IndisputableMonolith.Foundation.SubstitutivityForcing
The module shows that contextual substitutivity is already packaged inside a zero-parameter comparison ledger: the cost-sufficiency field forces like-for-like replacement under local binary comparison. Anyone citing ledger-based inevitability or calibration uniqueness will use it. The argument is a direct field extraction plus fixed-point uniqueness for the unit calibration map.
claimIf $L$ is a zero-parameter comparison ledger (countable carrier, local symmetric cost, conserved log-charge), then the cost-sufficiency axiom of $L$ yields contextual substitutivity: equal costs may be replaced in any local comparison context. The unit calibration $\lambda=1$ is the unique fixed point of the induced rescaling, and calibration is forced from that fixed point.
background
Recognition Science builds physics from a single comparison primitive rather than from free parameters. The upstream module LedgerCanonicality isolates that primitive as a ZeroParameterComparisonLedger: a countable discrete carrier, a local binary comparison equipped with a symmetric cost, and a conserved scalar (log-charge). The present module sits immediately downstream of that packaging.
Contextual substitutivity is the statement that if two states have equal cost under the ledger comparison, either may replace the other inside any larger local comparison without changing the outcome. In ordinary equational reasoning this is an extra congruence axiom; here the claim is that cost-sufficiency already supplies it.
Sibling results in the module treat the induced calibration map: $\lambda=1$ is its unique fixed point, and once that fixed point is forced, the numerical calibration of the ledger is fixed as well.
proof idea
The core theorem is a one-step extraction: the cost_sufficient field of a ZeroParameterComparisonLedger is exactly the data of contextual substitutivity, so no extra axiom is introduced. Uniqueness of the unit fixed point is an algebraic fixed-point argument on the rescaling induced by the ledger cost. Calibration forcing then composes that uniqueness with the ledger's conserved log-charge to pin the scale. The module is therefore a short forcing chain from ledger fields to substitutivity and calibration, not a definition-only file.
why it matters in Recognition Science
Substitutivity is a silent hypothesis in almost every equational derivation inside the Recognition forcing chain (T0–T8). By deriving it from the ledger rather than postulating it, the module removes one free structural assumption from the unconditional inevitability theorem. It feeds any later argument that rewrites costs inside larger contexts or that normalizes units via a unique calibration fixed point.
In the broader framework this keeps the comparison law (and ultimately the J-cost and the Recognition Composition Law) free of hidden congruence axioms. Downstream work that quotes ledger canonicality can therefore treat substitutivity and unit calibration as already forced rather than as extra hypotheses.
scope and limits
- Does not construct the ledger itself; assumes a ZeroParameterComparisonLedger is given.
- Does not derive the J-cost or the Recognition Composition Law from substitutivity.
- Does not address continuous or non-local comparison structures outside the ledger carrier.
- Does not prove existence of physical realizations; only forces substitutivity and calibration from ledger fields.
- Does not list external parent theorems; used_by edges are empty in the supplied graph.