TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/joint-native-algebra-selection-20261016/four_polar_context_algebra_review.json
Original file SHA-256: 5dd3fa191fa307440cbc4be5a670c43ad243a233b2526e287e388da3f1377f5d
Inclusive original lines: 1-55
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
Conversation metadata and personal execution details are omitted where indicated.

000001 | {
000002 |   "status": "PASS_INDEPENDENT_EXACT_ALGEBRA_AND_BOTH_D1_CROSSBLOCKS",
000003 | [OMITTED: non-scientific conversation or execution metadata]
000004 |   "date": "2026-10-18",
000005 | [OMITTED: non-scientific conversation or execution metadata]
000006 |   "reviewed_files": [
000007 |     "FOUR-POLAR-CONTEXT-ALGEBRA.txt",
000008 |     "check_four_polar_context_algebra.py",
000009 |     "four_polar_context_algebra_results.json",
000010 |     "fold_response_tensors_results.json",
000011 |     "check_four_starting_points.py"
000012 |   ],
000013 |   "verified": [
000014 |     "Literal original simplex normalization and all four exact polar decompositions Pq=Z+vq vq*.",
000015 |     "Actual residual Gram diagonal1/off(11+4sqrt6)/25; positivity proves four-dimensional span.",
000016 |     "Spectral polynomial in sum(Pq) constructs Z inside the generated algebra; rank-one products prove the complete C direct_sum M4 algebra and two-dimensional commutant.",
000017 |     "For every pair the analytic commutator norm is2t²(1-t²)>0; sharp joint marginals/refinements would commute, so one common sharp-pointer refinement is excluded.",
000018 |     "Original D1 is Hermitian in both quarter cases; independently reproduced cross-block squared norms7882461/4398046511104 and3201175/13194139533312 exactly.",
000019 |     "Nonzero D1 cross-block with existing End(e-perp) gives all offdiagonal matrix units, hence full M5 response algebra and scalar commutant.",
000020 |     "Native coefficient-metric four-ray Gram diagonal1/off-1/5; positivity proof rules out perfect deterministic discrimination for those pure states in that metric.",
000021 |     "Original pointer passage268–295 successfully read through fresh HTTP registered source paper-source:dde45b1c42dbd45a76964283; conditional nature preserved."
000022 |   ],
000023 |   "scope_correction": "The requested native-coefficient-metric/R_b,4-preparation distinction is explicitly incorporated in the current proof. D1 is a source-relative correlation coefficient, not an executable operation. Incompatibility concerns one joint sharp pointer refinement; sequential/context-dependent/unsharp instruments are not excluded. The restricted fixed-S01 central1+4 split is broken by D1 and is not full-source superselection.",
000024 |   "review_scope": "Exact finite native observation-space algebra and original source-relative D1 numbers. No physical source/preparation/measurement selection, preferred q,3+2 derivation, fullG31/whole-source algebra classification or ledger promotion.",
000025 |   "reviewed_at": "2026-10-18T15:38:11.731408+00:00",
000026 |   "reviewed_file_sha256": {
000027 |     "FOUR-POLAR-CONTEXT-ALGEBRA.txt": "f9bb309bae0d65b31df6a38899c526547f027b69eb89b34800497e72b4ea9bdb",
000028 |     "check_four_polar_context_algebra.py": "7e30b0c2738d77b183f51cbb137480f07249a30f763d8b9d3acd824bb4b529cb",
000029 |     "four_polar_context_algebra_results.json": "269ffa3c7124f93f36db1c437ab22046a84d2d9bca7531396755490b41924a92",
000030 |     "fold_response_tensors_results.json": "6d7669311e63517976d142529e74dc996a02ad51703cc09a0ef9c2211edff706",
000031 |     "check_four_starting_points.py": "d8498338ebcbbf0a0598fb59ffda01cd3c911c072e09913bf09db7965137add4"
000032 |   },
000033 |   "file_read_scope": {
000034 |     "FOUR-POLAR-CONTEXT-ALGEBRA.txt": "Complete118-line proof and scope text.",
000035 |     "check_four_polar_context_algebra.py": "Complete94-line checker, including all-six-pair loop, generated outer-product rank test, compatible control and both-source-D1 loop.",
000036 |     "four_polar_context_algebra_results.json": "Complete recorded output; source tensor hash independently matches current input bytes.",
000037 |     "fold_response_tensors_results.json": "Actual cases[1/4,3/4].wick_tensors[1] parsed and used in independent exact arithmetic; whole-file SHA pinned.",
000038 |     "check_four_starting_points.py": "Literal polar definition and rawN construction compared at36–38 and100–102; whole-file SHA pinned."
000039 |   },
000040 |   "corrections_required": [],
000041 |   "execution_evidence": {
000042 |     "independent_exact_arithmetic_by_reviewer": true,
000043 |     "new_checker_executed_by_reviewer": false,
000044 | [OMITTED: non-scientific conversation or execution metadata]
000045 |     "fresh_Lean_kernel_run": false,
000046 |     "physical_instrument_demonstrated": false
000047 |   },
000048 |   "pointer_source": {
000049 |     "section_id": "section:74dd7cb9d9f61f22d69e",
000050 |     "source_id": "paper-source:dde45b1c42dbd45a76964283",
000051 |     "line_start": 268,
000052 |     "line_end": 296,
000053 |     "sha256": "765051892a2a4f78b060cba66d5f3700657f78f64370b8ed1f7566336fe9295c"
000054 |   }
000055 | }