IndisputableMonolith.Physics.Structural_Physics_mod96
Module packaging mod-96 structural physics primitives: a domain cost, its nonnegativity and evaluation identities, a positive canonical threshold, and an inhabited certificate bundle. RS physicists working on discrete structural constraints cite it as the local API. Content is mostly definitions plus short positivity and equality lemmas over the Cost and Constants imports.
claimAt the mod-$96$ structural layer one has a domain cost $C_{\mathrm{dom}}$, the identity relating its pointwise evaluation, $C_{\mathrm{dom}}\ge 0$, a canonical threshold $\theta>0$, and an inhabited certificate packaging these structural-physics facts.
background
Recognition Science builds physics from the J-cost and the forcing chain (T0–T8). This module sits in the Physics domain and imports only Constants (RS-native time quantum $\tau_0=1$ tick) and Cost (the J-cost infrastructure).
The sibling surface introduces a domain-level cost functional, elementary comparison lemmas (evaluation identity and nonnegativity), and a canonical positive threshold. These are then bundled into a certificate type whose inhabitation records that the mod-96 structural package is available to downstream physics developments.
Mod $96$ is the discrete scale at which the module freezes structural claims; it is not itself derived here from the eight-tick octave, but is the naming convention for this layer of the physics API.
proof idea
This is primarily a definition-and-certificate module, not a deep proof development. Domain cost and the canonical threshold are introduced as defs; nonnegativity and positivity are short lemmas over the imported Cost/Constants facts; evaluation identity is an equality lemma. The certificate structure packages those facts, and inhabitation is a one-line constructor application.
why it matters in Recognition Science
Supplies the local structural-physics API at mod $96$: domain cost, threshold, and a certificate that downstream physics modules can assume inhabited. No used_by edges are recorded yet, so the module presently acts as a leaf packaging layer rather than a proved step inside T0–T8. It ties the Cost import (J-cost) and the RS tick constant into a named physics certificate, ready for later structural or mass-ladder arguments that need a frozen mod-96 interface.
scope and limits
- Does not derive mod 96 from the eight-tick octave or T7.
- Does not prove uniqueness of the domain cost or threshold.
- Does not connect to mass ladder, alpha band, or D=3 forcing.
- Does not discharge any open sorry outside its own certificate inhabitation.
- Does not state dynamical evolution, only structural cost/threshold data.