selfBootstrapCert
plain-language theorem explainer
The self-bootstrap certificate asserts that the meta-language distinguishes propositions and that the claim of carrier distinguishability differs from its negation. Researchers closing the absolute-floor program in Recognition Science cite it to complete Route A. The proof is a direct term construction that assembles the certificate by supplying the two required fields from prior theorems on propositional distinctions.
Claim. There exists a self-bootstrap certificate consisting of the facts that the meta-language distinguishes propositions ($∃ P, Q : Prop, P ≠ Q$) and that for every type $K$, the statement $∃ x y : K, x ≠ y$ is not equal to its negation $¬(∃ x y : K, x ≠ y)$.
background
The module SelfBootstrapDistinguishability records the Lean-checkable part of the self-bootstrap argument for the absolute-floor program. It proves meta-level facts used by the argument: the formal language already distinguishes propositions, and the proposition asserting object-level distinguishability is distinct from its denial. It does not pretend to derive an object-level non-singleton carrier from nothing.
proof idea
The proof is a term-mode construction of the SelfBootstrapCert structure. It directly assigns the meta_distinguishes field to the theorem meta_language_distinguishes_props and the claim_not_its_negation field to dist_claim_self_distinguishes.
why it matters
This theorem supplies the routeA field for absoluteFloorClosureCert, closing the absolute-floor program via the self-bootstrap route at the meta-language floor. It implements the module goal of recording theorem-backed meta-facts. In the Recognition framework it supports foundational closure without descending below the meta level, touching the question of how meta-distinguishability leads to object-level structure.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.
papers checked against this theorem (showing 2 of 2)
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Self-quenching suppresses plasmon decay in size-dependent way
"plasmonic quasi-particle functions as a quantum emitter embedded within a self-created resonant near-field nano-cavity"
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Multi-robot service prototype runs on Aggregate Programming
"the self-stabilizing nature and resilience to changes of AP operators, has made it possible to deal naturally with several dynamic/failure scenarios"