Non-dense fitting B: every E8 term with x·y ≠ 0 has rank ≥ 9; square root-code floors E8 ≥ 72, P112 ≥ 64, P104 ≥ 56, D4 ≥ 12 for any fitting B (no κ claim)

research/nondense-pairing-square-floors/LICENSE

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research/nondense-pairing-square-floors/MANIFEST.sha256

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+53232a5fb838466d0b5301b5fff23459075eaff418eff4928bf0518c7d1521d2  checks/brute_agree.py
+99b3cabe25ce291b30afbdaf1324bf49a51ef544e3204836766caf561488cd9b  checks/compare_orbits.py
+e1c43c4b030b2cebd0d7e1485b6762cdbee7031b4fe5dba209332000c039f73c  checks/counter_e8orth.py
+f21fabb3292885bbcc9d4b5f4dca94f9d3c74b884fb7ebd487b801b630ca5b0e  checks/decoders.py
+e5879757a5a84893a9e98ec738d1408ad0a95a171eddecd0211ff09134befe6f  checks/lib.py
+35a40b0341b4e8824526642f12d4b2521984a242e7f23911149542116dcf6b8b  checks/manifest_check.py
+634bb4bfde734f0eaedb15ece60d02a31dc7f7137ec01cf99cc9e47db5a6e6dd  checks/orbits_a.py
+2ddd99cc39ecc5643ea1132ca7d713095f58547bbbfab9f10a3d3551260820f0  checks/orbits_b.py
+046fd81ce21b3a55057029dc2fe55b06a788729bdb09e6f2e10f0294223ec328  checks/satA.py
+9721991a505cef90254583c02425227005c28cc967f27cc4e7c44db8b5111860  checks/satB.py
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+c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4  LICENSE
+486e0cfbb6fa50b0ca0cdb6e7d4db92833cd6033365faa2e382a3937d548e370  NOTICE.md
+392b29a8c4616c23eedbddf847d7b84cfa5ca63f94b733093d0714f59ae12972  PROOF_MAP.md
+328780fc5cdef9ceccb122a4cd196a3195fc028f7c9360f23899b4b8dc2601ad  README.md
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+71ab2a9dc5a294ad8fba4ccb8c45aaa8a439596d314a2a046ac9b62266872a18  vendor/drat-trim/LICENSE
+c27f6c65306226847266c8b9da4d8655a94106cc09a45ba2736a3ba0fc344c48  verify.sh

research/nondense-pairing-square-floors/NOTICE.md

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+# Notice
+
+Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code; Apache-2.0 (`LICENSE`, copied from the repository root).
+`vendor/drat-trim/` is Marijn Heule's drat-trim (`drat-trim.c`, its `LICENSE`), the same pinned source as `research/p111-minrank-proof-reconciliation/vendor/drat-trim/`.
+
+## Credits
+**#968** (frame-pair P104 cost-56 decoder; the 8/7 rule), **#1744** (E8 / P112 / P104 floors in their scopes), **#2176** (forced triangular minors; they cap at 7 per co-flat term and cannot close non-dense B), **#2338** (Theorems P and R, the pairing/CNF framework this note's `B` is the fitting matrix of), and `research/ideal-decoder-floors/` (Theorem 4, the dense-pairing root-code floor T·r_min that this note extends to non-dense B). None of their files is copied.

research/nondense-pairing-square-floors/PROOF_MAP.md

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+# PROOF_MAP: claim -> check (anything not listed is CONDITIONAL or OPEN in the README)
+| Claim | Status | Check (all run by `verify.sh`; log names in `OUT/logs/`) |
+|---|---|---|
+| Lemma 6.1 (per-term fitting minrank = mr2 on R∩A) | PROVEN (README §1) | exercised on every `mr2` in `brute_agree`, `d4`, `e7`, `d6`, `e8orth` |
+| Lemma 6.2 (normal-pair reduction) | PROVEN (README §1) | consumed by Theorem 6's type enumeration (`orbA`, `orbB`, `cmp`) |
+| Lemma 6.3 (orthogonal-set deletion) | PROVEN (README §1) | consumed by Cor 6.4 (P112/P104 scopes); no separate script |
+| 440 880 hyperplanes, 4022 non-orthogonal + 318 orthogonal types, min \|D\| = 30 | CHECKED, two implementations | `orbA`, `orbB`, `cmp` (`checks/orbits_a.py`, `orbits_b.py`, `compare_orbits.py`) |
+| CNF writers agree with exhaustive minrank over all fitting B | CHECKED | `brute` (`brute_agree.py`: 60 instances, both writers, DRAT + decoded SAT models) |
+| Theorem 6: all 4022 types UNSAT at rank <= 8, DRAT VERIFIED | CHECKED | FULL=1 steps `FULL writer A`, `FULL writer B` (`solve_types.py ... chunk:i/4`); default: fixed 32-type sample `solA`, `solB` (14 smallest \|D\| plus 18 spread) |
+| E8 >= 72 (every term x·y≠0 has rank >= 9, any fitting B) | PROVEN given Theorem 6 | as above |
+| P112 >= 64, P104 >= 56 (floor T·r_min, not per-term dense value) | PROVEN given Theorem 6 + Lemma 6.3 | as above; frames asserted in `dec` |
+| D4 >= 12 (192 D-sets, mr2 >= 3) | CHECKED | `d4` (`small.py D4`) |
+| Sharp: E8 72, P112 64, P104 56 exact decoders | CHECKED | `dec` (`decoders.py`) |
+| E8 orthogonal normals: \|D\| = 24, mr2 = 6 (dense block 9) | CHECKED | `e8orth` (`counter_e8orth.py`) |
+| D6: \|D\|=7 mr2=3; \|D\|=10,15,16,19 mr2<=4 (scan \|D\|<=19 only) | CHECKED (default: one witness per size; FULL: complete scan, 240 sets of \|D\|=7) | `d6` (`small.py D6 [full]`) |
+| E7: \|D\| = 11 type mr2 = 5 | CHECKED | `e7` (`small.py E7`) |
+| No decoder below any floor is shown | SCOPE STATEMENT | README §4 |
+| Overcomplete (48 types at 8, 19 undecided), E7/D6 square, gap (ii), D6 shared-B test | OPEN / CONDITIONAL | not checked |