IndisputableMonolith.Physics.RecognitionHamiltonianSpectrum
RecognitionHamiltonianSpectrum defines the vacuum sector of the Recognition Hamiltonian where J-cost vanishes and introduces spectral sectors classified by lattice gaps. Physicists constructing RS-derived quantum spectra reference these objects when building the energy ladder from phi-fixed points. The module consists entirely of definitions and certificates with no embedded proofs.
claimThe vacuum sector satisfies $J=0$. Spectral sectors are indexed by latticeSpacingGap, with vacuum_jcost and excited_jcost giving the J-values on each rung and HamiltonianSpectrumCert certifying the overall structure.
background
The module imports the RS time quantum τ₀ = 1 tick from Constants and the J-cost machinery from Cost. It introduces SpectralSector as the discrete classification of Hamiltonian levels, vacuum_jcost as the ground-state J-value fixed at zero, and latticeSpacingGap together with lattice_gap_witness for the discrete spacing inherited from the phi-ladder. The local setting is the Recognition Composition Law applied to the Hamiltonian operator in RS-native units.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
These definitions supply the Hamiltonian spectrum certification required for mass formulas and the alpha band in the Recognition framework. They rest on J-uniqueness (T5) and the eight-tick octave (T7) while preparing the ground for D = 3 spatial dimensions (T8). No downstream theorems are recorded yet.
scope and limits
- Does not derive explicit eigenvalues.
- Does not prove completeness of the sectors.
- Does not connect spectrum to measured particle masses.
- Does not include time evolution or dynamics.