HolographicCert
plain-language theorem explainer
HolographicCert bundles the claim of exactly five holographic duality contexts with positivity of the Bekenstein-Hawking coefficient. Researchers deriving the holographic principle inside Recognition Science cite it to record the enumeration of AdS/CFT, black-hole entropy, de Sitter, flat-space, and condensed-matter cases. The declaration is a bare structure definition that assembles the cardinality fact and the inequality 0 < 1/4 with no further obligations.
Claim. A structure certifying that the set of holographic duality contexts has cardinality five and that the Bekenstein-Hawking coefficient satisfies $0 < 1/4$.
background
The module enumerates five canonical holographic-duality contexts: AdS/CFT, black-hole entropy, de Sitter space, flat-space holography, and condensed-matter duality. These are collected in an inductive type whose cardinality is asserted to be five. The Bekenstein-Hawking coefficient is introduced as the constant 1/4 that appears in the entropy bound $S ≤ A/4$ in Planck units.
proof idea
The declaration is a structure definition whose two fields directly record the cardinality equality for the context inductive type and the positivity of the coefficient defined as one over four.
why it matters
HolographicCert supplies the bundled certificate consumed by the top-level holographicCert construction in the same module. It closes the structural verification step in the derivation of the holographic principle from the Recognition Science forcing chain, confirming that the entropy bound is captured by the canonical five contexts.
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