sennemmi · Oct 9, 2026 · Oct 9, 2026 · Oct 9, 2026
diff --git a/CONTRIBUTORS.md b/CONTRIBUTORS.md
@@ -143,3 +143,26 @@ verified posts, profile associations and unresolved account identities.
 
 - **Michiel Kosters** ([research repository](https://github.com/michielkosters/mathematics_ai/tree/2e0aa64ca09c87fc94f8575f59493f70cf929d71/problems/integer-multiplication-109); Douglas associates @one_line_proof) developed a parallel weighted-hypergraph/coordinate-frame candidate, compressed centers and aligned bit pairing. Our [review](research/parallel-announcements/README.md) reproduces the finite certificate with its transfer/precision limitations explicit.
 - **Abe / @abe_asfaw**, via a suggestion supplied by Douglas, identified the redundant complex center and its historical 26.5% numerical gain. We [checked the scalar identity, counts and assembly arithmetic](research/parallel-announcements/README.md), and credit this parallel observation alongside the already preserved rank-h center research.
+
+## Terminal-elision and shrunk-frame submissions
+
+**SovereignSteak, PR #122**, submitted the Round 15 terminal-accumulator
+elimination candidate and its exact majorization audit. The package redirects
+updates at their original gate indices and charges the transformed schedule.
+The PR's conditional finite certificate is not an unconditional multiplication
+theorem.
+
+**Joel Pulikkan (GamingPuzzled), PR #125**, submitted shrunk lifted frames with
+saturated deferral. The contribution delays selected frame growth while
+preserving the stated frame contract and exact downstream checks.
+
+The current stacked research candidate, prepared by **Sennemmi with substantial
+OpenAI Codex assistance**, composes those two ideas: it removes terminal roles
+from the #125 shrunk-frame profile and charges all direct redirects in the
+scalar bound. This is a distinct composition submitted for review; it does not
+claim global optimality, a complete theorem proof, or priority over either
+source. It is submitted as [Draft PR #140](https://github.com/CrocSwap/integer-mult-bounds/pull/140)
+against upstream `main`, with the construction snapshot at
+`9cdf73e8682fb12749482e710e50bc585d282a7c`; independent mathematical review is
+pending. Inclusion is an attribution record, not external acceptance. Original
+source licenses and each contributor's AI disclosures remain applicable.
diff --git a/docs/research/contribution-review.md b/docs/research/contribution-review.md
@@ -120,3 +120,11 @@ See [CONTRIBUTORS.md](../../CONTRIBUTORS.md) for contributions and parallel work
 
 - [#40](https://github.com/CrocSwap/integer-mult-bounds/pull/40), rohanarun: Both fixed bases and copied reversed corners: conditional κ = 3.918734894e-5 > 2^-15.
   Pinned `43f59ff533598762cbc43a5e14af2bbbc76fabbd`; not imported in the #39 integration pass.
+
+## Later stacked candidate: terminal elimination on shrunk frames (9 October 2026)
+
+- **Submission:** [Draft PR #140](https://github.com/CrocSwap/integer-mult-bounds/pull/140), based on upstream `main` with head `sennemmi:research/terminal-elision-shrunk-frames`.
+- **Candidate snapshot:** `9cdf73e8682fb12749482e710e50bc585d282a7c`.
+- **Pinned sources:** Joel Pulikkan's PR #125 head `dda535bdcfc321a13a1ebd3c2d70e2b5bb72368e`; SovereignSteak's PR #122 head `b1a6f24e57141637b3ff040d6f2ce9d896ffb9bb`.
+- **Submitted result:** conditional κ = `110875518403/10^15`, about 0.257% above the fixed #125 parent. The live upstream Draft PR #139 has a higher finite candidate on the separate triple-core lockstep route; this candidate makes no global-frontier claim.
+- **Review status:** draft awaiting independent mathematical review. Its finite verifier and controls pass; inherited transfer, analytic, fixed-tape and all-size assembly interfaces remain open proof obligations.
diff --git a/research/shrunk-frames/README.md b/research/shrunk-frames/README.md
@@ -1,13 +1,17 @@
-# Shrunk lifted frames with saturated deferred readouts
+# Terminal-elided shrunk frames with saturated deferred readouts
 
-Conditional **κ = 110591581647/10¹⁵ = 1.10591581647×10⁻⁴**, about
-**1.19920% above PR114** (1.09281094468×10⁻⁴), 1.35%
-above PR120 and 1.89% above PR118. The complex side still binds.
+Conditional **κ = 110875518403/10¹⁵ = 1.10875518403×10⁻⁴**, about
+**0.257% above the pinned PR #125 parent**
+(110591581647/10¹⁵ = 1.10591581647×10⁻⁴). The complex side still binds.
 
