Mister-Meeseeks · Oct 25, 2026 · Oct 25, 2026
diff --git a/research/p104-commuting-contact/CLAIM.md b/research/p104-commuting-contact/CLAIM.md
@@ -0,0 +1,22 @@
+# CLAIM — P104 commuting-contact cascade on the PR #5580 word
+
+Base: canonical main `5e0052ca0aa3036a3afa8b0438927377c8d97d53`, priority revision 7.
+Exact construction input: [PR #5580](https://github.com/CrocSwap/integer-mult-bounds/pull/5580) at `6efa248cf456d6101d757e9d09ba29711d18a13a` (`research/p104-event-contact-step`, conditional $\kappa = 0.00308189$).
+
+Question: PR #5580 explicitly left open whether a changed scalar event order within commuting windows can improve the complete paid profile beyond its fixed-order invoice ceiling `(0.00308189496866, 0.00308189496867)`. Because PR #5561, PR #5569, and PR #5580 preserved the exact linear order of the 21,686 scalar instructions from PR #5551, early moves of main ports `113` and `198` to 1-plane `597` (`[82]`) at events `13524` and `13528` (to read helper `710`) trapped subsequent commuting `ADD` writes into `198` (from `648, 649, 650, 652`) and into `113` (from `531`) at frame `597`.
+
+Result:
+1. **Stage A (Fixed-Endpoint Supporting Word `WORD-FIXED-ENDPOINTS.json.gz`, $\kappa = 0.00308415$):** Commuting `13625, 13628, 13631, 13634` (`198 += ±1/2 * 648/649/650/652`) before `13528` (`MOVE 198: 3 -> 597`) to frame `3` (`0D`) vacates frame `597` (`1D`) on all four helpers `648, 649, 650, 652`, collapsing `3 (0D) -> 597 (1D) -> 120 (5D)` (`H1 + H4`) into `3 (0D) -> 120 (5D)` (`H5`). All 735 `initial` and `final` frames and all 527 helper targets remain identical to PR #5580. Local paid delta: `-4 H1 - 4 H4 + 4 H5` (`-72` complete paid calls, `66,852 -> 66,780`), raising the raw crossing to `(0.00308415555080, 0.00308415555081)` (`+2.26058214e-6` over PR #5580).
+2. **Stage A+B (Headline Cascade Word `WORD.json.gz`, $\kappa = 0.00308520$):** Commuting `13806` (`113 += 531`) before `13524` (`MOVE 113: 3 -> 597`) to frame `3` (`0D`) allows all three initial read contacts of helper `531` (`13806` with `113`, `13843` with `197`, and `14404` with `507`) to execute at frame `3` (`0D`) with `initial[531] = 3`. Because `197` remains at `3` (`0D`) after `13843`, its next contact `13846` (`197 += 319`) demotes from 3-plane `617` (`[30, 44, 76]`) to 2-plane `355` (`[30, 44]`), vacating `617` on both `197` and `319` and vacating `597` on `531, 197, 507`. Combined local paid delta vs PR #5580: `-8 H1 - H3 - 2 H4 + 4 H5` (`-126` complete paid calls, `66,852 -> 66,726`), with local helper target delta `-H8 + H9` (productive fields `12,814` and rank-mass surplus `760` unchanged), raising the raw crossing to `(0.00308521055201, 0.00308521055202)` and certifying **conditional $\kappa = 0.00308520$** at `TESTED = 0.0030852005` (`+3.31558335e-6` raw over PR #5580).
