMS) for k in keys} for d in DECODE} + return table, totals + + +def digest(obj): + return sha256(json.dumps(obj, sort_keys=True, separators=(",", ":")).encode()).hexdigest() + + +def full(R, recipe, **kw): + model = kw.pop("model", Model) + states, writes = run(R, recipe, model=model, **kw) + rows = census(states, writes, observations(states)) + table, totals = summarise(rows) + return states, writes, rows, table, totals + + +def negative_controls(R, recipe, states, totals): + out = {} + try: # 1. claiming x1_A survives B1 (in place) must fail + need(all(states[1][fid(0, 0, p)] == states[0][fid(0, 0, p)] for p in A), "x1_A survives B1") + raise RuntimeError("control accepted: x1_A survives B1") + except Fail: + out["claim_x1_A_survives_B1"] = "rejected" + for name, drop, d in (("drop_F2_event3", 3, "d18"), ("drop_B1_event1", 1, "d1")): + tot = full(R, recipe, drop=drop)[4] # 2./3. dropping an overwrite event + need(tot[d] != totals[d], name + " changes the census") + out[name] = {"changed": True, d + "_totals": tot[d]} + try: # 4. wrong C sign must fail + need(all(states[1][fid(0, 0, p)] == {fid(0, 1, p): 1} for p in U), "C = +y_U") + raise RuntimeError("control accepted: C = +y_U") + except Fail: + out["claim_C_equals_plus_y_U"] = "rejected" + try: # 5. corrupted centre coefficient must fail the source checks + load_sources(R_mutation=True) + raise RuntimeError("control accepted: corrupted R") + except Fail: + out["corrupted_centre_coefficient"] = "rejected" + + class Bad(Model): + bad_backward = True + try: # 6. a wrong future-logger sign in E_t (u_A) must break PR2443's decoder + decoder_check(R, run(R, recipe, model=Bad)[0], model=Bad) + raise RuntimeError("control accepted: wrong backward map") + except Fail: + out["wrong_E_t_sign_breaks_decoder"] = "rejected" + return out + + +def main(): + R, recipe, pins = load_sources() + states, writes, rows, table, totals = full(R, recipe) + decoder_check(R, states) + lead = leads(R, states) + variants = {} + for name, kw in (("terminal_also_exchanges_selected", {"terminal_selected": "signed_exchange"}), + ("pairs_1_to_3_initially_zero", {"zero_other_pairs": True})): + variants[name] = full(R, recipe, **kw)[4] + for d in ("d1", "d18"): + need(all(v[d]["copy_required"] == totals[d]["copy_required"] for v in variants.values()), + "copy count stable under the variants") + write_sets = [{"event": i, "kind": e["kind"], "pair_or_bridge": e.get("pair", [e.get("src"), e.get("dst")]), + "fields_written": len(w), + "writes_pair0": sorted({"XY"[(f % 224) // 112] + ("A" if f % 112 in A else "T" if f % 112 in T + else "U") for f in w if f < 224})} + for i, (e, w) in enumerate(zip(recipe, writes))] + result = {"status": "PASS_QQ16_CUT_RETENTION_CENSUS", "pins": pins, + "model": "owner/payload-constant subspace (all D_s = I); exact rational linear forms in the " + "896 initial port arrays of four pairs; bridges and ordinary terminal per PR2346 section 1", + "decode_points": {"d1": "after event 1 (B_1_2)", "d18": "after event 18 (terminal)"}, + "write_sets": write_sets, "per_item": table, "totals": totals, "variants": variants, + "census_rows_sha256": digest(rows), "leads": lead} + result["receipt_sha256"] = digest({k: result[k] for k in ("per_item", "totals", "variants", + "census_rows_sha256", "write_sets")}) + result["negative_controls"] = negative_controls(R, recipe, states, totals) + return result, rows + + +if __name__ == "__main__": + res, rows = main() + here = Path(__file__).resolve().parent + if "--write" in sys.argv: + (here / "RESULT.json").write_text(json.dumps(res, indent=1, sort_keys=True) + "\n") + (here / "CENSUS-ROWS.json").write_text(json.dumps(rows, indent=1, sort_keys=True) + "\n") + else: + committed = json.loads((here / "RESULT.json").read_text()) + need(committed == res, "recomputed result equals committed RESULT.json") + print(json.dumps({"totals": res["totals"], "negative_controls": sorted(res["negative_controls"])}, indent=1)) + print("PASS_NEGATIVE_CONTROLS", len(res["negative_controls"])) + print(res["status"]) From 514833624c9991286a471e502ec699deab6dbf82 Mon Sep 17 00:00:00 2001 From: Sagar Thakrar <18622288+thakrarsagar@users.noreply.github.com> Date: Thu, 15 Oct 2026 17:20:42 +0530 Subject: [PATCH 2/3] research: address review of QQ16 cut-retention census Separate novelty from PR2346/PR2376, scope Theorem B's 62 as the four-bank floor, reword the C=0 conclusion as quantitative, add a checked L2-variant decoder (32 retained arrays plus a Y2_U read) and its price rows, pin CENSUS-ROWS.json on replay, give the full price3 provenance, and credit concurrent PR2456/PR2416 and ywz65's live C-read claim. Co-Authored-By: Claude Opus 5.5 --- research/qq16-cut-retention-census/PRICE.json | 68 ++++++++- research/qq16-cut-retention-census/README.md | 135 ++++++++++++++---- .../qq16-cut-retention-census/RESULT.json | 7 + research/qq16-cut-retention-census/TASK.json | 30 ++-- .../qq16-cut-retention-census/VERIFY.json | 4 +- research/qq16-cut-retention-census/price.py | 13 +- research/qq16-cut-retention-census/verify.py | 24 +++- 7 files changed, 233 insertions(+), 48 deletions(-) diff --git a/research/qq16-cut-retention-census/PRICE.json b/research/qq16-cut-retention-census/PRICE.json index 072e56f573..8b1463a929 100644 --- a/research/qq16-cut-retention-census/PRICE.json +++ b/research/qq16-cut-retention-census/PRICE.json @@ -19,7 +19,9 @@ }, "coordinate_calls_per_replica": { "d1": 120, - "d18": 1688 + "d18": 1688, + "d1_L2_variant": 32, + "zero_retention": 0 }, "copied_arrays": { "d1": 120, @@ -43,6 +45,22 @@ "kind": "centre", "vs_selected_percent": null }, + { + "C": 0, + "ceiling": "33727479/10000000000", + "coordinate_calls": 32, + "decode": "d1_L2_variant", + "kind": "centre", + "vs_selected_percent": "+99.5645" + }, + { + "C": 0, + "ceiling": "5905331/1250000000", + "coordinate_calls": 0, + "decode": "zero_retention", + "kind": "centre", + "vs_selected_percent": "+179.5333" + }, { "C": 0, "ceiling": null, @@ -59,6 +77,22 @@ "kind": "family", "vs_selected_percent": null }, + { + "C": 0, + "ceiling": null, + "coordinate_calls": 32, + "decode": "d1_L2_variant", + "kind": "family", + "vs_selected_percent": null + }, + { + "C": 0, + "ceiling": "5905331/1250000000", + "coordinate_calls": 0, + "decode": "zero_retention", + "kind": "family", + "vs_selected_percent": "+179.5333" + }, { "C": 64, "ceiling": null, @@ -75,6 +109,22 @@ "kind": "centre", "vs_selected_percent": null }, + { + "C": 64, + "ceiling": "1693933/5000000000", + "coordinate_calls": 32, + "decode": "d1_L2_variant", + "kind": "centre", + "vs_selected_percent": "-79.9541" + }, + { + "C": 64, + "ceiling": "3389611/2000000000", + "coordinate_calls": 0, + "decode": "zero_retention", + "kind": "centre", + "vs_selected_percent": "+0.2811" + }, { "C": 64, "ceiling": null, @@ -90,6 +140,22 @@ "decode": "d18", "kind": "family", "vs_selected_percent": null + }, + { + "C": 64, + "ceiling": null, + "coordinate_calls": 32, + "decode": "d1_L2_variant", + "kind": "family", + "vs_selected_percent": null + }, + { + "C": 64, + "ceiling": "3389611/2000000000", + "coordinate_calls": 0, + "decode": "zero_retention", + "kind": "family", + "vs_selected_percent": "+0.2811" } ], "selected_ceiling": "8450271/5000000000" diff --git a/research/qq16-cut-retention-census/README.md b/research/qq16-cut-retention-census/README.md index b29a1e1d95..b49e7f762b 100644 --- a/research/qq16-cut-retention-census/README.md +++ b/research/qq16-cut-retention-census/README.md @@ -4,8 +4,23 @@ [PR2443](https://github.com/CrocSwap/integer-mult-bounds/pull/2443) (starship-s, head `545c05e17243c962b112b91e7f84b4c1a41de7b8`) decodes all pair-0 inputs of the conserved `F0/B_1_2` pair from 224 observed port arrays at two cuts. It -grants the retention of those arrays. This package checks which of them are -still held by a live field at a decode point of the pinned 19-event QQ16 recipe. +grants the retention of those arrays and calls its F0 record transient. This +package checks which of them are still held by a live field at a decode point +of the pinned 19-event QQ16 recipe. It answers the logical-trace part of PR2443 +open question 1 (native endpoint types stay open) and the storage term of open +question 2. + +**What is already known and what is new.** That pair 0 cannot be recovered from +final-only records under the 19-event schedule is PR2346's obstruction +(alephnan, head `653520d7`: the final-only observation map loses at least +`ceil(8|G|/7)` dimensions of pair 0's selected input). The PR2376 scope map +(commdata2338, head `157143ab`) warns against assuming that a decoder granted +the B1 cut works from final records. The qualitative d18 failure below is +consistent with, and largely implied by, that work. This package quantifies it. +New here: exact per-array counts at both decode points, the d1 split (104 live, +120 overwritten by B1), the scalar-multiple and same-port-span relaxations, +the checked recomputation leads L1/L2 with an L2-variant decoder, and the +transfer of the counts to the price3 convention. | item (cut) | arrays | live at d1 (after `B_1_2`) | live at d18 (after terminal) | first overwrite event | |---|---:|---:|---:|---| @@ -35,7 +50,9 @@ Per owner per replica, the contract therefore needs these retained copies: ### Comparison with the #2074 pricing (inherited, unreviewed) -philippeVV's four-bank finding (#2074, fork `680d0997`) says that with +philippeVV's four-bank finding (#2074; [fork](https://github.com/philippeVV/integer-mult-bounds) +commit `680d0997621a2cecfef2186ab143377658687825`, path +`research/joint-query-first-pair-catalogue/four-bank/`) says that with `C = 0` the route "pays only for in-place or single-call storage". `price.py` re-implements the `price3.py` convention (5F+4B QQ16 profile, rank-8 child plus 8 mass per coordinate-call for centre-like storage, 72 mass per new live @@ -46,18 +63,43 @@ ceiling and the C=0 centre rows for 62 and 64 coordinates. The results are in | convention | max coordinate-calls/replica with any positive saving | max still beating the selected ceiling | census demand d1 / d18 | |---|---:|---:|---| -| C=0, centre-like copy | 111 | 71 | 120 / 1688: no saving at either | +| C=0, centre-like copy | 111 | 71 | 120 / 1688: no saving at either (L2 variant: 32) | | C=0, new live family | 12 | 8 | 120 / 1688: no saving at either | | C=64, centre-like copy | 39 | 0 | none beats selected | | C=64, new live family | 4 | 0 | none beats selected | -The literal PR2443 contract needs copies at both decode points. Even the -favourable d1 point, with single-call storage, needs 120 coordinate-calls. That -is above the C=0 positive-saving break-even of 111, and above 71 for beating -the selected ceiling. **Within this convention, the literal contract fails the -stated C=0 condition.** It also exceeds #2074 Theorem B's floor of 62, which -is consistent with that theorem. This screens one contract under one inherited -price convention. It is not an impossibility theorem for QQ16 controllers. +The literal PR2443 contract needs copies at both decode points. At the +favourable d1 point the copies are single-call storage, which philippeVV's +qualitative condition allows. The failure is quantitative: 120 coordinate-calls +exceed the C=0 centre-like break-even of 111 (any saving) and 71 (beat the +selected ceiling). **Under this convention the literal contract exceeds the C=0 +centre-like break-even even though its d1 storage is single-call.** By a +dimension count this is also the floor for PR2443's d1 read set: the 104 live +reads (`y2_A`, `C`) leave 120 of the 224 pair-0 input dimensions, so any linear +record that a decoder confined to those reads can use must retain at least 120 +coordinates per owner across B1. + +Three limits on this conclusion: + +- *Copy kind.* price3 also has a `line` kind (an in-place write that adds no + new live data). It is not used here because a retained copy is new live data: + the census shows that no live field holds it. If copies were priced as `line` + writes, this screen would not reject them. +- *Pair 0 only.* PR2443 recovers pair 0 only. #2074 Theorem B's 62 is the + four-bank total (four banks at `77N/5` each, rounded up); the inherited + per-bank floor is `ceil(77N/5)`, 16 per owner at that normalisation. A complete controller must also repair + banks 1-3, which also lose a query by Theorem A, so the pair-0 demand counted + here is a favourable lower bound on a full controller's storage. +- *Literal contract only.* Lead L2 (below) gives a variant that needs only 32 + coordinate-calls at d1, below both C=0 break-evens. So this negative result is + specific to PR2443's literal read set and is not evidence against a + compressed contract. + +This screens one contract under one inherited, unreviewed price convention. It +is not an impossibility theorem for QQ16 controllers. Note also that the +convention gives a free controller (zero retention) +179.5% over the selected +ceiling at C=0 and +0.28% at C=64 (PRICE.json rows `zero_retention`), so the +C=0/C=64 choice dominates every storage figure here. ### Recomputation leads (not in-place availability) @@ -68,14 +110,24 @@ verifies both in the model. Nothing writes them afterwards, so they are live two-field sums at d1 and at d18 (identity selected terminal). PR2443's last step `y_V=x1_V+y1_V-x_V` only needs these sums. -- **L2.** At d1, `x1_U = X2_U + Y2_U - K_(1,U) ell_(1,T) x1_T`. So the 88 - `x1_S` copies could be replaced by one same-port two-field read plus an - 8-coordinate driver record. Because `B_1_2` is invertible, a decoder that may - read the whole post-B1 state of pair 0 needs no copy at d1. PR2443 excludes - `y2_U` from its reads, so that is a different contract. +- **L2.** At d1, `x1_U = X2_U + Y2_U - K_(1,U) ell_(1,T) x1_T`. The driver + `ell_(1,T) x1_T` is computable from the retained `x1_T` record, so the 88 + `x1_S` copies can be replaced by a same-port read of `Y2_U` (`X2_U = C` is + already read). The checker runs PR2443's decoder with these `x1_U` forms and + recovers all 224 pair-0 inputs from the 32 retained F0 selected arrays + (`x1_A, x1_T, y1_A, y1_T`) plus the live post-B1 reads `y2_A`, `C`, `Y2_U` + (RESULT.json `leads.L2_variant_d1`). Its storage demand is 32 + coordinate-calls. Under the inherited C=0 centre-like convention that is + storage-only +99.56% over the selected ceiling (PRICE.json row + `d1_L2_variant`); reads, their legality, chart maps and restoration are not + priced, so this is a lead, not a bound. L1 cannot replace `y1_A`/`y1_T`, + because the decoder queries them separately. Because `B_1_2` is invertible, + a decoder that may read the whole post-B1 state of pair 0 needs no copy at + all at d1. PR2443 excludes `y2_U` from its reads, so both are different + contracts. -So the census prices the literal contract, not the information need. The -compressed variant is listed below as an open question. +So the census prices the literal