 This package keeps PR114's complete construction: PR117's immutable
 91,770-addition complex DAG (eumemic), the same carrier matching and 28,705
 dirty roles, PR110's lifted binary frames and deferred readouts, and PR114's
-saturated placement with priority 2^dim / reached_targets². One step is new.
+saturated placement with priority 2^dim / reached_targets². The frame shrink
+is PR #125 by Joel Pulikkan. The terminal-role deletion and source-time
+redirect idea follows PR #122 by SovereignSteak. This candidate composes them
+on the fixed PR #125 word; it does not claim either predecessor's mechanism as
+new.
 
 ## Shrunk frames
 
@@ -30,17 +34,28 @@ frames. Shrinking stays monotone. Lb_x contains every predecessor frame, and
 successors are processed later against the updated frames. Deferral
 candidates use the shrunk start frames.
 
-| Complex network (PR117 DAG) | PR114 | This |
+| Complex network (PR117 DAG) | PR #125 parent | This composition |
 |---|---:|---:|
-| roles / carrier links | 28,705 / 71,185 | 28,705 / 71,185 |
-| shrunk frames | — | 16,031 |
-| deferred readouts | 4,706 | 4,706 |
-| strict complex saving | 109305097/10¹² | **110616162/10¹²** |
-| κ | 1.09281094468e-4 | **1.10591581647e-4** |
-
-W = 124,390,992, recursive rank mass 71,647,349,312 and maximum child 574 of
-576 are unchanged. Only the split of each role chain into children changes.
-Every copied centre, exterior, source/target front, data projector and
+| physical roles / carrier links | 28,705 / 71,185 | 28,324 / 71,185* |
+| shrunk frames | 16,031 | 16,031 |
+| deferred readouts | 4,706 | 4,325 |
+| terminal roles removed / direct updates | — | 381 / 1,167 |
+| strict complex saving | 110616162/10¹² | **13862528107/125000000000000** |
+| κ | 1.10591581647e-4 | **1.10875518403e-4** |
+
+*The matched DAG's 71,185 links are retained; its `additions + roots - links`
+role count is the pre-elimination count. The final physical word removes 381
+terminal roles. Each is an ordinary deferred output role with no later
+consumer. For a removed role with old scratch value z and incoming updates
+uᵢ, the old pair of readouts contributes `-αz + α(z + Σuᵢ)`. The replacement
+adds each `αuᵢ` to its target at the original update time. The independent
+audit checks all 1,167 source-time updates, their frames and signs, and two
+modular dirty-scratch replays.
+
+W = 122,848,704, recursive rank mass 70,758,991,424 and maximum child 574 of
+576. The deficit remains 1,862,080. The full paid child histogram is
+reconstructed from both the forward and reflected frame traces. Every
+surviving copied centre, exterior, source/target front, data projector and
 endpoint correction remains paid. The bit supplier is unchanged:
 Swapnil Jain's round-seven word, stopped saving 1240189553/10¹³.
 
