Certify that the fragmentation of the #4610 word is rigid under free scalar reordering (negative result, no new kappa)

docs/ci-verification.md

@@ -1,8 +1,40 @@
 # CI verification
 
-## Current selected-family replay: #4610 with #5241
+## Current selected-family replay: #5413 with #5407 and #5414
 
 The [selected record](../certificates/selected-result.json) binds conditional
+κ = 0.003027288235, the [promotion and scope](research/pr-intake-evidence/pr5413-promotion/PROMOTION.md),
+[explicit source closure](../certificates/frontier5413-source.json),
+[review validation](research/pr-intake-evidence/pr5413-promotion/VALIDATION.json), and
+[integration receipt](research/pr-intake-evidence/pr5413-promotion/INTEGRATION.json).
+
+`make frontier5413-verify` authenticates the selected source manifest, derives
+the certificate from frozen numerical evidence, and exports the complete
+three-package execution closure. It replays #5407's five-stage provider audit,
+#5413's eight-stage admission, and #5414's independent companion screen serially.
+The exported inputs are checked again afterward. Source-bound #4610/#5241 and
+earlier BIT/native/compiler/tape/analytic foundation coverage is explicitly
+reused; its historical suites are not rerun.
+
+Each package runs under an external sampled 1 GiB aggregate descendant-memory
+guard, with timeouts of 660 seconds for the provider and primary packages and
+120 seconds for the companion. On macOS the replay uses the reviewed RLIMIT_AS
+adapter; on Linux it invokes the unmodified package wrappers. The recorded
+successful local macOS replay does not establish a hosted Linux pass.
+
+The [frontier5413 workflow](../.github/workflows/frontier5413.yml) is manual-only,
+uses Python 3.12 on Ubuntu, materializes the declared source closure, and uploads
+receipts and logs. Its status is separate from local validation and recorded in
+the integration receipt. Routine donor PRs do not launch this selected replay.
+
+`make selected-record-check` verifies metadata and source/proof hashes. It does
+not execute the operators or prove the five inherited framework assumptions.
+The finite checks do not establish the full integer multiplication theorem,
+and the uniform word remains unmaterialized.
+
+## Historical selected-family replay: #4610 with #5241
+
+The historical [selected record](../certificates/checkpoints/frontier4610.json) binds conditional
 κ = 0.0030217758, the [review](research/pr-intake-evidence/pr4610/PROOF-REVIEW.md),
 [explicit source closure](../certificates/frontier4610-source.json),
 [review validation](research/pr-intake-evidence/pr4610/VALIDATION.json), and