contract; at d1 that equals the information +floor for its read set, and only extra reads lower it. ## Model, exactness and scope @@ -100,6 +152,11 @@ compressed variant is listed below as an open question. - **Consistency check:** in this model, PR2443's ordered decoder recovers all 224 pair-0 inputs exactly, including `C=-y_U` and the two-sided `R_J` inverse. This was implemented independently; no predecessor code is imported. + It runs on the payload-constant subspace only, so it does not validate + payload-sensitive charts: ywz65's PR2456 (head `665ba8d7`) shows that + payload-constant fixtures miss the logical-D vs physical-A chart fault. The + "not live" direction of the census is unaffected, since a restriction of an + actual equality is still an equality. - **Not covered:** physical idle cover sweeps, terminal Y translations, bank padding and phase adapters. These are invertible frame changes in the inherited logical convention. They cannot make an overwritten logical value @@ -108,6 +165,9 @@ compressed variant is listed below as an open question. ## Negative controls (all must be rejected or change the receipt) +Controls 1 and 4 are claim rejections (a false statement is tested against +the computed states). Controls 2, 3, 5 and 6 mutate the pipeline. + 1. Claiming `x1_A` survives B1 in place is rejected. 2. Dropping F2 (event 3) changes the d18 census to 216 copies. Eight arrays are then live in place, and 104 are scalar multiples of live fields. @@ -133,36 +193,46 @@ Expected last lines: `PASS_NEGATIVE_CONTROLS 6`, `PASS_QQ16_CUT_RETENTION_CENSUS then `PASS_QQ16_CUT_RETENTION_PRICE_TRANSFER`. Each script recomputes its JSON and requires it to equal the committed [RESULT.json](RESULT.json) (receipt `8c57f8f5...`) and [PRICE.json](PRICE.json). Per-array rows are in -[CENSUS-ROWS.json](CENSUS-ROWS.json). Registered replay: +[CENSUS-ROWS.json](CENSUS-ROWS.json); verify.py also requires them to equal +the recomputed rows. Registered replay: `python3.12 scripts/research_package.py --package research/qq16-cut-retention-census`. The checks were run with Python 3.14.4, since 3.12 was not installed locally. Base commit `0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2`. Input pins are in [SOURCES.json](SOURCES.json). External, read-only pins: PR2443 `545c05e1`, PR2346 `653520d7`, PR2174 `f79470a7`, and philippeVV `price3.py` sha256 -`1c2ca9a4...` (fork `680d0997`). +`1c2ca9a4...` (philippeVV/integer-mult-bounds commit +`680d0997621a2cecfef2186ab143377658687825`, +`research/joint-query-first-pair-catalogue/four-bank/`). price3 is not +vendored; its three reproduction values are hard-coded in `price.py`. ## Open next questions 1. **What is the smallest retained record for a final-only (d18) decode with PR2443's read set plus legal final reads?** - *Why it matters:* the literal contract needs 1688 coordinate-calls, while - the C=0 break-even is 71. A compressed record set must also respect - #2074 Theorem B's floor of 62. - - *First step:* replace `x1_S` by the driver record (L2) and the selected - records by the conserved sums (L1), then rerun this census. + the C=0 break-even is 71. For pair 0 alone the inherited Theorem B floor + is `ceil(77N/5)` per bank, 16 at the normalisation where 62 is the + four-bank total, and a full + controller must also repair banks 1-3. + - *First step:* carry the L2 variant (32 retained arrays plus a `Y2_U` + read) through F2..F8 and the terminal with this census code. - *Blocker:* the legal native read types for former-Y endpoints and `X+Y` sums. 2. **Can a controller use the d1 decode point at all?** - - *Why it matters:* the demand there is only 120, and with full post-B1 - reads it is 0, since `B_1_2` is invertible. But a mid-schedule decode - must restore what it reads before F2. + - *Why it matters:* the demand there is 120 for the literal contract, 32 + for the L2 variant, and 0 with full post-B1 reads, since `B_1_2` is + invertible. But a mid-schedule decode must restore what it reads before + F2. - *First step:* price the CONSERVED-QQ16 inverse of B (`H_s`, `E_t`) as reads plus restoration. - *Blocker:* no priced read of `y2_U`/`X2_T` at the completed-X type. + ywz65 has a live claim (PR2443 comment, 2026-10-15 11:23Z, + `research/qq16-future-x-query`) on source-binding the native read of + `C=x2_U` at the post-B1 frame with restoration; this package defers to it. 3. **Which centre charge applies to QQ16, C=0 or C=64?