@@ -50,24 +65,25 @@ Swapnil Jain's round-seven word, stopped saving 1240189553/10¹³.
 python3 research/shrunk-frames/verify.py
 ```
 
-The verifier regenerates everything in a temporary tree. It pins the
-shrunk-frame count and all inherited graph counts. Section D of
-`complex_deferred.py` rechecks each role chain against the actual shrunk frames:
-start, every gate, linked continuations, root frame and F. It checks that each
-chain is nested and each frame nondegenerate. It also checks every deferral
-frame and target chain. Arbitrary-scratch replays are run over Z/(2^61−1).
-
-The independent reflection audit consumes the same frames. It covers the
-literal inverse, sign-negate and bank-swap word and the complemented frame
-incidences. It also checks the paid histogram in both directions, the
-bounded readout chunks and three mutations. `certificate.py` recomputes both
-moments exactly and rejects the next complex grid point. It also checks the
-expanded scalar charge, all 47 strict constraints, seven margins and the next
-κ grid point.
-
-A new control loads PR114's frozen unshrunk profile, which is
-`controls/pr114-complex-profile.json`. That profile contracts at PR114's saving
-and fails at the new one.
+The verifier regenerates the PR #125 parent in memory, checks its frozen
+profile and reflection receipt, writes a transient parent word, and builds the
+combined output in a temporary tree. Section D of `complex_deferred.py`
+rechecks each parent role chain against the actual shrunk frames: start, every
+gate, linked continuations, root frame and F. It checks each chain is nested
+and every frame is nondegenerate.
+
+`terminal_elision_audit.py` independently rediscovers the eligible terminal
+roles and rebuilds the simultaneous target schedule. It checks every event in
+chronological order, source-time snapshots, the exact local dirty-scratch
+identity, modular replay, forward and reflected frame transitions, and the
+complete child histogram. Four event mutations are rejected. `certificate.py`
+recomputes both moments exactly and rejects the next complex grid point. Its
+scalar-group bound explicitly includes all 1,167 direct updates; it checks all
+47 strict constraints, seven margins and the next κ grid point.
+
+Frozen comparison profiles are `controls/pr114-complex-profile.json` and
+`controls/pr125-complex-profile.json`. The PR #125 parent profile contracts at
+its own saving and fails at the composed candidate's larger saving.
 
 All retained transfer hypotheses remain unchanged:
 - simultaneous rational bases and opposite-bank factorization;
@@ -81,7 +97,10 @@ are not a new general theorem. This is a finite conditional witness, not an
 unconditional theorem, a measured speedup or a global optimum.
 
 Credits: eumemic (PR117 producer, PR114 saturated placement, reflection audit
-and scalar charge, with Anthropic Claude and OpenAI Codex assistance); Avi
+and scalar charge); Joel Pulikkan (PR #125 shrunk-frame step, Anthropic Claude
+assistance); SovereignSteak (PR #122 terminal-role elimination); this fixed-
+parent composition, independent audit and certificate integration were
+prepared with OpenAI Codex assistance. Avi
 Eisenberg / ikeboy (PR110 deferred complex compiler, PR62); Rohan Arun
 (PR111/113/116/118); icekylinx (PR104/115); Swapnil Jain (round-seven words,
 lifted frames, deferred readouts); Zhihao Chen / jacklightChen; Aurel Prosz /

diff --git a/research/shrunk-frames/SOURCE.json b/research/shrunk-frames/SOURCE.json
@@ -1,22 +1,30 @@
 {
-  "attribution": "Avi Eisenberg / ikeboy (PR62 and PR110, Anthropic Claude assistance); Rohan Arun (PR111, Anthropic Claude assistance); Swapnil Jain (round-seven bit word); icekylinx (retained stopped-product, copied-center and finite assembly interfaces); Zhihao Chen and RaD (retained assembly). PR117 scalar DAG is separate upstream work by eumemic with Anthropic Claude assistance, retained byte for byte with its original attribution. Saturated deferred-frame integration and verification for eumemic with OpenAI Codex assistance. Shrunk-frame step by Joel Pulikkan with Anthropic Claude assistance (PR114 base). Original source notices remain authoritative.",
