IndisputableMonolith.Foundation.RS_Wave_Function_Collapse
Foundation module for the Recognition Science treatment of wave-function collapse. It defines a domain cost, a canonical positive threshold, and a certificate type that packages nonnegativity of the cost with positivity of the threshold. Measurement-problem work in RS cites the certificate and the threshold lemmas. The module is mostly definitional, with short positivity and evaluation lemmas.
claimThe module defines a domain cost $C$, a canonical collapse threshold $\theta>0$, and a certificate asserting $C\ge 0$ together with $\theta>0$, as the RS packaging of a wave-function collapse criterion in native units ($\tau_0=1$ tick).
background
Recognition Science derives dynamics from a unique cost $J$ fixed by the Recognition Composition Law, with $J(x)=(x+x^{-1})/2-1$. Collapse and creation events are tied to cost crossing a threshold; the primer landmark is the Berry creation scale $\phi^{-1}$. This module sits in Foundation and imports Constants ($\tau_0=1$ tick) and Cost.
Sibling definitions introduce a domain-level cost (with an evaluation identity and a nonnegativity lemma), a canonical threshold (with a positivity lemma), and a certificate structure RSWFCollapseCert inhabited by a concrete cert. The local setting is the discrete RS ledger: costs are nonnegative and thresholds are strictly positive before any dynamical claim is made.
No external measurement postulates are assumed. The objects here only fix the cost-threshold interface that a later collapse or decoherence argument would invoke.
proof idea
Definition module, not a single theorem. Domain cost is introduced as a def; domainCost_at_eq is an evaluation identity; domainCost_nonneg is a short nonnegativity argument from the Cost import. Canonical threshold is a def; positivity is a one-line or elementary inequality. The certificate type bundles those facts; cert and cert_inhabited supply a concrete inhabitant. No deep tactic scripts: structure is defs plus elementary lemmas.
why it matters in Recognition Science
Gives the Foundation interface for RS wave-function collapse: cost on a domain, a fixed positive threshold, and a certificate that those inequalities hold. Downstream used-by edges are empty in the graph, so this module is a leaf provider rather than a step inside a larger proved chain (T0–T8 forcing, RCL, or the mass ladder).
It connects to the broader RS story where creation and collapse sit at cost thresholds (Berry scale $\phi^{-1}$ in the primer) and time is counted in ticks $\tau_0=1$. Anyone formalizing measurement, decoherence, or ledger update in RS would import this certificate rather than re-proving cost nonnegativity and threshold positivity ad hoc.
It does not close the measurement problem; it only standardizes the cost-threshold side conditions.
scope and limits
- Does not derive the Born rule or outcome probabilities.
- Does not prove dynamical collapse trajectories or timing.
- Does not identify the threshold with $\phi^{-1}$ inside this module.
- Does not connect to the T0–T8 forcing chain or mass ladder.
- Does not claim experimental uniqueness of the certificate.