`planck_scale_matching_cert`

definition

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module: IndisputableMonolith.Constants.PlanckScaleMatching
domain: Constants
line: 298 · github
papers citing: none yet

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IndisputableMonolith.Constants.PlanckScaleMatching on GitHub at line 298.

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formal source

 295  planck_ratio : lambda_rec_SI / ell_P = 1 / sqrt Real.pi
 296
 297/-- The Planck-Scale Matching Certificate is verified. -/
 298def planck_scale_matching_cert : PlanckScaleMatchingCert where
 299  J_bit_ok := J_bit_pos
 300  J_bit_numerical := J_bit_bounds
 301  extremum_determines := extremum_condition
 302  planck_ratio := lambda_rec_over_ell_P
 303
 304/-- Summary report for the Planck-Scale Matching derivation. -/
 305def planck_scale_matching_report : String :=
 306  "PLANCK-SCALE MATCHING (Conjecture C8)\n" ++
 307  "=====================================\n" ++
 308  "\n" ++
 309  "DERIVATION CHAIN:\n" ++
 310  "  1. J_bit = J(φ) = φ - 3/2 ≈ 0.118 [PROVED]\n" ++
 311  "  2. J_curv(λ) = 2λ² (curvature packet) [AXIOMATIZED]\n" ++
 312  "  3. Extremum: J_bit = J_curv → λ_rec [PROVED]\n" ++
 313  "  4. Face-averaging → 1/π factor [AXIOMATIZED]\n" ++
 314  "  5. λ_rec/ℓ_P = 1/√π ≈ 0.564 [PROVED]\n" ++
 315  "\n" ++
 316  "RESULT: λ_rec = √(ℏG/(πc³)) ≈ 0.564 ℓ_P\n" ++
 317  "\n" ++
 318  "STATUS: Hypothesis-level (curvature packet axiom)\n" ++
 319  "REMAINING GAP: Derive J_curv = 2λ² from Q₃ geometry"
 320
 321end PlanckScaleMatching
 322end Constants
 323end IndisputableMonolith

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