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Asteroid ore classes receive explicit rung assignments on the phi-ladder so each mineral type carries a unique spectral peak at omega_0 times phi to the power of its rung. Spectroscopists and mission planners would cite the mapping to convert observed peak ratios into ore identifications. The declaration is a direct def that encodes the seven-class rung table and delegates frequency computation to the existing peakFrequency function.

claimEach ore class $c$ possesses a characteristic spectral peak frequency satisfying $ω(c) = ω_0 ⋅ φ^{r(c)}$, where the rung map $r$ sends silicate to 0, carbonate to 1, oxide to 2, sulfide to 3, metallic_Fe to 4 and completes the set of seven classes, with observed ratios required to lie inside the interval $[1/(2φ), 2φ]$.

background

The module implements Track J3 of the Recognition Science engineering derivation: asteroid-ore identification via φ-ladder phonon resonance. Physical quantities occupy discrete tiers indexed by powers of φ, with rung supplying the integer index for each OreClass. The sibling rung definition fixes silicate at rung 0, carbonate at 1, oxide at 2, sulfide at 3 and metallic_Fe at 4; the sibling peak definition then sets peak(c) := peakFrequency(c.rung). Upstream results supply the discrete-tier structure from NucleosynthesisTiers.of and the abstract Constants bundle from CPM.LawOfExistence, together with the LedgerFactorization calibration of J.

proof idea

The declaration is a pure definition (def_or_abbrev) with zero proof lines. It directly enumerates the rung cases for each constructor of OreClass and re-exports the frequency via the already-defined peakFrequency function; no lemmas or tactics are invoked.

why it matters in Recognition Science

The mapping supplies the concrete engineering content for the module-level claim that seven mineral classes are ranked by k-rung on the phi-ladder. It is referenced by downstream results including const_one_is_geodesic and costRateEL_implies_const_one in the Euler-Lagrange action, as well as acceptanceBandRatio_eq and pentatonicSize in the aesthetics layer. The construction realizes the T6 phi fixed-point and T7 eight-tick octave landmarks inside an applied spectroscopy setting and leaves open the empirical closure against real asteroid spectra.

scope and limits

formal statement (Lean)

  11class has a characteristic spectral peak `ω_k = ω_0 · φ^k`. We rank
  12seven mineral classes by their k-rung and bound the discrimination
  13floor.
  14
  15## Falsifier
  16
  17Asteroid spectroscopy on a sample with > 5 distinct ore-class peaks
  18where peak ratios fall outside `[1/(2φ), 2φ]` of φ.
  19-/
  20
  21namespace IndisputableMonolith
  22namespace Engineering
  23namespace AsteroidOreSpectroscopy
  24
  25open Constants
  26
  27noncomputable section
  28
  29/-! ## §1. Ore class ladder -/
  30
  31/-- Reference spectral peak `ω_0` (silicate baseline). -/

used by (40)

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