[aliromman]

This scoped negative result proves that a BIT controller with a simple two-owner support graph cannot close its diagonal Q/D targets. Each call has a coordinate rank-four D support, a nonzero native main Jordan chain, and two arbitrary helper columns. Those columns may write outside the D support. The last call must nevertheless have a diagonal restricted q matrix, which contradicts its main chain. The complete kappa calculation does not improve.

The proof, exact result, and positive control state the claim and its boundary. The base is 32890bc5de034ab8fc93ac88ead7279a6a416d04. The mandatory verifier has no external executable dependency.

The proof applies to any finite number of calls with independent commuting D symbols, one or two owners per field, and pairwise support intersections of at most one field. It permits D-only target flags. It does not cover parallel edges, fields in three calls, non-coordinate supports, dependent D symbols, paid thin calls, or a different main block. A two-call, four-parallel-edge word passes the exact endpoint and chain checks; its complete declared invoice has rank deficit 126 and is uniformly worse under the signed concave-moment preflight.

The package separately preserves 80 solver-dependent outcomes: 48 K4/K4-minus-edge order cases and 32 explicit parallel-edge cases. These are recorded Z3 outcomes without proof certificates. The standard-library verifier checks their integrity, not their UNSAT claims. Publication did not repeat the failed searches. Optional replay pins z3-solver==5.3.1.0.

Run the mandatory checks with Python 3.12 and no third-party package:

python3 -B research/bit-simple-graph-obstruction/verify.py
python3 -O -B research/bit-simple-graph-obstruction/verify.py
python3 -B scripts/research_package.py --package research/bit-simple-graph-obstruction --check-only
python3 -B scripts/research_package.py --package research/bit-simple-graph-obstruction

Expected direct output:

PASS_BIT_SIMPLE_GRAPH_OBSTRUCTION fixtures=48 diagonal_cases=3840 control=PASS solver_run=false new_kappa=false

Normal and optimized exact reports match. The registered Python 3.12 replay, committed-byte check, committed export check, and normal/optimized replay in a fresh Git-free export passed. The mandatory verifier checks 48 last-call fixtures, all 3,840 diagonal-chain cases, the saved word's literal group-ring product, role bases, helper updates, and complete target debit. Four controls reject a changed q coefficient, a missing target Q, a zero main chain, and use of the simple-graph lemma on parallel edges.

The model is motivated by the early-helper entrance method of PR #5388, with its pinned proof. The declared pricing control uses the retained PR589/PR555 profile; PR #589 and PR #555 retain the eumemic/Anthropic Claude source credit and earlier contributors. These are conceptual and invoice sources, not executable dependencies. A parallel author-side researcher supplied the complementary-word comparison and a degree-two precursor. The last-call proof, code and package have substantial OpenAI Codex assistance; Apache-2.0.

No optional solver search, physical caller, ordinary-work tariff, uniform compiler, or multiplication assembly was run for publication. Hosted CI has not run at publication. The optional full-history guard is unavailable in this shallow checkout. The next question requires a literal funded word that changes an essential support hypothesis.