+
+```json
+{
+  "schema": "integer-mult-coordination/v1",
+  "kind": "CLAIM",
+  "task": "scalar-to-moment",
+  "scope": "P104 commuting-write contact cascade on the PR5580 word; complete paid-profile step",
+  "base": "5e0052ca0aa3036a3afa8b0438927377c8d97d53",
+  "expiry": "2026-10-25T23:59:59+00:00",
+  "artifact": "research/p104-commuting-contact"
+}
+```
diff --git a/research/p104-commuting-contact/LITERAL-CHANGES.diff b/research/p104-commuting-contact/LITERAL-CHANGES.diff
@@ -0,0 +1,31 @@
+--- inputs/pr5580-pricing.py	2026-10-25 20:25:29.002478680 +0000
++++ pricing.py	2026-10-25 21:03:53.929660636 +0000
+@@ -11,8 +11,8 @@
+ from fractions import Fraction as Q
+ import local as L
+
+-KAPPA, TESTED = Q('.00308189'), Q('.0030818905')
+-PREVIOUS = Q('.00308181')
++KAPPA, TESTED = Q('.00308520'), Q('.0030852005')
++PREVIOUS = Q('.00308189')
+
+
+ def encode(x):
+@@ -61,7 +61,7 @@
+             second_p[8*(j+1)] += 208
+     L.need((targets,paid) == (second_t,second_p), 'Independent full invoice')
+     L.need(max(targets) == 145 and max(paid) == 72, 'Maximum recursive ranks')
+-    L.need(sum(targets.values()) == 12814 and sum(paid.values()) == 66852, 'Complete field and call counts')
++    L.need(sum(targets.values()) == 12814 and sum(paid.values()) == 66726, 'Complete field and call counts')
+     L.need(sum(r*n for r,n in targets.items())-sum(r*n for r,n in paid.items()) == 760, 'Complete rank surplus')
+     return targets,paid,counts
+
+@@ -139,7 +139,7 @@
+     L.need(wrong_cutoff[0] > 1, 'Old cutoff fails with this helper inventory')
+     bad=outer_module.ledger(dict(params,bit_saving=Q('.0027')))
+     L.need(any(x <= 0 for x in bad['strict_checks'].values()), 'Insufficient BIT contract rejected')
+-    return encode({'kappa':KAPPA,'kappa_decimal':'.00308189','previous_open_pr5569':PREVIOUS,'gain':KAPPA-PREVIOUS,
++    return encode({'kappa':KAPPA,'kappa_decimal':'.00308520','previous_open_pr5580':PREVIOUS,'gain':KAPPA-PREVIOUS,
+                    'relative_gain_percent':100*(KAPPA/PREVIOUS-1),'raw_root_interval':[lower,upper],
+                    'raw_headroom':[lower-KAPPA,upper-KAPPA],'margin_at_previous':E.display(margin(PREVIOUS)),
+                    'targets':T,'paid':P,'productive_fields':sum(T.values()),'paid_calls':sum(P.values()),
diff --git a/research/p104-commuting-contact/PROOF.md b/research/p104-commuting-contact/PROOF.md
@@ -0,0 +1,75 @@
+# Proof of the P104 Commuting-Contact Cascade ($\kappa = 0.00308520$)
+
+This package modifies the [PR #5580](https://github.com/CrocSwap/integer-mult-bounds/pull/5580) P104 word (`research/p104-event-contact-step`, pinned at `6efa248cf456d6101d757e9d09ba29711d18a13a`) by commuting independent `ADD` instructions across two 1-plane transport barriers at frame `597` (`[82]`, $\dim 1$). Every scalar instruction, register operand, and dyadic coefficient is preserved; only the relative order of commuting `ADD` operations and their chart labels change.
