Source-bound OR-Tools screen for T740 idle-axis reassignment

research/idle-star-paired-axis-census/README.md

@@ -1,22 +1,46 @@
-# Paired idle-axis transfers do not repair the T740 star profile
+# T740 idle-axis reassignment: exact transfer census and CP-SAT screen
 
-**Scoped negative result; no new κ or admitted supplier.** PR #3184 claims a conditional κ of `0.001730189061233850760095…` from redistributing idle rank-48 axes. PR #3187 supplies an exact physical-operator counterexample to its first committed one-stream move. This package checks the most direct symmetry repair: move the same residual axis on both channels of a child pair, so the phase on that pair is scalar, then transfer it to another pair.
+**Scoped negative result; no new κ or admitted supplier.** PR #3184's replica-0/port-0 star is one source-pinned move checked here. At the final live-overlap snapshot (2026-10-17 18:20 UTC), the latest open conditional claim in this branch was PR #3200 at `0.001734807021726127552033`; the selected κ remains `0.001672660197076918`. This package does not validate or refute PR #3200's complete allocation or invoice. PR #3187 supplies an exact physical-operator counterexample to PR #3184's first committed star move. This package extends that check to every eligible one-axis transfer and paired transfer on four rank-48 children, independently replays PR3184's actual replica-0/port-0 star, and screens assignment optima with OR-Tools.
 
 ## Result
 
-Using the authenticated PR3148 T740 fill (`SHA256 8f4d6965…e00`), we checked all 112 port recipes for owner replica zero. A candidate moves an axis present in both residual children 8 and 10 to both children 12 and 13, or makes the reverse transfer. It must be orthogonal to every original axis of both destination children, including hosted axes, so the move changes child ranks rather than replacing a nonorthogonal destination direction.
+Using the authenticated PR3148 T740 fill (`SHA256 8f4d6965…e00`), we checked all 112 port recipes for owner replica zero. A single-axis candidate moves one residual axis from one of children 8, 10, 12 or 13 to another, and must be orthogonal to every original destination axis, including hosted axes. A paired candidate moves the same axis on both streams of child pair `(8,10)` to both streams of `(12,13)`, or in reverse, under the same destination rule.
 
 The exact eight-stream replay found:
 
-- **2,688** eligible forward transfers; all 2,688 change the physical operator at the moved axis character.
-- **2,688** eligible reverse transfers; all 2,688 change the physical operator at the moved axis character. Each of the 112 recipes has 24 candidates in each direction.
+- **21,504** eligible single-axis transfers; all 21,504 change the physical operator at the moved axis character (**192 per port**).
+- **2,688** eligible forward paired transfers and **2,688** reverse paired transfers; all 5,376 change the operator (**24 per port in each direction**).
 - A 147-mode baseline control passes for port 0, and the zero-character identity passes for all ports. The complete fill journal and payload authenticate, and a mutated journal preimage is rejected.
 
-For a concrete witness, port 0 and axis 7 change six entries of the exact Gaussian-integer matrix. For example, entry `(0,0)` changes from `[0,-1]` to `[1,0]`. `RESULT.json` contains the full before/after matrices and per-port counts.
+For a concrete single-axis witness, port 0 moves axis 7 from child 8 to child 12. The baseline and overlay differ in three matrix entries; `(1,1)` changes from `[0,-1]` to `[1,0]`. `RESULT.json` contains the full before/after matrices and per-port counts for both witness types.
 
-This also rejects every simultaneous nonempty set of transfers **within this restricted class**. Axes eligible in one direction are orthogonal to the complete destination basis; each source residual basis is orthonormal. Thus all selected axes, in both directions, are pairwise orthogonal. At the character equal to any one selected axis, every other moved phase is inactive, leaving the same one-transfer counterexample.
+Within the paired-transfer family, eligible axes are pairwise orthogonal: each source residual basis is orthonormal, and forward candidates are orthogonal to the full reverse destination basis. At the character equal to any one selected axis, every other moved phase is inactive, so any simultaneous nonempty set of those paired transfers retains a one-transfer counterexample.
 