research/fragmentation-reorder-rigidity/README.md

@@ -0,0 +1,114 @@
+# The fragmentation of the #4610 word is rigid under free scalar reordering
+
+**Scoped negative result; no new κ.** The selected record is unchanged.
+
+[#5226](../fragmentation-ceiling/README.md) (`fragmentation-ceiling`) prices the whole gap between Cao Yifan's
+final [#4610](../kappa-round3-warp-20261022/README.md) word and the +0.05 % bar as fragmentation loss: Λ = 23.86 per
+call, where Λ_f = Σ_j rank_j^t − R_f^t sums over the climbs of each field (Theorem B there). Its ship test asks which
+scalar-program changes can merge climbs. #4993 and #4610's own MILP re-chose frames at a **fixed chronological
+order** and found nothing; #4610 lists "change scalar chronological order" as open; `cao-trace-retiming-20261023`
+compresses commuting ADDs at fixed chronology and keeps every climb; `fusion-pair-scalar-rewiring` (#5422) shows
+no consecutive pair of rank-1 climbs can be fused by free same-frame rewiring.
+
+This package frees the **order**: scalar operations may be rescheduled anywhere their value dependencies allow,
+every field's frame chain and every contact's common frame are re-chosen jointly, and the eight owned-centre
+reads may move along their source chains. Under these rules **no intermediate level of any field can be
+removed at a gain**: every admissible re-routing of every one of the 2,526 droppable levels is enumerated
+(518,315 re-routings) and each is either infeasible or relocates a centre read to the full frame, which raises the
+bill by 0.983. The fragmentation of #4610 is a property of its operation set and centre interface, not of its schedule.
+
+## 1. Model (the retained frame contract, order freed)
+
+| rule | statement | source |
+|---|---|---|
+| chains | a field occupies a nested chain of binary subspaces S_f < F_1 < … < T_f; a climb costs its dimension gap (H1–H2 of #5226) | #4610 contract, #5226 §0 |
+| contacts | a two-field ADD/COPY happens at one common frame of both chains, with S_d + S_s ≤ F ≤ T_d ∩ T_s | one common frame per ADD (#5226 H1; `format-limits-2` S1) |
+| centre | a COPY C0 ← source may sit at any frame of the source chain of dimension ≥ 1 (the transport to frame 0 then costs that dimension); the 176 deliveries target += C0 at frame 0 are fixed, as are the 8 centre transports' endpoints | `native_extensions.literal_replay` checks the field's frame at every C0 contact |
+| order | scalar ops, warps, centre transports and adapters keep their value dependencies (write/read and write/write conflicts; ADDs into one destination commute); the markers `zero_frame_precondition`, `full_frame_cleanup`, `done` are barriers (the second interpreter needs the cleanup block last); every native warp stays anchored between its two frames; along a field, contacts occur in non-decreasing chain order (no descents) | exact interpreters of #4610; `verify_buffers.replay` |
+| fixed | operation set, coefficients, native maps, all 632 field endpoints, the 12 fields that revisit a frame | scope |
+
+A **level** is an intermediate frame of a chain that hosts at least one contact. Dropping it means re-routing all
+its contacts to other frames of the chain (a frame may be inserted into a partner's chain if nested there) and
+merging the two adjacent climbs into one; by strict concavity every merge lowers Λ. Feasibility of a re-routing is
+decided exactly: the operation DAG plus the per-field level order must stay acyclic (Pearce–Kelly incremental check).
+
+## 2. Results (`verify.py`, standard library, about 2 minutes)
+
+| # | statement | value |
+|---|---|---|
+| 1 | word census: 632 fields (224 mains, 408 helpers), 17,453 scalars, 3,290 climbs; profile {1: 2201, 2: 412, 3: 510, 4: 127, 5: 40} + 8 centre; Λ(t₀) at the word's root | **23.8626** (= #5226) |
+| 2 | contacts by common-frame dimension: 7,622 at dim 0, 4,808 at dim 9, **3,659 at intermediate dimensions** (these create Λ) | |
+| 3 | dependency DAG of the 18,159 operations (with the three barriers): critical path | **694** of 18,159 (order is loose; without barriers 493, median slack ≈ 50 positions) |
+| 4 | levels forced by the partners' **endpoints** alone (contact can neither be deferred to the next frame nor advanced to the previous one by endpoint containment) | **12 of 2,754** |
+| 5 | levels forced by the partners' **exact chains** (one-field-at-a-time: the next or previous frame of f must appear in the partner's chain) | **2,437 of 2,754** (Λ ≥ 19.1 with partner chains fixed) |
+| 6 | **exact rules, joint re-routing enumerated** over the 2,526 droppable levels (the 12 revisiting fields and the warp frames excluded): 518,315 re-routings tried; 322 levels have no admissible re-routing; 2,196 levels: every re-routing closes a cycle; 8 levels: feasible only by moving the centre read to the full frame, bill +0.983 each | **0 bill-improving drops** |
