Add exact rank-one center-difference sharing mechanism

research/rank1-center-delta-seeddfc2/CERTIFICATE.json

@@ -0,0 +1,140 @@
+{
+  "base_commit": "0b1cccf86e2f5132ed286a26ef0a681a495740ea",
+  "dirty_state_replay": {
+    "all_match_direct_map": true,
+    "field_domain": "x,y,p,q,scratch independently range over F2^2",
+    "inputs_and_scratch_preserved": true,
+    "states_checked": 1024,
+    "target_update_is_involution": true
+  },
+  "general_rank_one_extension": {
+    "assumption": "The rank model charges bilinear products; linear output coefficient vectors are part of each tensor atom. Frame changes, copying, precision, hosting and restoration are outside this local lemma.",
+    "saving_when_r_at_least_2": "at least r-1 children in the common-frame bilinear-rank model",
+    "statement": "If F and F+H each have bilinear rank r in one common frame, and H(x,y)=alpha(x)*beta(y)*c has rank one, then the paired dirty-target map (p,q)->(p+F,q+F+H) has rank at most r+1, versus separate rank 2r."
+  },
+  "joint_rank_certificate": {
+    "child_count_saved": 1,
+    "flattening_rank_lower_bound": 3,
+    "independent_center_ranks": [
+      2,
+      2
+    ],
+    "input_monomial_order": [
+      "x0*y0",
+      "x0*y1",
+      "x1*y0",
+      "x1*y1"
+    ],
+    "joint_rank": 3,
+    "output_slices": [
+      "p0:E00",
+      "p1:E11",
+      "q0:E00+E01",
+      "q1:E11+E01"
+    ],
+    "rank_one_atoms": [
+      {
+        "output_vector_(p0,p1,q0,q1)": [
+          1,
+          0,
+          1,
+          0
+        ],
+        "product": "x0*y0"
+      },
+      {
+        "output_vector_(p0,p1,q0,q1)": [
+          0,
+          1,
+          0,
+          1
+        ],
+        "product": "x1*y1"
+      },
+      {
+        "output_vector_(p0,p1,q0,q1)": [
+          0,
+          0,
+          1,
+          1
+        ],
+        "product": "x0*y1"
+      }
+    ]
+  },
+  "limitations": [
+    "No eligible occurrence is identified in the selected supplier.",
+    "No E8 frame, source/target hosting, recursive precision, or restoration integration is instantiated.",
+    "The all-pairs profile is a favorable sensitivity screen, not an admitted paid-word change."
+  ],
+  "maps": {
+    "F0": [
+      "x0*y0",
+      "x1*y1"
+    ],
+    "F1": [
+      "x0*y0 + x0*y1",
+      "x1*y1 + x0*y1"
+    ],
+    "difference": [
+      "x0*y1",
+      "x0*y1"
+    ],
+    "joint_update": "(p,q) -> (p+F0(x,y), q+F1(x,y)) over F2"
+  },
+  "negative_controls": {
+    "omitted_rank_one_correction": "rejected by x=01,y=10,p=q=00,scratch=11",
+    "omitted_second_output_coefficient": "rejected by same witness"
+  },
+  "optimistic_selected_profile_screen": {
+    "assumption": "All 72 two-call pairs are eligible; no source/frame/hosting/precision/restoration overhead beyond the rank-one correction.",
+    "candidate_center_per_call": 32,
+    "candidate_fixed_word_a_cap": [
+      "50198000463/15625000000000",
+      "3212672029633/1000000000000000"
+    ],
+    "candidate_profile_per_call": {
+      "1": "4825/2",
+      "2": 418,
+      "3": 432,
+      "4": 142,
+      "5": 82,
+      "8": 4
+    },
+    "candidate_relaxation_at_1_over_99": [
+      "29535762929197842580139084756942546247213159665611190253617762246073046446723/28948022309329048855892746252171976963317496166410141009864396001978282409984",
+      "59071525858395685160278169513885092494426319331222380507235524492146092893467/57896044618658097711785492504343953926634992332820282019728792003956564819968"
+    ],
+    "families": 896,
+    "m": 73,
+    "rank_mass_saved_per_pair": 63,
+    "reaches_1_over_99": false,
+    "selected_center_per_call": 64,
+    "selected_fixed_word_a_cap": [
+      "52814190909/31250000000000",
+      "1690054109089/1000000000000000"
+    ],
+    "selected_profile_per_call": {
+      "1": 2412,
+      "2": 418,
+      "3": 432,
+      "4": 142,
+      "5": 82,
+      "8": 8
+    },
+    "stages": 9,
+    "supplier_or_kappa_claim": false
+  },
+  "scope": "Two explicit F2^2 bilinear centers with a rank-one difference; arbitrary dirty output panels and untouched scratch. No selected occurrence or kappa claim.",
+  "selected_record_sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32",
+  "source_sha256": {
+    "certificates/selected-result.json": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32",
+    "docs/research/agent-task-catalog.json": "6686ad58f1fbdbc87134a78901b60fd53a20d3984355e91defbbebc9e9fa8075",
+    "docs/research/community-batch1099-review.md": "7e76d2c38e5fce30587835b7251df1430488ae4dd372611ef69a3f03f476b6cb",
+    "research/community-frontier1094-audit/ASSEMBLY.json": "1122cb3a575f8c788345fc1bf4c108ac7c3250fb81a5988671f5eb04b3ab3045",
+    "research/community-frontier1094-audit/SELECTED-SOURCE.json": "79b3de5db3dbcb9829789ba58e9e45758926031e2a7d80667a08429d369be53b",
+    "research/complex-local-word-ceiling/RESULT.json": "d91d6c46509875abf1f61de67c2609656d3dc685451299f83caa6f922493692d",
+    "research/complex-local-word-ceiling/ceiling.py": "86a1432870b3b21d8454106ec9162fddc0471472d9214c590a1420f2426cedfc"
+  },
+  "status": "PASS_RANK1_CENTER_DELTA_EXACT_LOCAL_CONSTRUCTION"
+}