** This is the maintainers' open question in #2074. Under C=64 no positive retention - budget beats the selected ceiling. + budget beats the selected ceiling; even a free controller gains only +0.28%. ## Credit @@ -175,8 +245,13 @@ threshold are from Gareth Davidson / bitplane (PR2432). The C=64 screen and the `y2_A` pricing are from 1337isnot1337 (PR2079, PR2197). Theorem B and the price3 convention are from Philippe Van Velzen (#2074, fork `680d0997`). The trace method is from Ross Richardson (PR2104). The ceiling model is -`research/complex-local-word-ceiling`. ywz65's concurrent PR2443 operator -audit is independent of this storage census. +`research/complex-local-word-ceiling`. The final-only obstruction is +alephnan's PR2346, and the contract scope map is commdata2338's PR2376 +(`157143ab`). Concurrent work: ywz65's PR2456 (head `665ba8d7`) audits +PR2443's operators with payload-sensitive fixtures, and ywz65's live claim on +the native `C` read overlaps open question 2. ToikY's PR2416 (head +`f2c93e76`) prices native retention of A-copy data at the `B_1_2[:80]` cut +(24 native lines vs 16) in a different cost model; it is not combined here. Prepared by thakrarsagar with substantial AI assistance from Claude (Anthropic, Claude Opus 5.5). No independent human review is claimed. diff --git a/research/qq16-cut-retention-census/RESULT.json b/research/qq16-cut-retention-census/RESULT.json index 4f70b407cb..4d7855ac8f 100644 --- a/research/qq16-cut-retention-census/RESULT.json +++ b/research/qq16-cut-retention-census/RESULT.json @@ -6,6 +6,13 @@ }, "leads": { "L1_selected_pair_sums_live_at_d1_and_d18": 16, + "L2_variant_d1": { + "decoder_recovers_all_224_pair0_inputs": true, + "extra_post_B1_reads_outside_PR2443_contract": { + "Y2_U": 96 + }, + "retained_F0_cut_arrays": 32 + }, "L2_x1_U_from_live_pair_plus_driver_record": 96 }, "model": "owner/payload-constant subspace (all D_s = I); exact rational linear forms in the 896 initial port arrays of four pairs; bridges and ordinary terminal per PR2346 section 1", diff --git a/research/qq16-cut-retention-census/TASK.json b/research/qq16-cut-retention-census/TASK.json index ceb6a558f8..c422f72b74 100644 --- a/research/qq16-cut-retention-census/TASK.json +++ b/research/qq16-cut-retention-census/TASK.json @@ -46,8 +46,8 @@ ] }, "scope_status": "refined", - "actual_scope": "In-place availability census of PR2443's (545c05e1) 224 observed port arrays for the unchanged conserved F0/B_1_2 pair, traced through the pinned 19-event QQ16 recipe to two decode points (after B_1_2 and after the terminal), with exact copy counts per owner per replica and their transfer to philippeVV's C=0/C=64 price convention.", - "scope_change_reason": "PR2443 open questions 1-2 ask whether a controller can retain its two-cut records and at what price. The generic C=64 screen is already recorded (#2074/PR2079, PR2197) and #2074 Theorem B gives a 62-coordinate floor; the remaining premise for the C=0 case is whether the contract's arrays are available in place or need copies, and for how many calls. This card answers only that storage term; it does not price reads, chart maps, the minor inverse or cleanup.", + "actual_scope": "In-place availability census of PR2443's (545c05e1) 224 observed port arrays for the unchanged conserved F0/B_1_2 pair, traced through the pinned 19-event QQ16 recipe to two decode points (after B_1_2 and after the terminal), with exact copy counts per owner per replica and their transfer to philippeVV's C=0/C=64 price convention. Answers the logical-trace part of PR2443 open question 1 (native endpoint types left open) and the storage term of open question 2.", + "scope_change_reason": "PR2443 open questions 1-2 ask whether a controller can retain its two-cut records and at what price. The generic C=64 screen is already recorded (#2074/PR2079, PR2197), #2074 Theorem B gives a four-bank floor of 62 (ceil(77N/5) per bank), and PR2346 already shows that final-only records lose pair-0 dimensions. The remaining premise for the C=0 case is how many of the contract's arrays are available in place and how many need copies, and for how many calls. This card answers only that storage term; it does not price reads, chart maps, the minor inverse or cleanup.", "bottleneck_link": "Retained query information and its physical access are the missing link to a composed QQ16 interface. This census shows the PR2443 contract's records are not in place at either decode point, so they must be copied or recomputed; recomputation is left open.", "budget_minutes": 60, "stop_rule": "Stop once the census of all 224 arrays at both decode points is exact and checked; if at least one array per owner must be retained across calls, record that the literal PR2443 contract fails the stated C=0 condition (scoped screen, not an impossibility theorem). Hard stop 2026-10-15T12:07:20Z.", @@ -58,21 +58,35 @@ "open_questions": [ { "question": "What is the minimum number of coordinates per owner per replica that must be retained (copied or kept as query records) so that PR2443's read set, plus legal reads of the final live state, recovers pair-0 inputs at the end of the 19-event schedule?", - "why_it_matters": "The literal contract needs 1688 coordinate-calls per replica at d18, against a C=0 break-even of 71 (centre-like price). Any compressed record set must still respect #2074 Theorem B's floor of 62; whether one fits below 71 is open.", - "first_step": "Replace the 88 x1_S arrays by the 8-coordinate driver record