+| 7 | control: centre interface ignored (C0 contacts not level-bound) | **51 improving drops** (test is live) |
+| 8 | recorded annealing with multi-step moves (insert a frame, re-route, drop), 37 M moves over three runs | best Λ = word; centre reads stay at dimension 8 |
+
+Rows 4–5 say that neither endpoints nor dependencies pin the fragmentation; row 6 says the joint structure does:
+the chains of a field and of its partners pin each other, and the centre interface (a source stands in a
+dimension-8 frame when C0 copies it, a target at frame 0 when C0 delivers) fixes the moments around which the
+rest cannot move. The only feasible drops are the eight centre-read levels themselves, and only by reading the
+centre in the full frame (transport rank 9 instead of 8). Row 7 is why earlier searches that forgot the centre
+interface reported Λ ≈ 23.45 (+1 % κ): those states are rejected by the exact interpreters.
+
+### What Λ would buy (kap-family controller formula of #5226 `verify.py`, p and a re-optimised)
+
+| per-call profile | κ (best p, a) | κ at p16 a7 |
+|---|---|---|
+| the word | 0.0030217759 (p16 a7) | 0.0030217759 |
+| mains one climb each (rank 8) | 0.0037103 (p13 a6) | 0.0036997 |
+| helpers one climb each (rank R_f) | 0.0051074 (p9 a4) | 0.0049744 |
+| Λ = 0 | **0.0081386 (p5 a2)** | 0.0071457 |
+
+So the kap family with centre 8 × 8, p − 1 query shears per port, idle at address width and zero fragmentation would
+reach 0.0081; the entire distance from 0.00302 to that number is Λ, and this package shows that none of it is
+available by rescheduling the #4610 word.
+
+## 3. Reproduce
+
+```sh
+python3.12 -I -B research/fragmentation-reorder-rigidity/verify.py
+python3.12 -I -B research/fragmentation-reorder-rigidity/test_verify.py
+python3.12 -B scripts/research_package.py --package research/fragmentation-reorder-rigidity
+```
+
+Expected marker: `PASS_FRAGMENTATION_REORDER_RIGIDITY`. `verify.py` pins both inputs by SHA256, rebuilds the model
+from the word, enumerates the re-routings, runs the control and the kap-family table, and compares
+[RESULT.json](RESULT.json) exactly. `--write` regenerates `RESULT.json` (authoring only). `test_verify.py` rejects a
+drifted input hash, a corrupted climb rank, a contact frame mismatch and a tampered result, and re-runs the live
+control. The recorded searches are in [search/](search/README.md).
+
+## 4. Scope and limits
+
+- The claim is about the frozen #4610 word: its operation set, coefficients, native maps and field endpoints.
+  A different operation set (for example the ADD-compressed word of `cao-trace-retiming-20261023`), new native
+  maps, changed helper endpoints, descents, or a different centre delivery frame are outside it. Warps keep their
+  two frames (72 fields carry one), and the 12 fields that revisit a frame are left as in the word.
+- "Level drop" is the single-merge move; multi-step moves were explored by annealing only (row 8, RECORDED). The
+  exhaustive certificate is for single drops with every admissible re-routing of their contacts, pruned only by
+  the necessary condition that an operation which must precede another (value dependency) cannot sit at a higher
+  frame of the same field.
+- The frame model is the one the exact interpreters of #4610 check (frames at contacts, nested climbs, C0 frames,
+  final frames). No physical phase, admission or outer-ledger replay was run, since no word is proposed.
+- This is a finite certificate on one word, not a floor for the family: Λ = 0 words are not excluded.
+
+## Open next questions
+
+1. **Skeleton-free floor.** Does every scalar synthesis of the #4610 endpoint identity with one common frame per ADD
+   need a stated number of intermediate levels per main field? First step: the chain-cover LP over the contact
+   hypergraph with free frames (the one-field relaxations here force nothing, so the floor must use the joint
+   structure and the centre interface).
+2. **Other operation sets.** Run the same enumeration on the compressed word of `cao-trace-retiming-20261023`
+   (151 fewer ADDs, same climbs): removed contacts may unpin levels.
+3. **Centre delivery frame.** The deliveries at frame 0 are fixed here because the 22 targets' frames meet the
+   source frame only in 0 (`owned-centre-wire-floor`); a changed delivery contract is a changed mechanism.
+
+## Credit
+
+Cao Yifan (intqwq), #4610, the word and its exact interpreters; DreamingOfClouds, #5226, the fragmentation
+decomposition and ship test whose kap-family formula is reused; the `cao-trace-retiming-20261023` author (ahrazzle)
+and Cinna Davis, #4692, for the fixed-chronology compression line; #4993 for the fixed-order frame search; Dugongue,
+#4534, and `owned-centre-wire-floor` (#5060) for the centre wire; the `fusion-pair-scalar-rewiring` package (#5422)
+for the pairwise fusion certificate. Prepared by Mark (Matarener) with substantial Claude Code (Claude) assistance.
+Apache-2.0.

