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General matching: literal backend prerequisite prevents a practical speedup claim

Family 120; construction addendum, 9 October 2026 Australia/Brisbane. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb.

The introduction and uniform program were read, together with selected engine-sizing definitions and the backend parameter/guard block. The input is a simple undirected unweighted graph with isolates charged in p=n+m. One finite program interleaves parameter branches with a deterministic exact fallback and outputs explicit matching edges. The common exponent envelope is defined by a supremum over actual instruction counts and is not a numerical practical crossover.

For accelerated branch t>=1, a=1000+t. The backend requires P_star<=b, with Lambda=2^(1000a^2)(1+u), P_star=Lambda^(400a^2), b=M^(1/a^2) and M=2^u<=S^2. Therefore u>=400000a^6 and log2(S)>=200000a^6. At a=1001, this is an astronomical necessary master-size bound, not a sufficient threshold. Structural easy cases and the fallback may still terminate. The bound neither contradicts the theorem nor excludes a redesigned algorithm.

Defer the literal accelerated backend for commercial speedups. An independent finite matching audit now checks candidate feasibility and a supplied odd-component upper bound, certifying maximum cardinality when attained. It passed tests on all 1,024 five-vertex graphs against brute-force optima. A loose bound leaves optimality unknown. This is a classical component, not the source's new solver or a certificate constructor. Weighted/fairness/side-constraint claims remain outside the model.

Exact source sections:

The full backend proof/update machinery and prescribed-degree factor construction have not been independently reproduced. No family formal scope is listed. See source metadata, revised dossier 007 and feasibility derivation. No profitability or demand is established.

Existing-solver integration addendum

The bounded adapter now uses NetworkX 3.4.2 to propose matching edges and, when needed, a subset from vertex-deletion solves. A separate integer graph audit accepts only a feasible matching attaining a valid upper bound. The public 34-vertex karate-club graph, a generated 41-vertex star and an 80-vertex regular graph all have saved attaining certificates. The adapter passed 72 additional checks against brute-force four-vertex optima, malformed-input/cap tests and these fixtures. It rejects weighted inputs. No source accelerated backend, formal program verification, customer workload or business value is demonstrated. Saved report.