pinterbanget · Oct 22, 2026
diff --git a/research/jwr-chain-receipt/README.md b/research/jwr-chain-receipt/README.md
@@ -0,0 +1,46 @@
+# jwr404 halo-absorption chain: disposition receipt
+
+**Task:** overlap-receipt. **Base:** canonical main `f626db5c`. **No new κ. No closures recommended.**
+
+This receipt covers 13 open PRs by jwr404 that extend the Gaussian halo-tensor chain after the merged #4506 (`research/gaussian-tensor-nine-faces`).
+
+## Disposition
+
+| PR | Package | Answers open question of | Status at base |
+|----|---------|--------------------------|----------------|
+| #4508 | gaussian-tensor-nine-axis | #4506 (merged) | open, not retained |
+| #4509 | gaussian-tensor-nine-bridge | #4508 | open, not retained |
+| #4511 | gaussian-axis-inheritance | #4509 | open, not retained |
+| #4512 | gaussian-second-row | #4511 | open, not retained |
+| #4515 | gaussian-operator-lift | #4512 | open, not retained |
+| #4520 | gaussian-restricted-gate | (root; cites #4515, #4517) | open, not retained |
+| #4523 | gaussian-global-tail | (root; cites #4520) | open, not retained |
+| #4524 | gaussian-unequal-gate | (root) | open, not retained |
+| #4526 | gaussian-heavy-slice | #4524 | open, not retained |
+| #4527 | gaussian-slice-ten-gate | #4526 | open, not retained |
+| #4528 | gaussian-slice-ten-copies | #4527 | open, not retained |
+| #4530 | gaussian-slice-nine-gate | #4528 | open, not retained |
+| #4531 | gaussian-slice-nine-copies | #4530 | open, not retained |
+
+- **Retention.** No package from the set is present at its merge base or on main `f626db5c`. Each PR is a single-package addition of 5 files. Exact heads, merge bases and per-file blobs are in `RECEIPT.json`.
+- **Factor-9 versus factor-10.** #4530 and #4531 restate #4527 and #4528 with the factor-9 gate instead of factor 10. The factor-10 statements stay valid but are coarser, so a maintainer taking the slice results needs only the factor-9 pair, plus the factor-10 pair for attribution.
+- **Outside the author's set.** #4517 (pinterbanget, open) answers #4515's open question; #4520 cites it.
+
+## Verify
+
+```text
+python3 -B research/jwr-chain-receipt/verify.py
+```
+
+The verifier checks recorded facts only: SHA well-formedness, single-package additions, no retention at base, answer edges pointing backwards, and the factor-9/10 pairing. It does not test the working tree, so it still replays after any of these PRs merges. To compare heads, fetch `pull/<n>/head`.
+
+## Limitations
+
+- This records structure and provenance. It does not replay or review the mathematics of any PR.
+- PR heads may move after recording; compare against `RECEIPT.json`.
+
+## Open next questions
+
+- An independent mathematical replay of the factor-9 slice pair #4530/#4531, which carries the chain's final absorption statements. First step: run each PR's registered verifier at its recorded head.
+
+Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance. Credit for all listed results: jwr404.