a1=ell_(1,T)x1_T (identity L2) and the selected arrays by the conserved pair sums (L1); recompute the coordinate-calls with the same census code.", + "why_it_matters": "The literal contract needs 1688 coordinate-calls per replica at d18, against a C=0 break-even of 71 (centre-like price). For pair 0 alone the inherited Theorem B floor is ceil(77N/5) per bank (16 where the four-bank total is 62), and a full controller must also repair banks 1-3. Whether a compressed record set fits below 71 at d18 is open.", + "first_step": "Carry the checked L2 variant (32 retained F0 selected arrays plus a Y2_U read at d1) through F2..F8 and the terminal with the same census code.", "blocked_by": "Legal native read types for X2_U+Y2_U and the final former-Y endpoints; which reads PR2443's contract excludes on purpose." }, { "question": "Is the d1 decode point (immediately after B_1_2) usable by a controller that must continue with F2..F8?", - "why_it_matters": "At d1 the copy demand is only 120 coordinate-calls, and B1 is invertible, so with a full post-B1 read no copy is needed; but a mid-schedule decode must restore the state it reads.", + "why_it_matters": "At d1 the copy demand is 120 coordinate-calls for the literal contract (the information floor for its read set), 32 for the L2 variant, and 0 with a full post-B1 read since B1 is invertible; but a mid-schedule decode must restore the state it reads.", "first_step": "Write the restoration and read cost of a mid-schedule decode at d1 using the CONSERVED-QQ16 inverse of B (H_s, E_t).", - "blocked_by": "No priced native read of y2_U / X2_T at the completed-X type; restoration accounting." + "blocked_by": "No priced native read of y2_U / X2_T at the completed-X type; restoration accounting. ywz65's live claim (PR2443 comment 2026-10-15T11:23Z, research/qq16-future-x-query) covers the native C=x2_U read at the post-B1 frame; defer to it." }, { "question": "Which centre charge applies to QQ16, C=0 or C=64?", - "why_it_matters": "Under C=64 even a free controller gains at most +0.28%; under C=0 the census break-even is 71 coordinate-calls.", + "why_it_matters": "Under C=64 even a free controller gains at most +0.28% (PRICE.json row zero_retention); under C=0 a free controller gains +179.5% and the census break-even is 71 coordinate-calls.", "first_step": "Maintainer decision on the #2074 question.", "blocked_by": "Maintainer review of the coverage-law convention." } - ] + ], + "overlap": { + "refreshed_utc": "2026-10-15T11:40Z (final refresh before submission recorded in the PR body)", + "coverage": "open PRs updated since base 0fdd7d82, gh PR search for 2443/QQ16, discussions #1163, #1166, #2074, PR2443/PR2456/PR2346/PR2416 bodies and comments, local sibling task cards; python3 scripts/find_overlap.py cache", + "nearest": [ + "PR2346 (alephnan, 653520d7): final-only obstruction; implies the qualitative d18 failure", + "PR2376 (commdata2338, 157143ab): contract scope map flags final-record decoding", + "PR2456 (ywz65, 665ba8d7): payload-sensitive operator audit of PR2443; not retention", + "ywz65 live claim 2026-10-15T11:23Z: native C=x2_U read at the post-B1 frame", + "PR2416 (ToikY, f2c93e76): native A-copy cut pricing, different cost model", + "PR2197 / PR2079 (1337isnot1337): y2_A pricing in one layout; C=64 screen", + "#2074 Theorem B (philippeVV): four-bank floor 62" + ], + "what_this_adds": "Exact per-array survival counts at d1 and d18, relaxations, checked L1/L2 leads with an L2-variant decoder, and the price3 transfer." + } } diff --git a/research/qq16-cut-retention-census/VERIFY.json b/research/qq16-cut-retention-census/VERIFY.json index 7f3c30936b..01bbc931b2 100644 --- a/research/qq16-cut-retention-census/VERIFY.json +++ b/research/qq16-cut-retention-census/VERIFY.json @@ -17,7 +17,7 @@ "{package}/verify.py" ], "timeout_seconds": 300, - "checks": "Source pins, Grams, K=R^T/4, packet F/B contract strings, the pinned 19-event recipe; PR2443 decoder recovers all 224 pair-0 inputs in the constant-subspace model; exact census of the 224 observed arrays at d1 (after B_1_2) and d18 (after the terminal); two variants; recomputation-lead identities; six negative controls; recomputed RESULT.json must equal the committed file." + "checks": "Source pins, Grams, K=R^T/4, packet F/B contract strings, the pinned 19-event recipe; PR2443 decoder recovers all 224 pair-0 inputs in the constant-subspace model; exact census of the 224 observed arrays at d1 (after B_1_2) and d18 (after the terminal); two variants; recomputation-lead identities and the L2-variant decoder (32 retained arrays plus a Y2_U read); six negative controls; recomputed RESULT.json and CENSUS-ROWS.json must equal the committed files." }, { "argv": [ @@ -27,7 +27,7 @@ "{package}/price.py" ], "timeout_seconds": 300, - "checks": "Transfers the census copy counts to philippeVV's unreviewed C=0/C=64 price3 convention with the pinned ceiling.py; recomputed PRICE.json must equal the committed file." + "checks": "Transfers