Mister-Meeseeks · Nov 10, 2026 · Nov 3, 2026
diff --git a/research/answered-open-questions-ledger/README.md b/research/answered-open-questions-ledger/README.md
@@ -0,0 +1,139 @@
+# Open next questions that merged packages already answer: a ten-row ledger
+
+**Navigation record. No new mathematical claim and no κ.** Ten open questions
+stored in merged research packages are tied to the later merged package whose
+README answers them (5 rows), answers them by scope inclusion (2 rows) or
+answers only part of them (3 rows). Each row gives the question exactly as
+stored in the asking package's `TASK.json`, the answering package, and one to
+four quoted README lines. All inputs are pinned to main
+`7c49fe32c55de02c2c873655c804b16e4c3fef0a`. The asking packages are frozen, so
+the missing cross-references live here instead of in their files.
+
+| Row | Question stored in | Answered in | Status |
+|---|---|---|---|
+| L01 | `length9-four-vertex-gap`: arc {0,1,2,3,4}, common far-rim root? | `length9-five-vertex-gap` | answered |
+| L02 | `length9-five-vertex-gap`: arc {0,1,2,3,4,5}, common far-rim root? | `length9-six-vertex-gap` | answered |
+| L03 | `length9-six-vertex-gap`: arc {0,1,2,3,4,5,6}, common survivor root? | `length9-seven-vertex-gap` | answered |
+| L04 | `gaussian-neumann-ten`: smallest integer c with U < c p^2 | `gaussian-neumann-nine` | answered |
+| L05 | `precision-blind-composite-rigidity`: even lengths | `weighted-reversal-rescaling` | answered |
+| L06 | `paired-plane-rematch-rank34`: minimum fitting rank over all matchings | `paired-plane-frame-packing`, `p112-frame-partition`, `paired-plane-frame-repair` | partial |
+| L07 | `triangular-parity-n8`: every n=8 symbol, prefixes at most 3/2 | `triangular-parity-forward-bound` | answered by scope inclusion |
+| L08 | `triangular-parity-prefix`: nested splits inside the product of one-level caps | `triangular-parity-forward-bound` | answered by scope inclusion |
+| L09 | `diagonal-pair-five-call-collisions`: six-call floor in odd characteristic or F4 | `diagonal-pair-collision-audit` | partial |
+| L10 | `connector-gray-growth`: sharp leading constant of N(c)/(c log2 c) | `connector-bounded-depth-cap` | partial |
+
+[ledger.json](ledger.json) holds the rows. Each row has a `note` that says in
+one or two sentences what the answering README settles and what it does not.
+
+## Statuses
+
+- `answered` means the answering README states a result for the object the
+  question names, in its title or first sentences.
+- `answered-by-scope-inclusion` means the answering README proves a quantified
+  statement whose scope includes the asked case, without saying it answers that
+  question. The inclusion is my reading. The `note` names the definitional step
+  it relies on: L07 and L08 read the asking package's proper prefixes as the
+  answering package's forward macro-prefixes, by inspecting the two definitions,
+  and that step is not proved here.
+- `partial` means part of the question, or only its stated first step, is
+  settled. L06: the stated first step (is 12 the maximum number of disjoint
+  orthonormal 8-frames?) is answered, but the cited READMEs give a matching with
+  fitting rank 32 and say they do not claim the optimum over all matchings.
+  L09: odd characteristic is addressed only for F3 at width two, and the
+  answering README labels its length-five row local SAT evidence. L10: the
+  leading constant is fixed at 1/2 only for concatenations of blocks of depth at
+  most two, and the general constant stays open in [1/2, 1].
+
+## Evidence and reproduction
+
+From the repository root, with CPython 3.12 and the standard library only:
+
+```sh
+/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/answered-open-questions-ledger/verify.py
+/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -O -W error -B research/answered-open-questions-ledger/verify.py
+/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/answered-open-questions-ledger
+/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/answered-open-questions-ledger --check-source-history
+```
+
+Any CPython 3.12 installation can replace the displayed interpreter path. Both
+direct runs print one line that begins
+`PASS_ANSWERED_OPEN_QUESTIONS_LEDGER rows=10 answered=5 scope_inclusion=2 partial=3`
+and takes about 0.03 s. The check authenticates the SHA256 of 30 pinned inputs
+(19 `TASK.json`, 11 `README.md`), requires each stored question to equal its
+`TASK.json` entry and to be unique there, requires each quote to lie inside one
+README line, requires that no answering README cites the asking package by a
+`research/<name>` or `../<name>` path (that absence is what makes the
+cross-reference missing), and rejects eleven mutated copies of a real row:
+changed question text, a moved index, a quote absent from the README, a quote
+spanning a newline, a quote that is too short, a package answering itself, an
+unpinned answering package, an unknown status, an empty answer list, a quote
+borrowed from another row, and an answering README that cites the asking
+package by path. Checks raise explicit exceptions, so `-O` does not disable
+them.