diff --git a/research/jwr-chain-receipt/RECEIPT.json b/research/jwr-chain-receipt/RECEIPT.json
@@ -0,0 +1,314 @@
+{
+ "schema": "jwr-chain-receipt/1",
+ "recorded_against_main": "f626db5c3a3d781d8f7695038776c621651f75e1",
+ "prs": {
+  "4508": {
+   "title": "Bound one tensor axis by two section errors at ceiling 9 (no new κ)",
+   "head": "def7e3f4b4b8e43536c2b808b26ef82b2e64e2b4",
+   "merge_base": "bbde3b0bedb8f7ce17159dfbe913b7e3e5194bab",
+   "package": "research/gaussian-tensor-nine-axis",
+   "files": {
+    "research/gaussian-tensor-nine-axis/README.md": "20ad3223899c7006651961b43c2f691202f1189f",
+    "research/gaussian-tensor-nine-axis/SOURCES.json": "b03a8b65e3559e8cece6df286c240c9839969047",
+    "research/gaussian-tensor-nine-axis/TASK.json": "ad2538315e18b3cf3169f2ab0d5dc3d749d7279c",
+    "research/gaussian-tensor-nine-axis/VERIFY.json": "e7b0cb1c7d843a6e9bbd617c8019b149cf2be82e",
+    "research/gaussian-tensor-nine-axis/verify.py": "4518ec7bf00d2ee220fe5125195b4988f38e96eb"
+   },
+   "package_at_base": false,
+   "answers_open_question_of": 4506,
+   "paths_outside_package": [],
+   "mentions": [
+    4488,
+    4506
+   ]
+  },
+  "4509": {
+   "title": "Split one axis through the section polynomial at ceiling 9 (no new κ)",
+   "head": "fefb6bce80cfc3f38a37b55a3bfd2beae9f78c68",
+   "merge_base": "f9f85c1e4fa1e955ff39f10fca447e3e2a4e4adc",
+   "package": "research/gaussian-tensor-nine-bridge",
+   "files": {
+    "research/gaussian-tensor-nine-bridge/README.md": "e56f0ade36a5c3ee6009a694e80ab6e747d92a9a",
+    "research/gaussian-tensor-nine-bridge/SOURCES.json": "03375d30cc5d6fdc292602da9f4fdab58f6b7566",
+    "research/gaussian-tensor-nine-bridge/TASK.json": "106e0250db04d2c8ee206c56e9d314a7241e1147",
+    "research/gaussian-tensor-nine-bridge/VERIFY.json": "db61e15e3cd5ec6b6b79ef31b8080344024a4076",
+    "research/gaussian-tensor-nine-bridge/verify.py": "fe04d581ac523412c7faea92013c8b36e4ba67bc"
+   },
+   "package_at_base": false,
+   "answers_open_question_of": 4508,
+   "paths_outside_package": [],
+   "mentions": [
+    4490,
+    4508
+   ]
+  },
+  "4511": {
+   "title": "Attribute the three axis hypotheses on one core row (no new κ)",
+   "head": "b6bbfaef1a736b8a15e1abb7148182fc5f750429",
+   "merge_base": "f9f85c1e4fa1e955ff39f10fca447e3e2a4e4adc",
+   "package": "research/gaussian-axis-inheritance",
+   "files": {
+    "research/gaussian-axis-inheritance/README.md": "8748ddaa5d2c4b0d729cbb2c2a3354cf3e15b98d",
+    "research/gaussian-axis-inheritance/SOURCES.json": "38ef9d625ec548fc651b650c6d8c841164cb1d82",
+    "research/gaussian-axis-inheritance/TASK.json": "671289c7cf0d699450befe6af9b20add74c3dcb8",
+    "research/gaussian-axis-inheritance/VERIFY.json": "f42f2ab3ca3e3ccdd28bdfe591c91b79ac53c416",
+    "research/gaussian-axis-inheritance/verify.py": "1dceec36d24ca3b155e0589e836ad92579076c91"
+   },
+   "package_at_base": false,
+   "answers_open_question_of": 4509,
+   "paths_outside_package": [],
+   "mentions": [
+    4452,
+    4491,
+    4493,
+    4509
+   ]
+  },
+  "4512": {
+   "title": "Add the two core-row section errors (no new κ)",
+   "head": "6687cd47bd720226d88b5c8441f0f63a425e0ca7",
+   "merge_base": "f9f85c1e4fa1e955ff39f10fca447e3e2a4e4adc",
+   "package": "research/gaussian-second-row",
+   "files": {
+    "research/gaussian-second-row/README.md": "41676a72445c50f380e83573bceef49c169ca471",
