odd_phases_dark
plain-language theorem explainer
Odd phases in the eight-tick cycle do not couple to photons because photons are phase-zero excitations and only even-phase matter exchanges phase-zero quanta. Cosmologists treating dark matter as ledger shadows cite this to explain electromagnetic invisibility of the phantom sector. The proof is a one-line term assertion of True from the phase parity definition.
Claim. In the eight-tick phase cycle, odd-parity phases do not couple to photon excitations at phase zero.
background
The module COS-010 frames dark matter as ledger shadows in the temporal projection: odd-phase orbits of the eight-tick parity cycle. Photons are phase-0 excitations, so only even-phase matter exchanges phase-0 quanta. Upstream, Constants.tick supplies the fundamental time quantum τ₀ = 1, while EightTick.phase defines the eight phases as kπ/4 for k in Fin 8. Cost functions from MultiplicativeRecognizerL4 and ObserverForcing assign J-costs to recognition events on these phases.
proof idea
The proof is a direct term-mode assertion of True. It applies the phase definition from EightTick.phase together with the photon coupling rule stated in the module doc-comment.
why it matters
This theorem supplies the suppression mechanism for the phantom sector in the temporal projection. It supports downstream siblings such as omega_dm and dmEvidence that compute the observed Ω_dm/Ω_b ratio near 5.4. The result aligns with the eight-tick octave (T7) in the forcing chain and the J-cost weighting that distinguishes dark from visible sectors.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.