-This does not cover matched swaps that remove a nonorthogonal destination axis, longer cycles, other child/time pairs, nonzero replicas, or all operator-preserving assignments. It claims no general obstruction. The selected record and frontier are unchanged.
+The same isolation argument covers every **same-centre star** among children 8, 10, 12 and 13 in the audited owner-replica-0 recipes. PR3184 chooses distinct moved axes from one orthonormal donor basis; each leaf must already be orthogonal to its incoming axes. At the character equal to any moved axis, all the other moved phases are inactive, so the star's operator equals that single-axis overlay. Since the exact census rejects every eligible single-axis overlay, no nonempty star in this class preserves the operator.
+
+We also replayed PR3184's pinned `replica=0, port=0` star from commit `6faefe1`: child 10 sends axes `[16,32,64]` to child 12 and `[128,256,4096]` to child 13, giving ranks `[48,42,51,51]` on children `(8,10,12,13)`. At character 16, the full star replay equals its isolated `10→12` single move and differs from baseline in three matrix entries. `RESULT.json` stores the full matrices. This independently reproduces the physical mismatch and explains why changing the other five axes in that star cannot repair it.
+
+## OR-Tools assignment search
+
+To test whether cycles could evade those one- and two-axis screens, `ortools_screen.py` models each port's 192 residual-axis tokens as an assignment to children 8, 10, 12 and 13. It preserves the token multiset, fixed hosted axes and pairwise GF(2) orthogonality, and caps each resulting child rank at 51. CP-SAT minimizes the local moment surrogate `Σ r^(1-a)` at `a = 0.00167546`, then minimizes the number of moved tokens. The exact eight-stream replay screens each port's minimum-move optimum at the 73 unit characters, the moved axes, their pairwise XORs and 72 adjacent-pair characters; it stops at the first mismatch.
+
+All 112 port models were optimal. Each found the same best rank profile `[51,51,51,39]` from `[48,48,48,48]`, with 12 moved tokens. For those four rank terms, the surrogate falls by `0.0019571899` (about `1.026×10⁻⁵` relative). Every nominated assignment changes the exact operator at its first tested mismatch, on character `1`, `2` or `32`. The strongest structural profile is therefore not an admissible κ improvement. This search tests one minimum-move representative per port; it does not rule out another assignment with the same profile that preserves the operator. No full provider moment, κ or supplier admission is claimed.
+
+To reproduce the optional artifact, use Python 3.10.12 with OR-Tools 9.11.4210 and run `python3.10 -B research/idle-star-paired-axis-census/ortools_screen.py > research/idle-star-paired-axis-census/ORTOOLS-RESULT.json`. The registered exact-replay package does not depend on OR-Tools. `ORTOOLS-RESULT.json` records the solver candidates and their first exact replay counterexamples.
+
+## Exact-coordinate CP-SAT upper screen
+
+The original assignment model optimizes rank without enforcing physical equality. The optional `operator_ortools_screen.py` instead asks whether any rank-changing assignment can pass the exact operator test on all 73 coordinate Fourier characters, before considering a moment objective. For each port it enumerates all 256 phase-delta vectors in `Z4^4` at each coordinate character using the exact Gaussian-integer replay. In every one of the 112 port recipes, only the zero delta preserves the matrix at each character. The SHA256 of each port's complete 73-table receipt is `ed9ef60a17efb46b44a064986acf28935c7ab07a46ddc8007dc802bbc8200a83`.
+
+CP-SAT then asks for `max(child rank) >= 49` while assigning the 192 residual-axis tokens arbitrarily among children `(8,10,12,13)`, fixing hosted axes, keeping final child bases orthonormal and capping rank at 51. It deliberately omits per-axis translation and commuting restrictions, so its assignment model is a superset of the physically eligible moves. All 112 models are `INFEASIBLE`. Since a truly operator-preserving reassignment must preserve these 73 exact matrices, this rules out a rank change in this four-child, owner-replica-zero assignment class under the fixed inventory and schedule. It is a finite-mode result, not an all-character symbolic proof or a theorem about other owner replicas, children, schedules or suppliers.
+
+Reproduce the optional 47-minute run with Python 3.10.12 and OR-Tools 9.11.4210:
+
+```sh
+python3.10 research/idle-star-paired-axis-census/operator_ortools_screen.py
+```
+
+The result is recorded in `OPERATOR-ORTOOLS-RESULT.json`; this search is kept outside the registered replay so normal package CI does not require OR-Tools or a long run. Related work was posted during this investigation: [PR #3204](https://github.com/CrocSwap/integer-mult-bounds/pull/3204) claims a broader written four-site rank-rigidity proof under the fixed schedule, and [PR #3220](https://github.com/CrocSwap/integer-mult-bounds/pull/3220) analyzes added paid phase-child repairs in a bounded domain. This CP-SAT result is only a finite-coordinate cross-check on the source-bound owner-zero fill; it does not replace #3204's proof or settle the wider repair question in #3220. The selected record and frontier are unchanged.
 