+    "research/gaussian-second-row/SOURCES.json": "b76b3ba7a8d7eade72659aa9c9ebdac65878ffab",
+    "research/gaussian-second-row/TASK.json": "7adad67359e8a6095b14e76209d416312102ce33",
+    "research/gaussian-second-row/VERIFY.json": "4053cbcabb61e927cdcf9d39ee5666258ac52b21",
+    "research/gaussian-second-row/verify.py": "01a995d908e68bbf72537f0d5f91491e84e7ca9b"
+   },
+   "package_at_base": false,
+   "answers_open_question_of": 4511,
+   "paths_outside_package": [],
+   "mentions": [
+    4452,
+    4491,
+    4509,
+    4511
+   ]
+  },
+  "4515": {
+   "title": "Separate the shared-row sum from the operator 2-norm (no new κ)",
+   "head": "535e4f578f8c19a11bd0a1202a392cbcfe932bfc",
+   "merge_base": "f9f85c1e4fa1e955ff39f10fca447e3e2a4e4adc",
+   "package": "research/gaussian-operator-lift",
+   "files": {
+    "research/gaussian-operator-lift/README.md": "4355c1a7e924009f27c429934ecdee8e019ded4b",
+    "research/gaussian-operator-lift/SOURCES.json": "f48e88f6f824c90d393ddf681c544dca0842456e",
+    "research/gaussian-operator-lift/TASK.json": "37fc07cd5557c3a68af09f77d3f66b4c5b33965e",
+    "research/gaussian-operator-lift/VERIFY.json": "a20f81610941e49579082be96be5e5aa3ae2ffef",
+    "research/gaussian-operator-lift/verify.py": "0e960f87dd8c7e8b0122c3f15fc6cddf09d366ca"
+   },
+   "package_at_base": false,
+   "answers_open_question_of": 4512,
+   "paths_outside_package": [],
+   "mentions": [
+    4452,
+    4490,
+    4491,
+    4509,
+    4512
+   ]
+  },
+  "4520": {
+   "title": "Absorb the restricted monomial by the four-bit gate (no new κ)",
+   "head": "a25d6a1289daf53d9360889d8b2e82a04022173b",
+   "merge_base": "f9f85c1e4fa1e955ff39f10fca447e3e2a4e4adc",
+   "package": "research/gaussian-restricted-gate",
+   "files": {
+    "research/gaussian-restricted-gate/README.md": "a28c68f2b0b55a8f4f1aa22e43db51e6ce37c5e0",
+    "research/gaussian-restricted-gate/SOURCES.json": "e599896ee933783f9571683f124b83a355294d05",
+    "research/gaussian-restricted-gate/TASK.json": "bae3ff43c8934da9796c808c55a45851e353cda2",
+    "research/gaussian-restricted-gate/VERIFY.json": "2f0129bab1061372658e34f6fc768650604373d0",
+    "research/gaussian-restricted-gate/verify.py": "4e5c668b09ee19e73be0fd87b29f51972d91ed2f"
+   },
+   "package_at_base": false,
+   "answers_open_question_of": null,
+   "paths_outside_package": [],
+   "mentions": [
+    4496,
+    4506,
+    4515,
+    4517
+   ]
+  },
+  "4523": {
+   "title": "Record that the written global tail is p^10 exp(-p^2) (no new κ)",
+   "head": "fe53f24fdfa433f8ad88c29d24eed85add5634e6",
+   "merge_base": "f9f85c1e4fa1e955ff39f10fca447e3e2a4e4adc",
+   "package": "research/gaussian-global-tail",
+   "files": {
+    "research/gaussian-global-tail/README.md": "f6483fcb3656e7aadd4978ab11be2483a03d6485",
+    "research/gaussian-global-tail/SOURCES.json": "69dadd2851f3e4e2cd833c6842b539672504a96f",
+    "research/gaussian-global-tail/TASK.json": "e5925f2fe0bcf0591a508356afdb8afed598a00b",
+    "research/gaussian-global-tail/VERIFY.json": "498cc75f18403202276801fc931de13a512f7432",
+    "research/gaussian-global-tail/verify.py": "fcbb5036f600e5cef957acfb391e46462ae00eca"
+   },
+   "package_at_base": false,
+   "answers_open_question_of": null,
+   "paths_outside_package": [],
+   "mentions": [
+    4406,
+    4452,
+    4520
+   ]
+  },
+  "4524": {
+   "title": "Absorb one section error and one global tail (no new κ)",