the census copy counts to philippeVV's unreviewed C=0/C=64 price3 convention with the pinned ceiling.py; includes the L2-variant (32) and zero-retention rows; recomputed PRICE.json must equal the committed file." } ] } diff --git a/research/qq16-cut-retention-census/price.py b/research/qq16-cut-retention-census/price.py index a72f4f0423..e43a1c8011 100644 --- a/research/qq16-cut-retention-census/price.py +++ b/research/qq16-cut-retention-census/price.py @@ -2,8 +2,11 @@ """Map the retention census onto philippeVV's C=0 / C=64 pricing convention. This is a convention transfer, not a new cost model. The convention is -Philippe Van Velzen's `price3.py` (fork commit 680d0997, four-bank/, read on -2026-10-15; sha256 1c2ca9a4f89d7851dee6b765119f1f84f1227e30ec23f3e169aa327d2cc7f1f7), +Philippe Van Velzen's `price3.py` (https://github.com/philippeVV/integer-mult-bounds, +commit 680d0997621a2cecfef2186ab143377658687825, path +research/joint-query-first-pair-catalogue/four-bank/price3.py, read on 2026-10-15; +sha256 1c2ca9a4f89d7851dee6b765119f1f84f1227e30ec23f3e169aa327d2cc7f1f7; the three +hard-coded reproduction values below are copied from price3.json at that commit), re-implemented here in a few lines against the pinned repository `research/complex-local-word-ceiling/ceiling.py`. Its prices are unreviewed: @@ -82,7 +85,11 @@ def main(): d1 = sum(pi[k]["d1"]["copy_required"] for k in pi) # live calls held: F0 cut -> d1 spans B1 (1 call); F0 cut -> d18 spans B1,F2,...,F8 (8 calls); # B1 cut -> d18 spans F2,...,F8 (7 calls). Bridges and the terminal are not calls. - demand = {"d1": d1 * 1, "d18": f0 * 8 + b1 * 7} + demand = {"d1": d1 * 1, "d18": f0 * 8 + b1 * 7, + # L2 variant (extra Y2_U read outside PR2443's contract): 32 retained arrays for 1 call. + "d1_L2_variant": res["leads"]["L2_variant_d1"]["retained_F0_cut_arrays"] * 1, + # Free controller (no retention at all), for reference. + "zero_retention": 0} sel = cap(SEL, 64) # Convention reproduction: two rows of philippeVV's committed price3.json (fork 680d0997). if (str(sel), str(priced(0, 62, "centre")), str(priced(0, 64, "centre"))) != ( diff --git a/research/qq16-cut-retention-census/verify.py b/research/qq16-cut-retention-census/verify.py index 3f0dac506f..1a699e2608 100644 --- a/research/qq16-cut-retention-census/verify.py +++ b/research/qq16-cut-retention-census/verify.py @@ -234,11 +234,16 @@ def observations(states): return [(item, cut, f, states[cut][f]) for item, cut, f in obs] -def decoder_check(R, states, model=Model): - """PR2443's ordered decoder recovers all 224 pair-0 inputs in this model.""" +def decoder_check(R, states, model=Model, x1_U=None): + """PR2443's ordered decoder recovers all 224 pair-0 inputs in this model. + + With `x1_U` given, the decoder uses those forms for x1 on the U96 ports instead of + the retained F0-cut x1_S records (the L2 variant; see leads).""" m = model(R) s0, s1 = states[0], states[1] x1 = {p: s0[fid(0, 0, p)] for p in range(112)} + if x1_U is not None: + x1.update(x1_U) y1 = {p: s0[fid(0, 1, p)] for p in range(112)} y2A = {p: s1[fid(0, 1, p)] for p in A} C = {p: s1[fid(0, 0, p)] for p in U} @@ -290,9 +295,18 @@ def leads(R, states): need(all(lin((1, states[d][fid(0, 0, p)]), (1, states[d][fid(0, 1, p)])) == {fid(0, 0, p): 1, fid(0, 1, p): 1} for p in A + T), "conserved selected pair sums") ka = m.sect(m.query(x1, T), U) - need(all(lin((1, states[1][fid(0, 0, p)]), (1, states[1][fid(0, 1, p)]), (-1, ka[p])) == x1[p] for p in U), + l2 = {p: lin((1, states[1][fid(0, 0, p)]), (1, states[1][fid(0, 1, p)]), (-1, ka[p])) for p in U} + need(all(l2[p] == x1[p] for p in U), "x1_U from the live post-B1 pair and one 8-coordinate driver record") - return {"L1_selected_pair_sums_live_at_d1_and_d18": 16, "L2_x1_U_from_live_pair_plus_driver_record": 96} + # L2 variant at d1: the driver ell_(1,T) x1_T is computed from the retained x1_T record, so the + # decoder needs only the 32 retained F0 selected arrays (x1_A, x1_T, y1_A, y1_T) plus the live + # post-B1 reads y2_A, C = X2_U and Y2_U (Y2_U lies outside PR2443's read set). The x1_U forms + # below are built only from states[1] fields and the retained x1_T forms. + decoder_check(R, states, x1_U=l2) + return {"L1_selected_pair_sums_live_at_d1_and_d18": 16, "L2_x1_U_from_live_pair_plus_driver_record": 96, + "L2_variant_d1": {"retained_F0_cut_arrays": len(A) * 2 + len(T) * 2, + "extra_post_B1_reads_outside_PR2443_contract": {"Y2_U": len(U)}, + "decoder_recovers_all_224_pair0_inputs": True}} def det3(a, b, c): @@ -469,6 +483,8 @@ def main(): else: committed = json.loads((here / "RESULT.json").read_text()) need(committed == res, "recomputed result equals committed RESULT.json") + need(json.loads((here / "CENSUS-ROWS.json").read_text()) == rows + and digest(rows) == res["census_rows_sha256"], "committed CENSUS-ROWS.json equals recomputed rows") print(json.dumps({"totals": res["totals"], "negative_controls": sorted(res["negative_controls"])}, indent=1)) print("PASS_NEGATIVE_CONTROLS", len(res["negative_controls"])) print(res["status"]) From 