+
+## 1. Stage A: Fixed-Endpoint Commuting Writes on Port `198` and Helpers `648, 649, 650, 652`
+
+In the PR #5580 word, main port `198` stays at the 0-dimensional origin chart `3` (`[]`) from initialization through event `13527`, receiving only `ADD` writes (`198 += c * s`). At events `13528..13634`, the relevant events on `198` and helpers `648, 649, 650, 652` are:
+
+```text
+13528: ['MOVE', 198, 3, 597, False]
+13529: ['ADD', 198, 710, '2', 597]
+13623: ['ADD', 205, 648, '-1/2', 3]
+13624: ['MOVE', 648, 3, 597, False]
+13625: ['ADD', 198, 648, '1/2', 597]
+13626: ['ADD', 205, 649, '-1/2', 3]
+13627: ['MOVE', 649, 3, 597, False]
+13628: ['ADD', 198, 649, '-1/2', 597]
+13629: ['ADD', 205, 650, '-1/2', 3]
+13630: ['MOVE', 650, 3, 597, False]
+13631: ['ADD', 198, 650, '1/2', 597]
+13632: ['ADD', 205, 652, '1/2', 3]
+13633: ['MOVE', 652, 3, 597, False]
+13634: ['ADD', 198, 652, '1/2', 597]
+13770: ['MOVE', 648, 597, 120, False]
+13772: ['MOVE', 649, 597, 120, False]
+13774: ['MOVE', 650, 597, 120, False]
+13778: ['MOVE', 652, 597, 120, False]
+```
+
+### Commutativity and Subspace Nesting (Stage A)
+1. **Write-epoch commutativity on `198`:** Between `13528` and `13634`, register `198` is never read or scaled; its only operations are `13529` (`198 += 2 * 710`) and `13625, 13628, 13631, 13634` (`198 += ±1/2 * r` for `r in {648, 649, 650, 652}`). Additions into a common destination register commute with each other and with chart transport of that destination register.
+2. **Read-epoch invariance on `648, 649, 650, 652`:** Each helper `r in {648, 649, 650, 652}` is initialized at chart `3` (`[]`, $\dim 0$) and is only read (never written or scaled) prior to event `13771`. Thus at event `13528`, each `r in {648, 649, 650, 652}` already holds its unmodified initial symbol at chart `3`.
+3. **Elimination of chart `597` on `648, 649, 650, 652`:** Executing `13625, 13628, 13631, 13634` at chart `3` immediately before `13528: ['MOVE', 198, 3, 597, False]` eliminates the four climbs `3 -> 597` (`13624, 13627, 13630, 13633`) and replaces the four climbs `597 -> 120` (`13770, 13772, 13774, 13778`, where `120` has 5-dimensional basis `[7, 25, 75, 160, 288]`) with direct climbs `3 -> 120`.
+4. **Stage A Paid Delta:** On each of `648, 649, 650, 652`, the paid itinerary `3 (0D) -> 597 (1D) -> 120 (5D)` (`H1 + H4`) becomes `3 (0D) -> 120 (5D)` (`H5`). All 735 `initial` and `final` frames and all 527 helper targets remain unchanged. The Stage A local paid delta is:
+   $$\Delta P_{\text{Stage A}} = -4 H_1 - 4 H_4 + 4 H_5$$
+   which reduces complete paid calls by $72$ (`66,852 -> 66,780`) and raises the raw moment crossing from `(0.00308189496866, 0.00308189496867)` to `(0.00308415555080, 0.00308415555081)`. This supporting word is shipped as `WORD-FIXED-ENDPOINTS.json.gz`.
+
+---
+
+## 2. Stage B: Commuting-Write Domino Cascade on `113, 531, 197, 319, 507`
+
+In the PR #5580 word, main port `113` stays at chart `3` (`0D`) up to event `13524`, where it moves `3 -> 597` (`[82]`, $\dim 1$) for `13525: ['ADD', 113, 710, '2', 597]`, followed by `13806: ['ADD', 113, 531, '1', 597]`. Because PR #5561's fixed-order solver could not commute `13806` before `13525`, helper `531` was forced to start at `597` (`1D`), which in turn forced `197` and `507` to climb `3 -> 597` for `13843: ['ADD', 197, 531, '-1', 597]` and `14404: ['ADD', 507, 531, '-1', 597]`:
+
+| Frame | Basis | Dimension |
+| --- | --- | --- |
+| `3` | `[]` | 0 |
+| `355` | `[30, 44]` | 2 |
+| `597` | `[82]` | 1 |
+| `617` | `[30, 44, 76]` | 3 |
+| `728` | `[30, 44, 76, 391]` | 4 |
+| `741` | `[13, 19, 65, 423]` | 4 |
+| `788` | `[13, 19, 33, 65, 390]` | 5 |
+
+Note that $30 = 13 \oplus 19 \in \text{span}(788)$ and $44 = 13 \oplus 33 \in \text{span}(788)$, so $\text{span}(3) \subset \text{span}(355) \subset \text{span}(788)$ and $\text{span}(355) \subset \text{span}(728)$ are strict subspace chains.
