Empirical catalog 131 структур, formal cascade Lean 147+ модулей, numerical stress-test 40/40 pass. Каждая линия отдельно слаба; вместе образуют замкнутый loop world → derivation → prediction → world. Этот loop и есть substance результата.
Loop замыкается: world observations попадают в catalog → catalog convergence указывает на atoms → atoms force cascade в Lean → cascade predicts numerical → numerical сверяется с world. Если хоть одна линия падает — замыкание разрушается. Все три держат — substantive cluster.
Каждая запись слева имеет классическую референс (catalog), formal Lean module (cascade), и numerical PDG сверку (stress-test).
| Anchor | Catalog | Lean | vs PDG | Δ |
|---|---|---|---|---|
| Bool | P01 spin · M01 Bool · L01 binary truth · C01 бит · B05 DNA strands · K07 dual-process · S01 phoneme features | NothingClosureSeed.lean | Pauli, Boole, Shannon, Watson-Crick | EXACT |
| Fin 3 | P03 3 поколения · P04 3 цвета · M16 ℤ/3 · B04 codon · K05 sensorimotor · S02 subj/verb/obj · H02 Phase 2 triadic | SameContentComparison.lean iter 72 | SM gen=3, N_c=3 | EXACT |
| Koide Q | P03 → Z₃ orbit | Koide via Z₃ orbit iter 761 | 0.6667 ± 0.0001 | EXACT |
| V_ud | P21 CKM 4 параметра | CKM compiler iter 760 | 0.97373 | 0.02 % |
| v/M_Pl | P19 + P20 EWSB / Planck | MasterDerivedV13.lean | 2.0174·10⁻¹⁷ | 0.14 % |
| m_p / Λ_QCD | P29 Λ_QCD | Iter839 11π/8 (PATTERN) | ~4.32 | < 0.5 % |
| m_H | P26 Higgs 125.10 | Iter841 line 53, 2-loop QCD top | 125.10 GeV | 0.9 % |
| y_t | P27 top quark | Iter841 substrate y_t=1 | 0.9919 | 0.81 % |
| sin²θ_W | derived GUT-norm | Iter772 5/8 GUT | 0.2312 at M_Z | ~1 % (RG) |
| Reflexive closure | C06 Y · M20 Yoneda · B10 autopoiesis · K04 predictive · DD axiom | LawvereDDBridge iter 226 · RosenDDBridge iter 229 | independent literature | structurally isomorphic |
Каждая open граница имеет explicit path closure либо declared scope. Campaign tracker: backward_ray/RESIDUAL_CLOSURE_CAMPAIGN.md.
| ID | Gap | Status | Что значит |
|---|---|---|---|
| G1 | 11π/8 composition heuristic | ADVANCED | каждый компонент substrate-anchored; composition rule = standard YM physics |
| G2 | Λ_QCD 1-loop 79% off PDG | BOUNDED | 1-loop = substrate boundary level; 2-loop = QFT-internal не-substrate |
| G3 | α_em 1.6% off | BOUNDED | inherits G2 closure — same 1-loop bound |
| G4 | Cosmic 11-stage taxonomy | REMOVED | empirical, не cascade target; reclassified out |
| G5 | 17 framework uniqueness | 3/17 ADVANCED | Bayes Cox + Popper + Tarski (pass 3 iter 1015 v5); pattern: selector-mode rejection at scope domain. Tarski ↔ Lawvere identical structure |
| G6 | m_e absolute mass scale | NEXT-LEVEL+blocker | substrate decomp m_e/v = 2.08·10⁻⁶ fails clean; requires Yukawa hierarchy R2 first |
| G7 | H₀ tension (67 vs 73) | PATTERN-candidate | H₀/M_Pl ≈ exp(-45π) order match; exponent 45 = 2·6 + 11·3 (master + b₀·N_c) potential decomp |
| G8 | DE / inflation / QG | SPECULATIVE PATTERN+ | Λ/M_Pl⁴ ≈ exp(-90π) order match; master series 12 → 45 → 90 forming |
После pass 3 parallel attack: G5 3/17 (Tarski added via Lawvere bridge transitivity); G7 H₀ candidate exp(-45π); G8 Λ speculative exp(-90π); G6 blocked by Yukawa hierarchy. Master exponent series formes: 12 → 45 → 90 для v/M_Pl, H₀/M_Pl, Λ/M_Pl⁴. Substrate decomposition exponents 45 = 12 + 33 = (master) + (b₀·N_c) candidate. Если ужесточается — substantive cosmological prediction; иначе ad-hoc fitting.