IndisputableMonolith.Foundation.RecognitionScience2026State
Status snapshot for the 2026 Recognition Science ledger: a nonnegative domain cost, a positive canonical threshold, and an inhabited state-3 certificate record. Foundation auditors cite it when checking that the RS numerical gates are packaged and inhabited. The module is mostly definitional, with short positivity and equality lemmas over the imported cost and constants layers.
claimThe module introduces a domain cost $C$, records $C\ge 0$ and an evaluation identity, fixes a canonical threshold $\theta>0$, and packages an inhabited RS 2026 state-3 certificate built from those data.
background
Recognition Science derives physics from a single cost functional and a forcing chain that pins $J$, $\varphi$, the eight-tick octave, and $D=3$. Native units set $c=1$ and use the fundamental time quantum $\tau_0=1$ tick from the constants layer.
The cost import supplies the $J$-cost infrastructure against which domain-level scores are measured. This module sits in Foundation and does not re-derive $J$; it only names a domain cost, a canonical threshold, and a certificate bundle meant to record the 2026 state of those gates.
Sibling objects include the domain cost and its nonnegativity, the positive canonical threshold, and the inhabited RS2026State3Cert record. Downstream use is not wired in this graph snapshot; the module is a self-contained status package.
proof idea
Definition-and-certificate module, not a deep proof development. Domain cost and canonical threshold are introduced as defs; nonnegativity and positivity are short lemmas over the imported cost/constants facts; the state-3 certificate is an inhabited structure packaging those fields. No multi-step forcing argument lives here.
why it matters in Recognition Science
Gives Foundation a single place to point at the 2026 RS state certificate: cost gate, threshold gate, and inhabited cert. It does not advance the T0–T8 forcing chain, the Recognition Composition Law, or the mass/alpha ladders; those remain upstream. With no recorded used-by edges, it functions as a ledger snapshot rather than a lemma feeding a parent theorem. Useful when auditing whether the numerical RS gates are packaged and inhabited in Lean.
scope and limits
- Does not prove uniqueness of $J$ or force $\varphi$ (T5–T6 live elsewhere).
- Does not derive $D=3$, the eight-tick octave, or RCL identities.
- Does not compute masses, $\alpha$, or continuum limits.
- Does not claim downstream theorems; used-by is empty in this graph.
- Does not replace the Cost or Constants modules; it only packages status data.