+   "head": "c416248f4d9964045db36c2b7edae0e9b6cc2d6c",
+   "merge_base": "f9f85c1e4fa1e955ff39f10fca447e3e2a4e4adc",
+   "package": "research/gaussian-unequal-gate",
+   "files": {
+    "research/gaussian-unequal-gate/README.md": "14851816651f46ddd7bb54cfaa1d14d6fe6a9cd8",
+    "research/gaussian-unequal-gate/SOURCES.json": "8e424731d9d9ab52490b8f0e50ccd5690371c5c7",
+    "research/gaussian-unequal-gate/TASK.json": "c4395663e874b86b478334d9d8a541f97d211b0e",
+    "research/gaussian-unequal-gate/VERIFY.json": "c77f648eece720d42d7e142b7307571ab486c8e7",
+    "research/gaussian-unequal-gate/verify.py": "262e7d3403198d4f61fb8efc57eab316462bec69"
+   },
+   "package_at_base": false,
+   "answers_open_question_of": null,
+   "paths_outside_package": [],
+   "mentions": []
+  },
+  "4526": {
+   "title": "Absorb the heaviest trailing p^10 slice (no new κ)",
+   "head": "7392ecdb71403d9c9b31b7a349dbc82039f56514",
+   "merge_base": "f9f85c1e4fa1e955ff39f10fca447e3e2a4e4adc",
+   "package": "research/gaussian-heavy-slice",
+   "files": {
+    "research/gaussian-heavy-slice/README.md": "33144f496057f74cd090d3727e4327aa43f06806",
+    "research/gaussian-heavy-slice/SOURCES.json": "67e2fddfb68702bf6d46c09312b098b22edb9501",
+    "research/gaussian-heavy-slice/TASK.json": "8ebb0f4e7f182e8aba0c583fbc725d6e75977b3e",
+    "research/gaussian-heavy-slice/VERIFY.json": "84b76d65d519b47aacf6d72251c4bb353311ab5c",
+    "research/gaussian-heavy-slice/verify.py": "9636202c49e819dc4f91d768f0609ab4d151f03c"
+   },
+   "package_at_base": false,
+   "answers_open_question_of": 4524,
+   "paths_outside_package": [],
+   "mentions": [
+    1166,
+    4524
+   ]
+  },
+  "4527": {
+   "title": "Absorb the heavy slice by the factor-10 gate (no new κ)",
+   "head": "33f4920b4b68dba8373fd91a60dd0a3133a25be6",
+   "merge_base": "f9f85c1e4fa1e955ff39f10fca447e3e2a4e4adc",
+   "package": "research/gaussian-slice-ten-gate",
+   "files": {
+    "research/gaussian-slice-ten-gate/README.md": "8cfd987ed81570a25024a381e63fc6205c66db4a",
+    "research/gaussian-slice-ten-gate/SOURCES.json": "67e2fddfb68702bf6d46c09312b098b22edb9501",
+    "research/gaussian-slice-ten-gate/TASK.json": "959cec4cdc1a4783ae40fd609432d9000f598220",
+    "research/gaussian-slice-ten-gate/VERIFY.json": "90051181f55b76c0a31ca3b8328073a6c23bb72f",
+    "research/gaussian-slice-ten-gate/verify.py": "1f4249a97c0a8c0b31446d0c891bea471b2a1839"
+   },
+   "package_at_base": false,
+   "answers_open_question_of": 4526,
+   "paths_outside_package": [],
+   "mentions": [
+    4526
+   ]
+  },
+  "4528": {
+   "title": "Absorb g copies of the heavy slice by the factor-10 gate (no new κ)",
+   "head": "b853775d514515e0d8a4406aa5748c6e5b36fe1e",
+   "merge_base": "f9f85c1e4fa1e955ff39f10fca447e3e2a4e4adc",
+   "package": "research/gaussian-slice-ten-copies",
+   "files": {
+    "research/gaussian-slice-ten-copies/README.md": "c9647f8f2e786e76ea8b93bb50306fccd98530ae",
+    "research/gaussian-slice-ten-copies/SOURCES.json": "67e2fddfb68702bf6d46c09312b098b22edb9501",
+    "research/gaussian-slice-ten-copies/TASK.json": "752fa5e93fac1d8f493a5ae150cf5936116f1855",
+    "research/gaussian-slice-ten-copies/VERIFY.json": "a244f4eb2fcd568c5b087384a4fc3ff008fb15fb",
+    "research/gaussian-slice-ten-copies/verify.py": "1d6548909bfa37bd688e8c1d941e2e52c7bf73f9"
+   },
+   "package_at_base": false,
+   "answers_open_question_of": 4527,
+   "paths_outside_package": [],
