IndisputableMonolith.Physics.Cyclotron5
Defines the domain cost and canonical threshold for the fifth cyclotron resonance channel in RS-native units, plus a small certificate packaging nonnegativity and positivity. Anyone matching cyclotron ratios to the phi-ladder would cite the threshold and cost identities. The module is mostly definitional; positivity facts are elementary.
claimIntroduces a domain cost $C$ on the cyclotron-5 sector, a canonical threshold $\theta>0$, and a certificate bundling $C\ge 0$ with threshold positivity in RS-native units ($\tau_0=1$).
background
Recognition Science scores mismatches with the J-cost calculus from the Cost module and normalizes time to the fundamental tick $\tau_0=1$ from Constants. Cyclotron channels are read as discrete resonance slots on that tick lattice; the fifth channel is the local specialization treated here.
The module therefore needs only two imports beyond Mathlib: Constants for the RS time quantum, and Cost for the underlying cost primitives. Sibling definitions name a domain cost, its evaluation identity and nonnegativity, a canonical threshold with positivity, and a certificate type that packages those facts.
proof idea
Definition-first module, not a deep derivation. domainCost and canonicalThreshold are introduced by definition; domainCost_at_eq is an evaluation identity; domainCost_nonneg and canonicalThreshold_pos are discharged by direct nonnegativity or Mathlib positivity reasoning. Cyclotron5Cert bundles the facts; cert and cert_inhabited exhibit an inhabited certificate.
why it matters in Recognition Science
Supplies the local cost and threshold layer for fifth-channel cyclotron matching in the RS physics stack. The mirror graph currently lists no downstream dependents; the certificate is the natural handoff for higher resonance or phi-ladder comparisons that need a verified fifth-channel bound. It sits downstream of Cost and Constants only, so it does not itself close forcing-chain steps T5–T8.
scope and limits
- Does not derive cyclotron frequencies from the T0–T8 forcing chain.
- Does not equate the threshold to measured SI cyclotron data.
- Does not prove uniqueness of the fifth channel among other resonances.
- Does not introduce new mass-ladder or alpha-band identities.
- Does not record downstream consumers in the current mirror graph.