IndisputableMonolith.Foundation.SubstitutivityForcing
The SubstitutivityForcing module shows that contextual substitutivity follows directly from the cost sufficient field inside the zero-parameter comparison ledger, removing any need for a separate axiom. Researchers building the unconditional inevitability theorem cite it to keep the foundation minimal. The argument is a direct extraction from the ledger definition imported from LedgerCanonicality.
claimContextual substitutivity holds in the zero-parameter comparison ledger via its sufficient cost field, with no additional axiom required.
background
The module sits in the foundation layer of Recognition Science and imports the zero-parameter local conserved comparison ledger. That ledger packages a countable carrier of discrete states, a symmetric cost for local binary comparisons, and a conserved log-charge scalar. The present module isolates the cost sufficient field as the source of contextual substitutivity.
proof idea
This is a theorem module whose single main result extracts substitutivity as an immediate consequence of the ledger definition. No new assumptions are added; the proof is a direct appeal to the cost sufficient component already present in the imported structure.
why it matters in Recognition Science
The module removes an extraneous axiom from the forcing chain and thereby supports the unconditional inevitability theorem. It feeds the sibling results on lambda-one uniqueness and calibration from the fixpoint. The doc-comment states explicitly that the cost sufficient field suffices, confirming the ledger is self-contained for substitution.
scope and limits
- Does not introduce new axioms beyond the zero-parameter ledger.
- Does not treat continuous or non-countable carriers.
- Does not supply explicit cost values or numerical bounds.
- Does not extend to multi-parameter or non-symmetric comparisons.