IndisputableMonolith.Physics.Structural_Physics_mod26
Module packaging structural-physics quantities tied to a mod-26 domain: a nonnegative domain cost functional, a positive canonical threshold, and an inhabited certificate bundle StructPhysicsM26Cert. Physicists working the RS structural layer cite it for the cost/threshold interface rather than for a single theorem. Content is definitional plus elementary positivity and evaluation lemmas over Cost and Constants.
claimThe module introduces a domain cost $C_{\mathrm{dom}}$, proves $C_{\mathrm{dom}}\ge 0$ and an evaluation identity at equality points, a canonical threshold $\theta_*>0$, and an inhabited certificate record bundling these structural-physics facts for the mod-26 setting.
background
Recognition Science builds physics from the J-cost and the forcing chain (T0–T8). This module sits in the physics layer and imports only Constants (RS-native units, including the time quantum $\tau_0=1$ tick) and Cost (the J-cost infrastructure).
Sibling definitions indicate a domain-restricted cost domainCost, its nonnegativity, an evaluation lemma domainCost_at_eq, a positive canonicalThreshold, and a certificate type StructPhysicsM26Cert with an inhabited instance. The “mod26” tag marks a discrete structural sector (period or residue class 26) rather than a continuum field theory.
No external paper proposition is attached at module scope; the local job is to expose a small, checkable interface (cost, threshold, cert) for downstream structural claims.
proof idea
Definition module with thin lemmas. Domain cost and canonical threshold are introduced as defs; nonnegativity and positivity are short inequality proofs over the Cost layer; domainCost_at_eq is an evaluation identity. The certificate record packages those facts, and cert_inhabited supplies a witness. No deep tactic development or forcing-chain argument lives here.
why it matters in Recognition Science
Supplies the structural-physics cost/threshold certificate surface for the mod-26 sector inside the RS physics tree. Downstream edges are not yet wired at audit time (used_by empty), so the module is an interface seed rather than a proved parent theorem. It keeps domain cost and the canonical threshold in one inhabited cert, aligning with the RS pattern of packaging local physics facts for later forcing or mass-ladder work. Does not itself touch T5–T8, RCL, or the alpha band; those remain upstream/downstream of this interface.
scope and limits
- Does not prove uniqueness of the domain cost or threshold.
- Does not derive mod-26 from the eight-tick octave or T7.
- Does not connect to mass ladder, alpha band, or continuum field equations.
- Does not discharge any forcing-chain step T0–T8.
- Does not assert experimental bounds; only formal nonnegativity/positivity.