Astrophysics Gravitational Wave From Jcost Gravitational Wave Cert

The gravitational wave certificate

Gravitational waves are ripples in spacetime, first measured in 2015 by the LIGO collaboration from a binary black hole merger. Astronomers sort these sources into categories: two neutron stars merging (NS-NS), a black hole with a neutron star (BH-NS), two black holes (BH-BH), supermassive black holes (SMBH), and a stochastic background hum from many weak sources. The Recognition Science framework defines a certificate, a machine-checked bundle of formal statements, that records two facts about these categories.

The first fact is a count: there are exactly five canonical source categories. The framework's library proves this by exhaustive enumeration of its own inductive type, giving the number 5 with no axioms beyond the standard logical ones. The second fact concerns strain, the fractional stretching of space a passing wave causes. The framework defines a sequence of strain values at integer rungs, and proves that each rung's strain divided by the previous rung's strain equals the golden ratio phi, approximately 1.618. Written in symbols: strainAtRung (k+1) / strainAtRung k = phi.

In Recognition Science, this phi ratio is not fitted to data. It derives from the framework's forced cost function, which yields phi as the unique self-similar scaling. The certificate bundles the five-category count and the phi ratio into one structure, built from two proved theorems. The claim is purely structural: within the framework's model, the strain ratios between adjacent source classes follow the phi-decay law.

What the certificate does not claim matters. It does not assert that any gravitational wave was detected, that the phi ratio matches observed LIGO or Virgo data, or that the five categories are physically exhaustive. The certificate is a formal object about a model, not an empirical result. The framework's library proves the internal consistency of its own definitions; comparing those definitions against measured universe is a separate, empirical step that this certificate does not perform.

theorem gwSourceCount : Fintype.card GWSourceCategory = 5 := by decide

theorem strainRatio (k : ℕ) :
    strainAtRung (k + 1) / strainAtRung k = phi := by
  unfold strainAtRung
  have hpos := pow_pos phi_pos k
  rw [pow_succ]; field_simp [hpos.ne']

What this page does not claim

No gravitational wave detection is claimed. No match between the phi ratio and observed astrophysical data is claimed. The five source categories are a definitional choice, not a proved physical taxonomy.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Astrophysics/GravitationalWaveFromJCost.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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