cert
plain-language theorem explainer
Packages three structural facts about the astrophysics domain cost at recognition rung 91 into a single certificate record: diagonal vanishing, non-negativity for positive mass/energy arguments, and positivity of the canonical threshold. Anyone citing the mod-91 astrophysics structural layer would reference this bundle. The body is a pure record assembly of three already-proved sibling lemmas.
Claim. There exists a structural certificate for the astrophysics domain at recognition rung 91 consisting of: (i) $\mathrm{domainCost}(r,r)=0$ for all $r\neq 0$; (ii) $\mathrm{domainCost}(m,e)\ge 0$ whenever $m>0$ and $e>0$; (iii) the canonical threshold is strictly positive.
background
This module states a structural Recognition Science prediction for the astrophysics domain at recognition rung 91 (Plan v7, 120th pass). Status is a structural theorem: zero sorry, zero axioms.
The certificate structure bundles three properties of domainCost, the local cost functional on mass/energy-like real arguments. Diagonal vanishing says matched arguments carry zero cost. Non-negativity mirrors the global J-cost law: recognition cost never goes negative. The third field asserts that the module's canonical threshold (the cutoff used to gate structural claims) is positive.
Upstream, the foundation result cost_nonneg records that every recognition event has non-negative cost via Jcost_nonneg on a positive state. The domain-level non-negativity lemma is the local analogue of that global fact.
proof idea
One-line record construction. The three structure fields are filled by the sibling lemmas domainCost_at_eq, domainCost_nonneg, and canonicalThreshold_pos respectively. No additional tactics or algebraic work occur at this declaration.
why it matters
Gives a single named inhabitant of the mod-91 astrophysics structural certificate, so downstream astrophysics arguments can assume the three cost axioms as one package rather than re-importing each lemma. The module frames this as the structural RS prediction for astrophysics at rung 91 on the phi-ladder. No used_by edges are recorded yet; the immediate consumer is the companion inhabitance fact in the same file. Framework role is bookkeeping for domain-level cost hygiene (diagonal zero, non-negativity, positive threshold), not a new forcing-chain step (T0–T8) or a mass-ladder evaluation.
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