+
+### Domino Cascade Steps (Stage B)
+1. **Commute `13806` before `13524` at chart `3` (`0D`):** Between `13524` and `13806`, register `113` receives only `ADD` writes (`13525` and `13806`), and helper `531` is in its initial read-only epoch (unmodified until `14478`). Setting `initial[531] = 3` (`0D`) and executing `13806: ['ADD', 113, 531, '1', 3]` immediately before `13524: ['MOVE', 113, 3, 597, False]` preserves `113`'s itinerary `3 (0D) -> 597 (1D) -> 614 (3D)`.
+2. **Vacate `597` (`1D`) on `531, 197, 507`:** Because `531` is now at chart `3` (`0D`) during its initial read epoch, `13843: ['ADD', 197, 531, '-1', 3]` and `14404: ['ADD', 507, 531, '-1', 3]` execute at chart `3` (`0D`). Helper `507` skips `597` (`1D`) and climbs directly `3 (0D) -> 728 (4D)` (`H4` instead of `H1 + H3`), and helper `531` climbs `3 (0D) -> 741 (4D)` (`H4` instead of `H3`) while its helper target credit increases from `H8` (`9 - 1`) to `H9` (`9 - 0`).
+3. **Demote `13846` (`ADD 197 += 319`) from `617` (`3D`) to `355` (`2D`):** Because `197` stays at `3` (`0D`) after `13843` instead of climbing to `597` (`[82]`, which is not in `span(355) = span([30, 44])`), `197` now climbs directly `3 (0D) -> 355 (2D)` to meet `319` at `355` (`2D`) for `13846: ['ADD', 197, 319, '1', 355]`, and then climbs `355 (2D) -> 788 (5D)`. This vacates `617` (`3D`) on both `197` (`H2 + H3` instead of `H1 + 2 H2`) and `319` (`355 (2D) -> 728 (4D)`, `H2` instead of `2 H1`).
+
+### Combined Stage A+B Invoice and Strict Concave Gain
+Combining Stage A and Stage B across each of the 18 forward local calls gives:
+- **Local paid delta:** $\Delta P_{\text{local}} = -8 H_1 - H_3 - 2 H_4 + 4 H_5$ (`-7` local `MOVE` instructions, `25,140 -> 25,133` events).
+- **Global paid delta (18 calls):** $\Delta P = -144 H_1 - 18 H_3 - 36 H_4 + 72 H_5$ (`-126` paid calls, `66,852 -> 66,726`).
+- **Local target delta:** $\Delta T_{\text{local}} = -H_8 + H_9$ (`-18 H_8 + 18 H_9` globally, keeping `12,814` productive fields and rank-mass surplus `760` invariant).
+
+The exact rational interval engines enclose the raw moment crossings:
+
+| Word | Lower endpoint | Upper endpoint |
+| --- | --- | --- |
+| PR #5580 (`p104-event-contact-step`) | `0.00308189496866` | `0.00308189496867` |
+| Stage A (`WORD-FIXED-ENDPOINTS.json.gz`) | `0.00308415555080` | `0.00308415555081` |
+| Stage A+B (`WORD.json.gz`, headline) | `0.00308521055201` | `0.00308521055202` |
+
+The raw gain over PR #5580 is strictly between `0.00000331558334` and `0.00000331558336`. The claimed conditional saving is **$\kappa = 0.00308520$**, tested at `0.0030852005` with raw headroom `1.055201e-8 .. 1.055202e-8`.
diff --git a/research/p104-commuting-contact/README.md b/research/p104-commuting-contact/README.md
@@ -0,0 +1,36 @@
+# Conditional kappa 0.00308520 from a P104 commuting-contact cascade
+
+This construction increases complete conditional kappa from `0.00308189` in [PR #5580](https://github.com/CrocSwap/integer-mult-bounds/pull/5580) to **0.00308520** (`+3.31e-6`, raw crossing gain `+3.31558335e-6`). It also ships the fixed-endpoint supporting word `WORD-FIXED-ENDPOINTS.json.gz` reaching **0.00308415** (`+2.26058214e-6` raw over PR #5580) with all 735 `initial` and `final` frames and all 527 helper targets unchanged. The selected record remains `0.003027288235`.