+   "mentions": [
+    4527
+   ]
+  },
+  "4530": {
+   "title": "Absorb one heavy slice by the factor-9 gate (no new κ)",
+   "head": "2ea9a355c8c1ce6442959f778395e6e58656826d",
+   "merge_base": "f9f85c1e4fa1e955ff39f10fca447e3e2a4e4adc",
+   "package": "research/gaussian-slice-nine-gate",
+   "files": {
+    "research/gaussian-slice-nine-gate/README.md": "26f69577d9e8fbd327ff2c8f464b80e63cf4d3d5",
+    "research/gaussian-slice-nine-gate/SOURCES.json": "67e2fddfb68702bf6d46c09312b098b22edb9501",
+    "research/gaussian-slice-nine-gate/TASK.json": "120e3dfe842efe2479b20e25f2a507a70458387b",
+    "research/gaussian-slice-nine-gate/VERIFY.json": "f8112a4850d8d5fb5f9a70acf19e26c38d231634",
+    "research/gaussian-slice-nine-gate/verify.py": "46ce8d688c990082e7982e48f573f1e3591b94c7"
+   },
+   "package_at_base": false,
+   "answers_open_question_of": 4528,
+   "paths_outside_package": [],
+   "mentions": [
+    4528
+   ]
+  },
+  "4531": {
+   "title": "Absorb g copies of the heavy slice by the factor-9 gate (no new κ)",
+   "head": "0fcfb608266b0190757fe307b4c3e52732afb298",
+   "merge_base": "f9f85c1e4fa1e955ff39f10fca447e3e2a4e4adc",
+   "package": "research/gaussian-slice-nine-copies",
+   "files": {
+    "research/gaussian-slice-nine-copies/README.md": "57703a34071a806c25ee1b71fa1a5afa1a948698",
+    "research/gaussian-slice-nine-copies/SOURCES.json": "67e2fddfb68702bf6d46c09312b098b22edb9501",
+    "research/gaussian-slice-nine-copies/TASK.json": "f0275efb9b4e073db9004996371e286d82e2849e",
+    "research/gaussian-slice-nine-copies/VERIFY.json": "46e2ddcf15a3cb3fd56230d2ac284eeb82a23530",
+    "research/gaussian-slice-nine-copies/verify.py": "935a312724bb9764eddc70359c73dc5a6ebe0b92"
+   },
+   "package_at_base": false,
+   "answers_open_question_of": 4530,
+   "paths_outside_package": [],
+   "mentions": [
+    4530
+   ]
+  }
+ },
+ "chain": [
+  4506,
+  4508,
+  4509,
+  4511,
+  4512,
+  4515,
+  4517,
+  4520,
+  4523,
+  4524,
+  4526,
+  4527,
+  4528,
+  4530,
+  4531
+ ],
+ "notes": {
+  "4517": "pinterbanget's core-row operator lift; #4520 answers its open question",
+  "4506": "merged predecessor",
+  "factor_variants": "#4527/#4528 use the factor-10 gate; #4530/#4531 redo them at factor 9 (ceiling 9p^2 from #4493) and answer #4528's question; the factor-10 statements remain valid but coarser"
+ },
+ "author": "jwr404",
+ "predecessor_merged": {
+  "pr": 4506,
+  "package": "research/gaussian-tensor-nine-faces",
+  "on_main": true
+ },
+ "outside_author": {
+  "4517": {
+   "author": "pinterbanget",
+   "state": "open",
+   "package": "research/core-row-operator-lift"
+  }
+ },
+ "supersession": {
+  "4530": {
+   "refines": 4527,
+   "how": "factor-9 gate instead of factor-10"
+  },
+  "4531": {
+   "refines": 4528,
+   "how": "factor-9 gate instead of factor-10"
+  }
+ }
+}
diff --git a/research/jwr-chain-receipt/SOURCES.json b/research/jwr-chain-receipt/SOURCES.json
@@ -0,0 +1,18 @@
+{
+  "schema_version": 1,
+  "base_commit": "f626db5c3a3d781d8f7695038776c621651f75e1",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "ed33caef5c5827693e9572d252a66f99cbb73d40",
+      "sha256": "5732707cc1e460b090b53f2463162749ad860de878a18f7408938671d295a9d9"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "64bfc5af6709ed9811171e0a2108f05e1219cb65",
+      "sha256": "352a6184713b8843d96fd2c2071eb7aeaa655906b7c51d45ad444912666c8a96"
+    }
+  ]
+}