+
+## What this does and does not establish
+
+- It establishes that the quoted lines exist in the pinned READMEs and that the
+  stored questions match the pinned `TASK.json` files.
+- It does **not** re-verify any answering result, and it does not decide by
+  program that a quote answers a question. That reading is mine and is recorded
+  in each row's status and note.
+- The ten rows are chains I met while looking for an open question to take. They
+  are not a census, and they support no statement about how many other stored
+  questions are already answered.
+- In all ten rows, no answering README cites the asking package by a
+  `research/<name>` or `../<name>` path; the verifier enforces this on the
+  pinned READMEs. It does not look at the answering packages' other files, so
+  a citation there is not excluded. A path-citation index built from READMEs
+  would therefore not link these pairs.
+- In the length-9 chain, the five-vertex package's stop rule says not to start
+  the six-vertex arc, and its stored question points at that arc. Rows L01 to
+  L03 record where each next step was taken. I did not check whether the other
+  asking packages were meant to stop at their stated question.
+
+## Scope
+
+`scope-navigation` card, scope refined: the card asks for one navigation repair
+or one related family index, and this ledger spans seven small question chains.
+No frozen package is edited. The card's first working command,
+`python3 -B scripts/research_selected_baseline.py`, printed
+`PASS_RESEARCH_BASELINE_BINDINGS_ONLY` at the base commit; that command checks
+source bindings only and is not a scientific replay.
+
+## Open next questions
+
+The structured list with relevance, first step and blocker is in
+[TASK.json](TASK.json).
+
+1. Which other merged packages store an open question that a later merged
+   package already answers? First step: for packages whose questions no other
+   package cites by path, search later PR titles and README first lines for the
+   named objects, and add a row only when the answering README states the result
+   in its own words. An automatic match is only a lead.
+2. L06: what is the minimum exact fitting rank over all perfect matchings of the
+   P112 plane ports? The cited READMEs give a rank-32 matching and a floor of 30
+   that is stated only for the two-support even-group colouring construction.
+3. L09: does the six-call diagonal-pair floor hold over F4, over F5 and at
+   widths above two? The cited audit settles F3 at width two only.
+4. L10: is the general leading constant of N(c)/(c log2 c) above 1/2? Check live
+   PRs and discussions for a depth-three block construction before choosing it.
+
+Questions 2 to 4 are pointers to questions other contributors stored. They are
+not claimed here.
+
+## Credit
+
+This contribution was produced by Nick Petalas. Apache-2.0.
+
+Every row depends on predecessor work that is cited, not re-verified:
+jwr (James Reed) for `length9-four-vertex-gap`, `length9-five-vertex-gap`,
+`length9-six-vertex-gap`, `length9-seven-vertex-gap`, `gaussian-neumann-ten`,
+`gaussian-neumann-nine`, `triangular-parity-n8` and `triangular-parity-prefix`;
+Wentao Li for `precision-blind-composite-rigidity`; Matarener (Mark) for
+`paired-plane-rematch-rank34`; Tekalign (tekuuu) for `paired-plane-frame-repair`;
+Brian (JoyboyBrian) for `triangular-parity-forward-bound`; JoyboyBrian for
+`diagonal-pair-five-call-collisions`; Josie Elliston for
+`diagonal-pair-collision-audit` and `connector-bounded-depth-cap`; apoursh for
+`connector-gray-growth`; and Nick Petalas for `weighted-reversal-rescaling`,
+`paired-plane-frame-packing` and `p112-frame-partition`. Each package's
+`README.md` and `TASK.json` retain its own credit line.