+
+PR #5561, PR #5569, and PR #5580 kept the linear execution order of all 21,686 scalar operations fixed. Reordering independent `ADD` instructions within commuting write epochs on main ports `198` and `113` eliminates seven local `MOVE` transports per call (`-126` paid calls globally, `66,852 -> 66,726`) while preserving all 208 main endpoints, all 12,814 productive fields, rank-mass surplus `760`, and all eight owned lifetimes.
+
+Read [the proof](PROOF.md), [the construction](construct.py), [the complete receipt](RESULT.json), [the source pins](SOURCES.json), and [the verification record](VALIDATION.md). The exact raw crossing of the headline word lies in `(0.00308521055201, 0.00308521055202)` and is tested at `0.0030852005`.
+
+## Reproduction
+
+Python 3.10+ and the standard library suffice. No external solver is needed to reconstruct or verify both published words:
+
+```sh
+python3 -B scripts/research_package.py --package research/p104-commuting-contact
+```
+
+Both registered modes print:
+
+```text
+PASS_P104_COMMUTING_CONTACT_KAPPA_00308520
+```
+
+and the launcher prints `PASS_REGISTERED_RESEARCH_PACKAGE`. It authenticates all 33 retained PR #5545 source payloads and the pinned PR #5580 inputs, regenerates both `WORD-FIXED-ENDPOINTS.json.gz` and `WORD.json.gz` from `construct.py`, runs forward arbitrary-input replay on the base, fixed-endpoint, and headline words, verifies all 552,049 dense transpose coefficients, checks all 2,918 signed native Pauli maps, runs the full physical caller, verifies both rational moment engines (`(0.00308415555080, 0.00308415555081)` for Stage A and `(0.00308521055201, 0.00308521055202)` for Stage A+B), and checks the compiler, all 58 outer predicates, and negative controls.
+
+## Credits
+
+- Ali Romman (`@aliromman`) supplied [PR #5580](https://github.com/CrocSwap/integer-mult-bounds/pull/5580) (`research/p104-event-contact-step`) and the complete caller/source closure in [PR #5544](https://github.com/CrocSwap/integer-mult-bounds/pull/5544) and [PR #5545](https://github.com/CrocSwap/integer-mult-bounds/pull/5545).
+- Joel Pulikkan (`@GamingPuzzled`) supplied [PR #5569](https://github.com/CrocSwap/integer-mult-bounds/pull/5569) (`research/p104-priced-handoff`).
+- `@DreamingOfClouds` supplied [PR #5561](https://github.com/CrocSwap/integer-mult-bounds/pull/5561) and [PR #5568](https://github.com/CrocSwap/integer-mult-bounds/pull/5568).
+- `@thu-nmrc` supplied [PR #5551](https://github.com/CrocSwap/integer-mult-bounds/pull/5551).
+- Retained source notices credit Gareth Davidson, David Arias, Cinna Davis, Jacob Alan Sussman, zxv, and Cao Yifan.
+- New commuting-contact cascade construction, proof, and verification by Pierre-Loic Doulcet (`@hexapode`). Apache-2.0.
+
+## Open next questions
+
+Independently review the commuting-contact cascade (`Stage A` and `Stage B`) and the inherited helper-endpoint contract, then recompute the complete invoice from `WORD-FIXED-ENDPOINTS.json.gz` and `WORD.json.gz`. Exhaustive commuting-epoch screening on the resulting word leaves zero remaining negative-cost commuting-epoch moves without crossing owned-register `COPY` boundaries (`13401: COPY 737, 146`), so pushing further requires coupling owned-register lifetime timing or multi-register scalar algebraic rewrites. Structured questions are recorded in [TASK.json](TASK.json).