canonical_phi_lattice
plain-language theorem explainer
The definition constructs a uniform phi-lattice regularity instance whose edge length is exactly phi squared times 1.47. Researchers certifying nonlinear Regge convergence for strong-field gravity would cite it to supply the required CMS regularity structure. The construction is a direct record that assigns the length and discharges the three field obligations by positivity, triviality, and reflexivity.
Claim. Let $d = 1.47$ and let $L = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{backbone} = d_{back
background
The Nonlinear Regge Convergence module asks whether the Cheeger-Muller-Schrader regularity theorem can be applied to close the black-hole interior gap once the linearized regime is already certified. PhiLatticeRegularity is the structure that encodes the required lattice properties: a real edge length that is strictly positive, identical for every pair of indices, and exactly equal to phi squared times 1.47. The constant phi is the self-similar fixed point imported from Constants; the numerical factor 1.47 is the RS-native backbone scale in the phi-ladder.
proof idea
The definition is a direct record construction. It sets the edge_length field to phi^2 * 1.47, discharges edge_positive by the positivity tactic, sets edge_uniform to the trivial predicate that holds for all natural-number indices, and proves edge_from_phi by reflexivity.
why it matters
canonical_phi_lattice supplies the concrete lattice instance that appears in both nonlinear_regge_cert_exists (which constructs a nonempty NonlinearReggeCert) and phi_lattice_satisfies_cms (which verifies the three CMSConditions). It therefore occupies the exact point in the RS path where the uniform phi-lattice is shown to satisfy the regularity hypothesis needed for the nonlinear regime, linking the eight-tick octave and phi-ladder directly to strong-field gravity.
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