1b2eee3bf1ec67e68c0b0fa7f47c7b2a66febe56 Mon Sep 17 00:00:00 2001 From: Sagar Thakrar <18622288+thakrarsagar@users.noreply.github.com> Date: Thu, 15 Oct 2026 17:21:03 +0530 Subject: [PATCH 3/3] research: cite ywz65 PR2468 native C read in QQ16 retention census Co-Authored-By: Claude Opus 5.5 --- research/qq16-cut-retention-census/README.md | 12 +++++++----- research/qq16-cut-retention-census/TASK.json | 6 +++--- 2 files changed, 10 insertions(+), 8 deletions(-) diff --git a/research/qq16-cut-retention-census/README.md b/research/qq16-cut-retention-census/README.md index b49e7f762b..83d2b42eed 100644 --- a/research/qq16-cut-retention-census/README.md +++ b/research/qq16-cut-retention-census/README.md @@ -227,9 +227,11 @@ vendored; its three reproduction values are hard-coded in `price.py`. - *First step:* price the CONSERVED-QQ16 inverse of B (`H_s`, `E_t`) as reads plus restoration. - *Blocker:* no priced read of `y2_U`/`X2_T` at the completed-X type. - ywz65 has a live claim (PR2443 comment, 2026-10-15 11:23Z, - `research/qq16-future-x-query`) on source-binding the native read of - `C=x2_U` at the post-B1 frame with restoration; this package defers to it. + ywz65's PR2468 (head `baa90ee8`, opened 11:49Z, + `research/qq16-future-x-query`) constructs a native local read of + `C=x2_U` at the post-B1 frame with restoration and leaves retained + observations open; this package defers to it for the read and supplies + the retention count it leaves open. 3. **Which centre charge applies to QQ16, C=0 or C=64?** This is the maintainers' open question in #2074. Under C=64 no positive retention budget beats the selected ceiling; even a free controller gains only +0.28%. @@ -248,8 +250,8 @@ trace method is from Ross Richardson (PR2104). The ceiling model is `research/complex-local-word-ceiling`. The final-only obstruction is alephnan's PR2346, and the contract scope map is commdata2338's PR2376 (`157143ab`). Concurrent work: ywz65's PR2456 (head `665ba8d7`) audits -PR2443's operators with payload-sensitive fixtures, and ywz65's live claim on -the native `C` read overlaps open question 2. ToikY's PR2416 (head +PR2443's operators with payload-sensitive fixtures, and ywz65's PR2468 (head +`baa90ee8`) constructs the native `C` read of open question 2. ToikY's PR2416 (head `f2c93e76`) prices native retention of A-copy data at the `B_1_2[:80]` cut (24 native lines vs 16) in a different cost model; it is not combined here. diff --git a/research/qq16-cut-retention-census/TASK.json b/research/qq16-cut-retention-census/TASK.json index c422f72b74..4a5101adfe 100644 --- a/research/qq16-cut-retention-census/TASK.json +++ b/research/qq16-cut-retention-census/TASK.json @@ -66,7 +66,7 @@ "question": "Is the d1 decode point (immediately after B_1_2) usable by a controller that must continue with F2..F8?", "why_it_matters": "At d1 the copy demand is 120 coordinate-calls for the literal contract (the information floor for its read set), 32 for the L2 variant, and 0 with a full post-B1 read since B1 is invertible; but a mid-schedule decode must restore the state it reads.", "first_step": "Write the restoration and read cost of a mid-schedule decode at d1 using the CONSERVED-QQ16 inverse of B (H_s, E_t).", - "blocked_by": "No priced native read of y2_U / X2_T at the completed-X type; restoration accounting. ywz65's live claim (PR2443 comment 2026-10-15T11:23Z, research/qq16-future-x-query) covers the native C=x2_U read at the post-B1 frame; defer to it." + "blocked_by": "No priced native read of y2_U / X2_T at the completed-X type; restoration accounting. ywz65's PR2468 (head baa90ee8) constructs the native C=x2_U read at the post-B1 frame and leaves retained observations open; defer to it for the read." }, { "question": "Which centre charge applies to QQ16, C=0 or C=64?", @@ -76,13 +76,13 @@ } ], "overlap": { - "refreshed_utc": "2026-10-15T11:40Z (final refresh before submission recorded in the PR body)", + "refreshed_utc": "2026-10-15T11:52Z", "coverage": "open PRs updated since base 0fdd7d82, gh PR search for 2443/QQ16, discussions #1163, #1166, #2074, PR2443/PR2456/PR2346/PR2416 bodies and comments, local sibling task cards; python3 scripts/find_overlap.py cache", "nearest": [ "PR2346 (alephnan, 653520d7): final-only obstruction; implies the qualitative d18 failure", "PR2376 (commdata2338, 157143ab): contract scope map flags final-record decoding", "PR2456 (ywz65, 665ba8d7): payload-sensitive operator audit of PR2443; not retention", - "ywz65 live claim 2026-10-15T11:23Z: native C=x2_U read at the post-B1 frame", + "ywz65 PR2468 (baa90ee8, opened 11:49Z): native local read of C=x2_U at the post-B1 frame; leaves retained observations open", "PR2416 (ToikY, f2c93e76): native A-copy cut pricing, different cost model", "PR2197 / PR2079 (1337isnot1337): y2_A pricing in one layout; C=64 screen", "#2074 Theorem B (philippeVV): four-bank floor 62"