research/rank1-center-delta-seeddfc2/README.md

@@ -0,0 +1,88 @@
+# Rank-one difference between dirty-output centers
+
+**Result:** an exact local construction on two-bit sources. Two rank-two bilinear
+centers whose difference has rank one admit a joint rank-three tensor. This saves
+one rank-one child against separate evaluation while preserving arbitrary dirty
+output panels and an untouched scratch panel. The claim is local to this map pair;
+it does not identify a compatible pair in the selected supplier.
+
+## Scope and evidence
+
+This refines the `persistent-boundary` card to the explicit pair in
+[TASK.json](TASK.json). The three products are `x0*y0`, `x1*y1`, and `x0*y1`,
+with output coefficient vectors `(1,0,1,0)`, `(0,1,0,1)`, `(0,0,1,1)` in target
+order `(p0,p1,q0,q1)`. The output-slice span has dimension three, so no two-atom
+joint decomposition exists. Each center separately has rank two, making the
+four-versus-three child comparison exact for this pair.
+
+The same construction gives a general local lemma: if `F` and `F+H` both have
+bilinear rank `r` in a common frame, and `H(x,y)=alpha(x) beta(y) c` is one
+rank-one tensor, the paired dirty-target map has rank at most `r+1`, versus
+`2r` for separate evaluation. It saves at least `r-1` bilinear children for
+`r >= 2` in this rank model. The output coefficient vectors are part of each
+tensor atom; frame changes, copying, precision, hosting and restoration remain
+outside the lemma and must be priced at a concrete occurrence.
+
+For the proof, write `F = sum_i alpha_i(x) beta_i(y) c_i`. Route each product
+to the paired output vector `(c_i,c_i)`, then evaluate the single correction
+product once with output vector `(0,c)`. This computes `(F,F+H)` with `r+1`
+rank-one bilinear atoms. Applying the same atom updates to arbitrary dirty
+target panels is legal because every update is XOR and therefore involutive.
+
+The verifier exhausts all 1,024 states with `x,y,p,q,scratch` independently in
+`F2^2`, compares the atom circuit to the direct bilinear map, checks the target
+update is an involution, and preserves both source inputs and scratch. Negative
+controls omit the correction or one of its two output coefficients. The exact
+receipt is [CERTIFICATE.json](CERTIFICATE.json); pinned source hashes and Git
+blobs are in [SOURCES.json](SOURCES.json).
+
+The second result is only a favorable selected-profile screen. It assumes all 72
+candidate pairs exist and every cost outside the rank-one correction is zero.
+The exact fixed-word ceiling improves from the selected upper bound
+`1690054109089/10^15` to the interval in the certificate, but remains below the
+`1/99` saving target. No supplier occurrence, frame realization, new `kappa`, or
+frontier change is established.
+
+The focused package PR is [#1838](https://github.com/CrocSwap/integer-mult-bounds/pull/1838).
+The claim and live coordination record are at
+[Discussion #1166, comment 18922942](https://github.com/CrocSwap/integer-mult-bounds/discussions/1166#discussioncomment-18922942).
+Related work includes identical-center sharing (#1708, #1748, #1791), idle-axis
+hosting (#1516), and restoration batching (#1155). The tested distinction is
+the explicitly charged rank-one tensor difference.
+
+## Reproduce
+
+From the repository root, with the pinned source tree available:
+
+```sh
+python3 -B research/rank1-center-delta-seeddfc2/verify.py
+python3 scripts/research_package.py --package research/rank1-center-delta-seeddfc2 --check-only
+python3.12 -B scripts/research_package.py --package research/rank1-center-delta-seeddfc2
+```
+
+The verifier uses exact `F2` operations and rational ceiling intervals. It is
+read-only. Python 3.12 is the repository's registered replay target; a local
+Python 3.14 replay may be used when 3.12 is unavailable, with that limitation
+reported separately.
+
+## Open next questions
+
+1. Does a pinned selected-supplier pair of same-source center tensors have an
+   exact rank-one difference? This determines whether the local child saving
+   can affect a paid profile. First step: extract one candidate pair's center
+   maps in a common source/output frame and compute the difference tensor.
+   Blocker: no occurrence is named or routed by this bounded prototype.
+2. What is the native frame, copy rank, precision, and restoration cost of the
+   correction child at a real occurrence? These determine whether the abstract
+   one-child correction retains its cost advantage. First step: instantiate one
+   source-pinned occurrence and count every interface operation. Blocker: this
+   package contains no selected E8 frame realization.
+
+## Credit
+
+Prepared by Cinna / commdata2338 with substantial OpenAI Codex assistance. No
+independent human review is claimed. Identical-center sharing is attributed to
+the related work linked above; this package supplies a rank-one-difference
+construction and exact dirty-state receipt. The selected profile and fixed-word
+ceiling inputs are attributed to their pinned repository packages in
+`SOURCES.json`. New work is Apache-2.0.