diff --git a/research/answered-open-questions-ledger/SOURCES.json b/research/answered-open-questions-ledger/SOURCES.json
@@ -0,0 +1,198 @@
+{
+  "schema_version": 1,
+  "base_commit": "7c49fe32c55de02c2c873655c804b16e4c3fef0a",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "d59b5035e7b4cbaa9d688a1d32dd0d6eb79c466a",
+      "sha256": "9b8d0eea95b3bf0dfcb7938a732a6439b87a2685dec2a5ab9e525b3b34debbfa"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "3404fbdd5e7529a0674eef26114b5071e4586cec",
+      "sha256": "ead6cdc9d0af6d58e8a49744d8ec8c7c15e13d2ba93c276c434bcf9b51b93a81"
+    },
+    {
+      "path": "research/connector-bounded-depth-cap/README.md",
+      "usage": "input",
+      "git_blob": "0127ee20090453b48024f8a1b279427a6612b0bf",
+      "sha256": "9e8800a27375b92b77b20cf3594f647a507bf17fd9bff2c4da1be10db2db98fa"
+    },
+    {
+      "path": "research/connector-bounded-depth-cap/TASK.json",
+      "usage": "input",
+      "git_blob": "8bd9ab8d37c6486af6700152b4d8f652dffd6ad0",
+      "sha256": "d4a7afa712bba008cebd7c54d17766916fd6efec1a0ca7e2d21ea7c86a1cdba0"
+    },
+    {
+      "path": "research/connector-gray-growth/TASK.json",
+      "usage": "input",
+      "git_blob": "21478f695b5d26f6259597fa31cf9d054ee456a2",
+      "sha256": "ecf631c4ca42f336822de0b12aa97e92330e77712a522e02e25d944c11e5f281"
+    },
+    {
+      "path": "research/diagonal-pair-collision-audit/README.md",
+      "usage": "input",
+      "git_blob": "7b8d36d096438ee17b91de51d7e3e9dc32a9cf06",
+      "sha256": "5ab441cf115d5e188a01bc5c06b0299732b99d79e7c84f1aab4daa0aaf4c2b78"
+    },
+    {
+      "path": "research/diagonal-pair-collision-audit/TASK.json",
+      "usage": "input",
+      "git_blob": "94bff758ec4ad994f3f451e66b95e8add568114b",
+      "sha256": "931af1805e1c8deab93f1358373d631eed5c667d089fa2bd78cd628a90bdfe58"
+    },
+    {
+      "path": "research/diagonal-pair-five-call-collisions/TASK.json",
+      "usage": "input",
+      "git_blob": "da30f03b65a5ae3aaf94f1e4098be280a49a13a6",
+      "sha256": "14cbec29ffc99ab83d46bc3a1180f0167e68bd69a9f6a2d0e54c70097d8f8c8e"
+    },
+    {
+      "path": "research/gaussian-neumann-nine/README.md",
+      "usage": "input",
+      "git_blob": "54a8ce117a233e54e5057fd1edfa378e59527592",
+      "sha256": "189a0fb9ede1649ffea24ea22605a573366170e172ac563dd001c68d65b966ac"
+    },
+    {
+      "path": "research/gaussian-neumann-nine/TASK.json",
+      "usage": "input",
+      "git_blob": "04fbc1f53346e6ec6071e80ee74f8dc28a6b8b58",
+      "sha256": "9bdf58a80bc9f80df92e4af60be1ff7821b4ebb7fb4e707d9dc606f88138905a"
+    },
+    {
+      "path": "research/gaussian-neumann-ten/TASK.json",
+      "usage": "input",
+      "git_blob": "b01410a62f5fd085f097b2e0da99558b9772a33d",
+      "sha256": "f13dbc62b3806a3362a5b7ba4a62e66a2534355d2e4788c419e9ebbd4afc2fc9"
+    },
+    {
+      "path": "research/length9-five-vertex-gap/README.md",
+      "usage": "input",
+      "git_blob": "e1efad786d6efcae365e11809093621621d34d2e",
+      "sha256": "a00f08a15f9b86923ff43151380244bacea8fd0a1db771d619b0453966d82a83"
+    },
+    {
+      "path": "research/length9-five-vertex-gap/TASK.json",
+      "usage": "input",
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+      "sha256": "62e8ce24434ce64f8a60761239db5904c623f674c671038186fe15ac7f8f8883"
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+    {
+      "path": "research/length9-four-vertex-gap/TASK.json",
+      "usage": "input",
+      "git_blob": "f0a5d863e11d9c7a43fcfb415ac8a31a45905343",
+      "sha256": "7a053be14725fa2ced586744f04554f16645351a8632bccaa6cc7e36386cc1ed"
+    },
+    {
+      "path": "research/length9-seven-vertex-gap/README.md",
+      "usage": "input",
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+      "sha256": "96bff830e20fff43990c97bb0d6dab7f9f10440df373ebcabd951d7aa4384f2a"
+    },
+    {
+      "path": "research/length9-seven-vertex-gap/TASK.json",
+      "usage": "input",
