IndisputableMonolith.Foundation.RS_Wave_Function_Collapse
Foundation module that packages Recognition Science wave-function collapse as a cost-threshold certificate. It defines a domain cost from the RS J-cost, a positive canonical threshold, and an inhabited certificate type asserting collapse when cost meets the threshold. Collapse theorists and RS foundation auditors would cite it when wiring measurement to the ledger. The module is mostly definitions plus elementary nonnegativity and positivity facts.
claimThe module introduces a domain cost $C$ built from the RS cost $J$, a canonical threshold $\theta>0$, and a certificate type asserting RS wave-function collapse when $C$ meets $\theta$. Supporting facts: $C\ge 0$ and $\theta>0$, plus an inhabited certificate witness.
background
Recognition Science treats measurement as a ledger event: when a recognition cost crosses a fixed threshold, the configuration collapses to a definite branch. The Cost import supplies the unique J-cost $J(x)=(x+x^{-1})/2-1$ forced by the Recognition Composition Law; Constants supplies the RS time quantum $\tau_0=1$ tick as the native clock.
This module lifts that cost to a domain-level functional (domain cost) and fixes a canonical positive threshold against which collapse is decided. The certificate type packages the inequality "domain cost at least threshold" as a first-class Prop that later layers can inhabit or discharge.
Sibling definitions cover evaluation of the domain cost, its nonnegativity, positivity of the threshold, and an inhabited certificate record. No forcing-chain step (T0--T8) is proved here; the module only sets the collapse interface.
proof idea
Definition-heavy module, not a single theorem. Domain cost is defined from the imported J-cost; equality-at-evaluation and nonnegativity are short algebraic facts. The canonical threshold is a positive constant (positivity proved directly). The certificate is a structure packing the cost-threshold comparison; inhabitation is a one-line witness construction. No deep tactic scripts or multi-lemma chains.
why it matters in Recognition Science
Gives the Foundation layer a named collapse certificate so measurement can be stated as a cost crossing rather than an external postulate. Downstream pages can require RSWFCollapseCert (or the inhabited cert) whenever a derivation needs a definite outcome after recognition. Ties to the J-uniqueness landmark (T5) and the RCL-forced cost: collapse is decided by the same $J$ that generates the phi-ladder and the eight-tick octave, not by an ad hoc Born rule. Currently unused by other modules in the graph (used_by_count = 0), so it is an interface waiting on measurement and decoherence developments.
scope and limits
- Does not derive the Born rule or outcome probabilities.
- Does not prove uniqueness of the canonical threshold from T0--T8.
- Does not model multi-particle entanglement or EPR correlations.
- Does not connect collapse timing to the eight-tick octave dynamics.
- Does not discharge physical units beyond RS-native cost.