IndisputableMonolith.Foundation.RS_FalsifiabilityMasterThm3
Module packaging the third RS falsifiability master certificate: a nonnegative domain cost, a strictly positive canonical threshold, and an inhabited certificate record tying them together. Experimental or theoretical auditors cite it when checking whether a claimed RS domain stays below the falsification cut. The argument is definitional plus elementary positivity lemmas from the Cost and Constants imports.
claimDefine a domain cost $C$ with $C\ge 0$, a canonical threshold $\theta>0$, and an inhabited certificate record asserting that the RS falsifiability criterion (master theorem 3) is witnessed by comparing $C$ against $\theta$.
background
Recognition Science measures mismatch with a nonnegative cost functional (the $J$-cost lineage from the Cost module). Falsifiability statements turn that cost into a cut: if an observed or derived domain cost exceeds a fixed positive threshold, the claim is rejected.
This module sits in Foundation and imports Constants (RS-native units, including the tick $\tau_0$) and Cost. It introduces a domain-level cost, proves nonnegativity and an evaluation identity, fixes a canonical positive threshold, and packages both into a certificate structure RSFalsifiability3Cert with an inhabited instance.
No forcing-chain step (T0–T8) is re-proved here; the module only freezes the numerical/structural witnesses needed for master falsifiability theorem 3.
proof idea
Definition module with short positivity lemmas, not a deep derivation. Domain cost is introduced and shown equal at a reference point, then nonnegative by reduction to the underlying Cost API. The canonical threshold is defined and proved strictly positive. The certificate record bundles these facts; inhabitation is a one-line constructor application. No tactic-heavy chain and no sorry path in the sibling surface listed.
why it matters in Recognition Science
Gives auditors a single inhabited certificate for RS falsifiability master theorem 3: cost nonnegativity plus a positive cut. Downstream pages can import the cert rather than rebuild threshold arithmetic. It does not itself close the UnifiedForcingChain (T5 $J$-uniqueness, T6 $\varphi$, T7 eight-tick, T8 $D=3$); it only supplies the falsifiability witness layer those results are checked against. With no further used_by edges in the graph snapshot, it is a leaf packaging module for external citation and test harnesses.
scope and limits
- Does not prove the full RS forcing chain (T0–T8) or $J$-uniqueness.
- Does not derive numerical values of $c$, $\hbar$, $G$, or $\alpha^{-1}$.
- Does not claim empirical data already exceed or stay under the threshold.
- Does not define mass-ladder rungs or Berry-threshold physics.
- Does not export a general falsifier for arbitrary non-RS models.