research/fragmentation-reorder-rigidity/RESULT.json

@@ -0,0 +1,165 @@
+{
+ "climb_profile": {
+  "1": 2201,
+  "2": 412,
+  "3": 510,
+  "4": 127,
+  "5": 40
+ },
+ "contacts_by_dimension": {
+  "0": 7622,
+  "1": 582,
+  "2": 449,
+  "3": 316,
+  "4": 982,
+  "5": 345,
+  "6": 240,
+  "7": 448,
+  "8": 297,
+  "9": 4808
+ },
+ "control_no_centre": {
+  "cycle": 2153,
+  "feasible": 51,
+  "first_drops": [
+   [
+    8,
+    274,
+    -0.007537
+   ],
+   [
+    9,
+    624,
+    -0.007537
+   ],
+   [
+    11,
+    621,
+    -0.007537
+   ],
+   [
+    16,
+    279,
+    -0.006778
+   ],
+   [
+    17,
+    619,
+    -0.007537
+   ],
+   [
+    18,
+    254,
+    -0.007537
+   ],
+   [
+    20,
+    280,
+    -0.006778
+   ],
+   [
+    22,
+    279,
+    -0.007537
+   ],
+   [
+    23,
+    280,
+    -0.007537
+   ],
+   [
+    26,
+    621,
+    -0.007537
+   ]
+  ],
+  "improving": 51,
+  "levels": 2526,
+  "no_plan": 322,
+  "plans": 517771
+ },
+ "dag": {
+  "critical_path": 694,
+  "edges": 204174,
+  "ops": 18159
+ },
+ "exact": {
+  "cycle": 2196,
+  "feasible": 8,
+  "feasible_drops": [
+   [
+    9,
+    624,
+    0.983017
+   ],
+   [
+    11,
+    621,
+    0.983017
+   ],
+   [
+    57,
+    274,
+    0.983017
+   ],
+   [
+    81,
+    619,
+    0.983017
+   ],
+   [
+    92,
+    254,
+    0.983017
+   ],
+   [
+    224,
+    279,
+    0.983017
+   ],
+   [
+    240,
+    280,
+    0.983017
+   ],
+   [
+    256,
+    281,
+    0.983017
+   ]
+  ],
+  "levels": 2526,
+  "no_plan": 322,
+  "plans": 518315
+ },
+ "forced_by_partner_chains": 2437,
+ "forced_by_partner_endpoints": 12,
+ "kap_family": {
+  "helpers_one_climb": {
+   "a": 4,
+   "kappa_best": "0.0051074492",
+   "kappa_p16a7": "0.0049744372",
+   "p": 9
+  },
+  "lambda_zero": {
+   "a": 2,
+   "kappa_best": "0.0081385514",
+   "kappa_p16a7": "0.0071456789",
+   "p": 5
+  },
+  "mains_one_climb": {
+   "a": 6,
+   "kappa_best": "0.0037103076",
+   "kappa_p16a7": "0.0036996562",
+   "p": 13
+  },
+  "word": {
+   "a": 7,
+   "kappa_best": "0.0030217759",
+   "kappa_p16a7": "0.0030217759",
+   "p": 16
+  }
+ },
+ "lambda_word": 23.8626371,
+ "levels_with_two_field_contacts": 2754
+}

research/fragmentation-reorder-rigidity/SOURCES.json

@@ -0,0 +1,48 @@
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