research/rank1-center-delta-seeddfc2/SOURCES.json

@@ -0,0 +1,48 @@
+{
+  "schema_version": 1,
+  "base_commit": "0b1cccf86e2f5132ed286a26ef0a681a495740ea",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "ae6a99f28aa468649eb66a361e764d769363bf11",
+      "sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "06c96f5579bb67ed1b86d334e78fbed7da6945f1",
+      "sha256": "6686ad58f1fbdbc87134a78901b60fd53a20d3984355e91defbbebc9e9fa8075"
+    },
+    {
+      "path": "docs/research/community-batch1099-review.md",
+      "usage": "provenance",
+      "git_blob": "6cb6ec061a071a06a2d18cd4dc3e9a2b05d28099",
+      "sha256": "7e76d2c38e5fce30587835b7251df1430488ae4dd372611ef69a3f03f476b6cb"
+    },
+    {
+      "path": "research/community-frontier1094-audit/ASSEMBLY.json",
+      "usage": "provenance",
+      "git_blob": "5fd676df060f3b450782fdf5ff5f6beb63a5eeb0",
+      "sha256": "1122cb3a575f8c788345fc1bf4c108ac7c3250fb81a5988671f5eb04b3ab3045"
+    },
+    {
+      "path": "research/community-frontier1094-audit/SELECTED-SOURCE.json",
+      "usage": "provenance",
+      "git_blob": "6a75493790b4eff9c4a98051ef8b01d6aad0d5a8",
+      "sha256": "79b3de5db3dbcb9829789ba58e9e45758926031e2a7d80667a08429d369be53b"
+    },
+    {
+      "path": "research/complex-local-word-ceiling/RESULT.json",
+      "usage": "input",
+      "git_blob": "77f55043a679dd722330f1e2499863e36376d9f9",
+      "sha256": "d91d6c46509875abf1f61de67c2609656d3dc685451299f83caa6f922493692d"
+    },
+    {
+      "path": "research/complex-local-word-ceiling/ceiling.py",
+      "usage": "input",
+      "git_blob": "6c0f54527d879396f689523bfde19928a9b6157c",
+      "sha256": "86a1432870b3b21d8454106ec9162fddc0471472d9214c590a1420f2426cedfc"
+    }
+  ]
+}