IndisputableMonolith.Nuclear.RS_NUC_Structural_005
Nuclear-sector module that packages RS-NUC-Structural-005: a domain cost functional, elementary nonnegativity and evaluation lemmas, a positive canonical threshold, and an inhabited certificate record. Nuclear auditors cite it when wiring cost bounds into larger RS nuclear claims. The file is mostly definitions plus short positivity facts over Cost and Constants.
claimDefines a nuclear domain cost $C_{\mathrm{dom}}$, records $C_{\mathrm{dom}}\ge 0$ and a pointwise evaluation identity, fixes a canonical threshold $\theta>0$, and packages these data into an inhabited structural certificate for RS-NUC-Structural-005.
background
Recognition Science treats nuclear structure claims with the same cost accounting used elsewhere in the monolith. The Cost import supplies the global cost infrastructure (J-cost style defect accounting); Constants supplies RS-native units, including the fundamental time quantum $\tau_0=1$ tick.
This module localizes that machinery to a domain cost for structural item 005, together with a canonical positive threshold against which the cost is compared. Sibling names indicate equality-at-a-point and nonnegativity lemmas, then a certificate type with an inhabited instance so downstream nuclear developments can assume the structural package without re-proving the basics.
proof idea
Definition-and-certificate module, not a deep derivation. Domain cost and canonical threshold are introduced as defs; nonnegativity and positivity are short lemmas over the Cost layer; evaluation-at-equality is a one-line identity. The certificate record bundles those facts, and inhabitation is by direct construction of the cert value. No forcing-chain or RCL algebra appears here.
why it matters in Recognition Science
Earns its place as the structural certificate shell for RS-NUC-Structural-005 in the Nuclear domain. Downstream used_by edges are empty in the graph, so it is presently a leaf package: later nuclear binding, stability, or mass-ladder claims can import the cert rather than rebuild domain-cost hygiene. It does not itself touch T5–T8, the eight-tick octave, or the phi-ladder mass formula; it only standardizes the cost/threshold interface those developments will need.
scope and limits
- Does not derive nuclear binding energies or experimental mass defects.
- Does not prove uniqueness of the canonical threshold beyond positivity.
- Does not connect domain cost to T0–T8, RCL, or the phi-ladder.
- Does not establish any numerical match to nuclear data tables.
- Does not record downstream consumers yet (used_by is empty).