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+      "sha256": "df5751b7c822b53232a00c6e2ac16959a624272b6aa04867eb539376dec28728"
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+    {
+      "path": "research/length9-six-vertex-gap/README.md",
+      "usage": "input",
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+      "sha256": "9979f55f13ccf0b3d92d995c68e7121f3ec20fcd4a1f9544ce52dbe736369494"
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+      "sha256": "8cf851cbdd82c05982fdb502b257fdbd0ddd773f6534d16999975b11bd6e7aff"
+    },
+    {
+      "path": "research/p112-frame-partition/README.md",
+      "usage": "input",
+      "git_blob": "8e8e7fab75ca65f704c1b72ac971d4819ba95fab",
+      "sha256": "ebb7771c4e517ee22f72918cf7f6d2827fb133003c65f92ce9aa4bb0722a9ef8"
+    },
+    {
+      "path": "research/p112-frame-partition/TASK.json",
+      "usage": "input",
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+      "sha256": "a2a87aea504bb5d190e0eac9444b453b70d0ab1ad28e59dd697a653151373543"
+    },
+    {
+      "path": "research/paired-plane-frame-packing/README.md",
+      "usage": "input",
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+      "sha256": "2dde74c4c3922a8cd83f1e2a675361198f1dae883ee94e2779ed3c34f900835c"
+    },
+    {
+      "path": "research/paired-plane-frame-packing/TASK.json",
+      "usage": "input",
+      "git_blob": "3d1264311a3bfe7b24baa1cfe4c4aeb39e476254",
+      "sha256": "630d3bf12fa09aa1721355b3412bbcbd7737d304cda22208f37a7176a1f12019"
+    },
+    {
+      "path": "research/paired-plane-frame-repair/README.md",
+      "usage": "input",
+      "git_blob": "98015779a08b2dfe2199d34cf00fa2e10d576fb8",
+      "sha256": "18cab7d6b27d6cbb91efa6d60b4a4c89a15909b2d2169fb54fc17b3abe334771"
+    },
+    {
+      "path": "research/paired-plane-frame-repair/TASK.json",
+      "usage": "input",
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+      "sha256": "92f813d7dbb8c6000896d774d75fd532d347e96a1aa2c412f240aca3cdc9a0bf"
+    },
+    {
+      "path": "research/paired-plane-rematch-rank34/TASK.json",
+      "usage": "input",
+      "git_blob": "a8ca6cd376f1df59cfac809db6f37e355ebd725f",
+      "sha256": "fce1710226d0d0da4d1922bc8a6538e6202f85c7419495df4560ea0127dc6643"
+    },
+    {
+      "path": "research/precision-blind-composite-rigidity/TASK.json",
+      "usage": "input",
+      "git_blob": "f12e2ed53749667a1be3af2a2f05fa494fc3ce54",
+      "sha256": "a7236dac4cf73276bfbb0321a56bdeda225e0cd39a3bae8df947f1e916e5c630"
+    },
+    {
+      "path": "research/triangular-parity-forward-bound/README.md",
+      "usage": "input",
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+      "sha256": "745c2105fc614e6ba453327a37e483b808425a40ce3e2b44e2643b0ea1db3781"
+    },
+    {
+      "path": "research/triangular-parity-forward-bound/TASK.json",
+      "usage": "input",
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+      "sha256": "b4ed309711ad195c5f066625c0abb26c9c624830b64d5a079428ac0dea4fa586"
+    },
+    {
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+      "usage": "input",
+      "git_blob": "d214b1cfe4449510dd1cf4d3a94fafb18a0f466f",
+      "sha256": "87502efa58b2b5918a76a0ea8c7b877aa7dd825c4402cbd515d9833968e0f265"
+    },
+    {
+      "path": "research/triangular-parity-prefix/TASK.json",
+      "usage": "input",
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+      "sha256": "6f4099f92d4bfb91d26a683e92b715439d5559ed1b10a540fca2f3bff79e0247"
+    },
+    {
+      "path": "research/weighted-reversal-rescaling/README.md",
+      "usage": "input",
+      "git_blob": "d192032d732526f3fe20b4c59808c531bdc1a8dd",
+      "sha256": "c455b51a41a4d217390c4286e6b310f0ac7fe802bf624eb83bf5e35868774308"
+    },
+    {
+      "path": "research/weighted-reversal-rescaling/TASK.json",
+      "usage": "input",
+      "git_blob": "7cd7c5da614a272a924312aedf974d53b1598dba",
+      "sha256": "84ff71dedb70ac86fbf2bb852337c7817fedd2c5c64e602e86b3259537f87717"
+    }
+  ]
+}