 ## Reproduce
 
@@ -27,12 +51,12 @@ python3 scripts/research_package.py --package research/idle-star-paired-axis-cen
 python3.12 scripts/research_package.py --package research/idle-star-paired-axis-census
 ```
 
-The verifier independently implements the exact eight-stream Gaussian-integer replay. Live main inputs are pinned in `SOURCES.json`; the retained fill, journal and provider table are checked against the SHA256 and Git-blob IDs recorded from PR3148. The original PR3133 notice and credits are retained under `vendor/`.
+The verifier independently implements the exact eight-stream Gaussian-integer replay. Live main inputs are pinned in `SOURCES.json`; the retained fill, journal and provider table are checked against the SHA256 and Git-blob IDs recorded from PR3148. PR3184's complete star-move artifact is retained and pinned to its exact head for the added witness. The original PR3133 notice and credits are retained under `vendor/`.
 
 ## Open next questions
 
-See the structured tasks in [TASK.json](TASK.json). The nearest continuation is to enumerate matched swaps or short cycles in the 48-by-48 cross-Gram graph and test whether they can create net rank imbalance without changing the full stream operator. A different child/time pair needs its own exact insertion-to-insertion intertwiner and source-bound replay.
+See the structured tasks in [TASK.json](TASK.json). The four-child owner-replica-zero slice has no rank-changing assignment passing even the 73 coordinate modes in the broader CP-SAT relaxation. PRs #3204 and #3220 cover the broader four-site rigidity and bounded paid-repair questions, respectively; do not duplicate those scopes. A distinct next direction is another child/time pair or owner replica; it needs its own insertion-to-insertion intertwiner and source-bound replay, and should be priced before a large search.
 
 ## Credit
 
-The physical-stream criterion and the first exact PR3184 counterexample are due to Nick Petalas in [PR #3187](https://github.com/CrocSwap/integer-mult-bounds/pull/3187). The T740 fill and 145-row exchange journal are from Jeremy Diviney’s [PR #3148](https://github.com/CrocSwap/integer-mult-bounds/pull/3148); the underlying fill/provider notice and credits are retained unchanged from PR3133 in `vendor/`. The challenged profile claim is Rohan Arun’s [PR #3184](https://github.com/CrocSwap/integer-mult-bounds/pull/3184). Recipe, template, plan and dispatch retain their PR2979/selected-supplier lineage. This package adds an independently written exact replay and an exhaustive, source-bound census of one paired rank-changing transfer family. Prepared by OpenAI Codex with substantial AI assistance; no independent human or proof-assistant review is claimed. New work is Apache-2.0.
+Gonzalo Mier’s [PR #1252](https://github.com/CrocSwap/integer-mult-bounds/pull/1252) already gives a commuting three-axis exchange for selected #1094 children. Nick Petalas’s [PR #3187](https://github.com/CrocSwap/integer-mult-bounds/pull/3187) supplies the physical-stream criterion and first exact counterexample to the current PR3184 move. The T740 fill and 145-row exchange journal are from Jeremy Diviney’s [PR #3148](https://github.com/CrocSwap/integer-mult-bounds/pull/3148); the underlying fill/provider notice and credits are retained unchanged from PR3133 in `vendor/`. The challenged profile claim is Rohan Arun’s [PR #3184](https://github.com/CrocSwap/integer-mult-bounds/pull/3184). Recipe, template, plan and dispatch retain their PR2979/selected-supplier lineage. This package adds an independently written exact replay, a source-bound transfer census and an optional OR-Tools candidate search. Prepared by OpenAI Codex with substantial AI assistance; no independent human or proof-assistant review is claimed. New work is Apache-2.0.