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Fixed-margin tables: law distinction and literal schedule exclusion

Family 115; construction/scope addendum, 9 October 2026 Australia/Brisbane. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb.

The uniform sampler's introduction, parameter definitions, outer schedule, exact law tabulation and rare correction were read. Its d=10+(m+1)(n+1), T=d^200(k+b)^2 general schedule is a theoretical bit-complexity construction with enormous finite constants. Exactness uses a rare exhaustive residual-law branch and expected time, not a deadline bound on every execution. Zero-total and one-dimensional shortcuts are separate.

The cell-bounded paper's introduction, tightening/scales and selected algorithm schedule were read. It counts each bounded table once, allows structural zeros and explicitly targets complexity rather than practical runtime. The selected family scope covers both companion claims; no independent check was run. Full proof and numerical-subroutine audit remain pending.

The commercially material model distinction is uniform tables versus fixed-margin conditional independence. Existing SciPy/Patefield sampling targets the latter. With margins [2,2] in each direction, table masses differ from uniform by exact total-variation distance 1/3. This is a distinct valid law, not an existing-tool error.

The new bounded exact reference passed 325 checks, but does not implement the unrestricted theorem. It respects bounds, records ranks, and returns unknown on budget exhaustion. Defer the literal research backend; investigate the narrower law/constraint integration described in dossier 004. Buyer demand and profitability remain hypotheses.

Exact source paths read:

See source metadata and feasibility analysis. No independent proof verification or buyer validation is implied by these readings.

Public event-law workflow and bounded flows

The new exact data-law audit evaluates the same declared event under intended and candidate laws, with explicit conditioning for cell bounds. It passes 617 controls and produces public documentation examples, including a threshold classification change. No actual customer review or successful live SciPy/R comparison occurred. Revised data dossier.

The cell-bounded paper's flows.tex (complete 209 lines) and history.tex (complete 92 lines) are newly recorded in the ledger. Private-vertex subdivision preserves signed lower bounds, loops and parallel arc identities. The approximate flow sampler always stays feasible and has polynomial 1/tau cost; it is not the exact uncapped sampler or a logarithmic-only accuracy scheme. The selected ContingencyTables configuration has table statements only; its flow bridge/sampler is a separate paper-level claim. Dossier 041.

The reduction/exact reference passes 460 direct arc-enumeration/round-trip controls. The existing NetworkX baseline adds 13 controls and a public five-node model. That model reduces to dimension 14/total 3,422, so the exact reference leaves counts unknown while an existing solver separately finds a feasible vector. Costs are not an extra constraint in the source count law. The source FPRAS, actual scenario value and proof/program verification remain unimplemented/unverified. A fifteenth documentary contract adds seven controls and rejects unsupported exact/multicommodity/cost-optimal/formal-badge transfers; its supplied statuses are not evidence verification.