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Decidable word-problem embedding contract

Family 250: Boone–Higman embeddings with higher finiteness. First application triage, 9 October 2026 Australia/Brisbane.

Problem and potential new use

Record the claimed equivalence between decidable word problem and embedding into a finitely presented simple group, with finiteness-property companions.

Applicability and commercial boundary

Embedding existence does not transfer an efficient word-problem algorithm or bound presentation growth.

Initial business decision

Research reference or conditional symbolic/verification engineering. No recurring buyer need, practical implementation or profitability has been demonstrated. Defer a standalone commercial product until a constructive example and a measurable workflow improvement exist. These records also identify unsupported inferences that an evidence platform could flag.

Next verification action

Read constructive embedding costs and exact source/target finiteness assumptions.

Evidence scope

The repository catalog statement was individually read. Main-paper construction, effectiveness and selected formal-scope comparison remain queued for this record. No independent Lean verification was run. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. See source metadata.

Finite algebraic envelopes and the Boone–Higman conjecture.