IndisputableMonolith.Foundation.SubstitutivityForcing
The SubstitutivityForcing module shows that contextual substitutivity follows directly from the cost_sufficient field of ZeroParameterComparisonLedger with no added axiom. Researchers deriving the unconditional inevitability theorem cite it to justify state replacement in local comparisons. The result is immediate from the ledger packaging of symmetric cost and conserved log-charge.
claimLet $L$ be a ZeroParameterComparisonLedger. Then the cost_sufficient field of $L$ yields contextual substitutivity: if two states are equivalent under the symmetric cost, they may be interchanged while preserving the conserved log-charge.
background
This module builds directly on the Zero-Parameter Local Conserved Comparison Ledger from the LedgerCanonicality import. That ledger packages discrete state generation (countable carrier), local binary comparison with symmetric cost, and a conserved scalar (log-charge). The setting is the refined primitive object for the unconditional inevitability theorem in the Recognition Science foundation.
proof idea
The module contains a direct theorem that extracts substitutivity from the cost_sufficient field already defined in the ledger. It is a one-line wrapper with no additional lemmas or tactics required.
why it matters in Recognition Science
This module feeds the unconditional inevitability theorem by removing the need for a separate substitutivity axiom. It closes a foundational gap in the forcing chain (T0-T8) where contextual replacement must hold from the ledger alone.
scope and limits
- Does not specify the explicit form of the symmetric cost function.
- Does not extend to non-local or multi-state substitutions.
- Does not incorporate phi-ladder or mass formulas from downstream modules.
- Does not address global conservation beyond the local ledger.