IndisputableMonolith.Physics.RS_PHY_Structural_005
Module packaging the structural certificate for domain-cost nonnegativity and a positive canonical threshold in RS-native units. Physicists citing structural ledger claims use the inhabited certificate bundle. Definitions and elementary positivity lemmas sit beside a thin cert record; no deep forcing argument lives here.
claimDefine a domain cost $C$ with $C\ge 0$, a canonical threshold $\tau_*>0$, and an inhabited certificate record asserting those structural facts for RS physics claim Structural-005.
background
Recognition Science measures mismatch by a nonnegative cost built from the unique $J$-functional forced at T5, $J(x)=(x+x^{-1})/2-1$. The Cost import supplies that infrastructure; Constants supplies the RS time quantum $\tau_0=1$ tick and related native units.
This module sits in the physics structural layer. It introduces a domain-level cost (evaluated at equality cases and proved nonnegative) and a canonical positive threshold against which structural comparisons are made. The certificate record bundles those facts so downstream ledger or audit code can demand a single inhabited witness rather than re-proving elementary inequalities.
proof idea
Definition-heavy module with short positivity lemmas. Domain cost is introduced, evaluated on equality configurations, and shown nonnegative by reduction to the Cost layer. The canonical threshold is defined and proved positive. A certificate structure packages the claims; inhabitation is a one-line constructor application. No multi-step forcing or RCL algebra appears here.
why it matters in Recognition Science
Supplies the Structural-005 certificate bundle used when physics ledger entries need a machine-checkable witness that domain cost is nonnegative and the comparison threshold is strictly positive. No downstream edges are recorded in the mirror graph yet, so the module is a leaf cert provider rather than a step inside T0-T8. It keeps structural bookkeeping separate from the deeper uniqueness and dimension-forcing chain.
scope and limits
- Does not derive J-uniqueness, phi, eight-tick structure, or D=3.
- Does not prove mass ladder, alpha band, or dynamical field equations.
- Does not connect domain cost to experimental observables beyond the cert interface.
- Does not discharge unrelated structural claim numbers outside 005.