IndisputableMonolith.Physics.RecognitionHamiltonianSpectrum
RecognitionHamiltonianSpectrum module defines spectral sectors of the recognition Hamiltonian, beginning with the vacuum sector at J-cost zero. Physicists constructing RS-derived energy levels or lattice models cite these definitions when applying the J-cost function to quantum operators. The module consists of definitions and certificates with no proof obligations.
claimThe vacuum sector satisfies $J=0$. The module defines the set of spectral sectors, their count, the J-cost values for vacuum and excited states, the lattice spacing gap, and a certificate for the full Hamiltonian spectrum.
background
The module sits in the Physics domain and imports the RS time quantum τ₀ = 1 tick from Constants together with the J-cost machinery from Cost. It introduces SpectralSector as the partition of the Hamiltonian into sectors indexed by J-cost, with the vacuum sector fixed at J = 0 per the module doc-comment. The latticeSpacingGap and lattice_gap_witness capture discrete spacing derived from the phi-ladder in upstream Cost definitions.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the Hamiltonian spectrum definitions that feed the mass formula and energy calculations in the Recognition framework. It directly supports the J-uniqueness step (T5) by anchoring the vacuum at J = 0 and prepares the ground for the eight-tick octave and D = 3 spatial structure. No downstream theorems are recorded yet.
scope and limits
- Does not contain any theorems or proofs.
- Does not reference the full UnifiedForcingChain.
- Does not compute explicit numerical spectra or alpha values.
- Does not address Berry creation threshold or Z_cf.