+  "attribution": "Avi Eisenberg / ikeboy (PR62 and PR110, Anthropic Claude assistance); Rohan Arun (PR111, Anthropic Claude assistance); Swapnil Jain (round-seven bit word); icekylinx (retained stopped-product, copied-center and finite assembly interfaces); Zhihao Chen and RaD (retained assembly). PR117 scalar DAG is separate upstream work by eumemic with Anthropic Claude assistance, retained byte for byte with its original attribution. PR125 shrunk-frame step by Joel Pulikkan with Anthropic Claude assistance. PR122 terminal-role elimination by SovereignSteak is the predecessor for source-time redirects. Their work is preserved and cited; the fixed-parent composition, candidate generation, independent audit, and certificate integration were prepared with OpenAI Codex assistance. Original source notices remain authoritative.",
   "package_files": {
+    "README.md": "ad2c1d9efa34895d13409ccb22301a975e60463fc2dca84460a93cb9a96eec9e",
     "bit-profile.json": "7293f330518b78650bd86d76b93681e43f3a55541cdb8110993714148a4b4a6a",
     "bit_round7.py": "35d261a9248c2e06f9179e3c47e554a96b8fe763a9a3de2731256b8c0fbc74b0",
-    "certificate.json": "e5965daf4346b6a695384f8eda957d954529add921cb384f969856cdef81f845",
-    "certificate.py": "fa1846facc5eeb33017afd96e9a7b440d3a3d7ff813f76312f1ea865bf2277ca",
-    "complex-profile.json": "7e7c0c28c0983d117b3006b96719a6102ce31ec0273160dd7fc8b9a0fef0dbeb",
+    "certificate.json": "a01c78475fd3eac03cde6610a47866176852c6a7dc2375645f599f6e36a54125",
+    "certificate.py": "f5daca7c764595db596a33f84ac9224a56d085ddaf7381a283d0ba53fd01f78a",
+    "complex-profile.json": "5d0f6c0d455f187bea24a990560880b11f81bf44281b399cbf40cf00dc3a4bad",
     "complex_deferred.py": "fa1125e85ec73b185dc9eee117f62d10356bb6422c07ec793a7f77296c87707e",
     "controls/pr114-complex-profile.json": "a54d2a6023ff73f7476057b5f6a4ff02e65ded840b7254d906aadde2dd01940d",
+    "controls/pr125-complex-profile.json": "7e7c0c28c0983d117b3006b96719a6102ce31ec0273160dd7fc8b9a0fef0dbeb",
     "inputs/complex-dag.json.gz": "3c034d0aae388ef567a454826f4f48b26fd8a94c71e8ffed4835271b349a783b",
     "inputs/deferred_23.json.gz": "8c38e947ff9e021e308000dd82bb5e2194eb265d8b75194e22ce783d3e75317c",
     "inputs/witness_23.json.gz": "b2486aa2bb222bacea6e52162a3920780e45dd8edc5d7cb03eabea336a1c6588",
+    "prepare.py": "a6bfc5a547a98575ee9fff0cf3572841981c14bda2005e6bb38601d75b11680b",
     "producer.py": "017e50713943e6c2a98d1c23ec93e7da9580896de1b6bde24563b4b6961c74c0",
     "reflection-audit.json": "7caee26f3747b88b41137527175d41b08c4849a7302368bd50b1cfae74779c5a",
     "reflection_audit.py": "6761fb01f93ef89f2455388b2f5a71f19c0bbd870e6aaeba457ede0a949a163b",
     "replayed_producer.py": "99c1e3694ae06a7ce7a370b04ecb45ea3fcfe69a6e6e7f4c4606e0a6c74c3184",
-    "test_controls.py": "87dbc9945a5057cf1b7b6ba776590f5c20548f5b2b63893b34bd6280f534f036",
-    "verify.py": "b49c45f0fa06ab7de987110f3756c445220e1b2e08127cfa891eca7330e6d8da"
+    "terminal-elision-audit.json": "976d0f873521142a1e1ccacd06357daafb350232690a56191932cd647acc2c0d",
+    "terminal-elision.json.gz": "2c199d3df56bdeedf0832a23ddf1dea1330724182378c67188aead06c53a0d9b",
+    "terminal-selection.json": "96ca9b7a465041aa333149a9695bce1b392616279b16effa66ebee11bd91306b",
+    "terminal_elision.py": "f1113d3a1e6bd2fc3cd906a24db9c9d8ccff17c548de6096e556284684ac0d4b",
+    "terminal_elision_audit.py": "0c19cbc0389c4a668a22561ee4529472022e2e0819783e36e488c5043068f540",
+    "test_controls.py": "41b8de5feb8620fb6eb3964f800a8039c4ce409ef28f067e3d1aae083dad9a07",
+    "verify.py": "867b9314427fa33549d6f78daae0fa05ea6c8f1dd1342b2d73f9fc7945e4f1a3"
   },
   "provenance": {
     "base": "https://github.com/CrocSwap/integer-mult-bounds/pull/110",
@@ -36,6 +44,14 @@
       "file": "inputs/complex-dag.json.gz",
       "pull_request": "https://github.com/CrocSwap/integer-mult-bounds/pull/117",
       "sha256": "3c034d0aae388ef567a454826f4f48b26fd8a94c71e8ffed4835271b349a783b"
+    },
+    "shrunk_frame_parent": {
+      "commit": "dda535bdcfc321a13a1ebd3c2d70e2b5bb72368e",
+      "pull_request": "https://github.com/CrocSwap/integer-mult-bounds/pull/125"
+    },
+    "terminal_elision": {
+      "commit": "b1a6f24e57141637b3ff040d6f2ce9d896ffb9bb",
+      "pull_request": "https://github.com/CrocSwap/integer-mult-bounds/pull/122"
     }
   },
   "reflection": {
@@ -64,6 +80,6 @@
     "scripts/shared_point_network.py": "a85e7f0d8c42d6a27e3846308571ca324a1824ac5c2d59e4daa5c7673c33c697",
     "scripts/structured_bulk_assembly.py": "e99467e14211fba699878ed036e1e2362eb8e395dc22f9ecdcecc7fbf2cc736d"
   },
-  "schema": 1,
-  "scope": "Frozen finite producer, profiles, exact assembly and reflection audit; inherited all-size transfer remains conditional."
+  "schema": 2,
+  "scope": "Frozen finite terminal-elided producer, profiles, exact assembly, parent reflection and independent terminal audit; inherited all-size transfer remains conditional."
 }