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allaun 14cde6d09c docs: refresh READMEs, AGENTS.md, and project maps for recent Lean surface 
- Update README.md and 0-Core-Formalism/README.md with build baseline
  (3314 jobs, 0 errors) and new modules (SDPVerify, GoormaghtighCert,
  Hachimoji, SieveLemmas, InteractionGraphSidon, GeneticBraidBridge)
- Update AGENTS.md and 0-Core-Formalism/lean/Semantics/AGENTS.md blessed
  surface tables and build baselines
- Add 6-Documentation/PROJECT_MAP.md and update existing project maps
  (MATH_MODEL_MAP*, LEAN_PORT_ORCHESTRATION_MAP, SIDON_FAMM_MAP,
  BEGINNERS_MAP) with new components and Gremlin mathblob graph loader
2026-06-20 20:34:09 -05:00

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MATH_MODEL_MAP — Sorted by Domain

Generated: 2026-04-19 Last Updated: 2026-04-27 Total Models: 739 across multiple families (including Neural Development, Cephalopod Distributed, Neurodivergent) Sorting: Grouped by domain, then by model number

Status: ⚠️ OUTDATED - This document shows 206 models but current MATH_MODEL_MAP.tsv contains 739 models. Regeneration required.

[BEAUTIFUL_PROVISIONAL - All claims marked as "✅ PROVEN" require Lean theorem verification evidence. All claims marked as "🔄 SORRY" violate AGENTS.md rule "Never Leave sorry in Committed Code" and must be eliminated or quarantined. Per AGENTS.md v2.1, LLM agreement, beauty, elegance, and coherence are not evidence. PROVEN status requires actual Lean theorem proof or #eval witness evidence.]

Layer A: COMPRESSION (14 models)

# Model Equation Purpose
1 Intrinsic Load L_I = -Σ p(b|x) log₂ p(b|x) Shannon entropy
2 Extraneous Load L_E = BPB(x, w_prior) - BPB*(x) Suboptimal routing cost
3 Germane Load L_G = Σ γˢ · ΔL_E(x_s, t+1) Learning effort
4 Routing Load L_R = Σ c_j·1[f_j] + Σ log₂|M_l| Decision tree cost
5 Memory Load L_M = log₂|E| + α·1[hit] + ... Engram burden
6 Total Load L_total = λI·l̂I + λE·l̂E - λG·l̂G + ... Aggregate burden
7 Efficiency η = l̂I / (l̂I + l̂E + l̂R + l̂M + ε) Routing efficiency
8 Regret-Adjusted L_ρ = L_total · (1 + ρ/ρ_max) Performance penalty
9 Basin-Conditional L(x|B) = L_I + L_E(x|B) + L_R^B Basin load
10 MoE Predictor P_w(x_i) = Σ w_j · P_{m_j}(x_i|x_{<i}) Mixture-of-experts
71 Mutual Information MI(x) = baseline_bpb - actual_bpb Structural density
72 k-NN MI MI_pred = Σ (w_i·MI_i·S_i) / Σ (w_i·S_i) Local estimation
73 Surprise surprise = log(1 + |MI_act - MI_pred|) Learning trigger
74 Structure Yield ρ(x) = MI(x) / (cost(x) + ε) ROI computation

Key Intersection: A ↔ B (Load → Routing), A ↔ M (Compression → Lean)

Layer B: ROUTING (18 models)

# Model Equation Purpose
16 Coupling Weight w_ij = g(Δθ,Δφ,χ_i,χ_j) · h(Δp) Mu-seed compatibility
17 Rotational Alignment g = cos(Δθ·2π/16)·cos(Δφ·π/8)·(1-2|χ_i-χ_j|) Frame match
18 Spatial Proximity h = exp(-|Δp|²/2σ²)·1_{|Δp|<r_max} Distance decay
19 Interaction Force F_ij = w_ij·(a_j-a_i)·Δp_ij/|Δp_ij| Activation flow
20 Energy Function E = -½Σ w_ij·a_i·a_j + Σ V(a_i) Energy landscape
21 Frame Evolution θ_i(t+1) = θ_i(t) + α_θ·F_{i,θ} + ξ_θ Discrete update
22 Continuous Flow df_i/dt = -α∇_{f_i}E(f) + ξ(t) Langevin SDE
23 Energy Monotonicity dE/dt = -αΣ|∇_{f_i}E|² ≤ 0 Convergence
75 Weighted Distance d(z₁,z₂) = √Σ w_i·((z₁_i-z₂_i)/s_i)² Scale-normalized
82 Raw Event Weight w(e|V) = ε + spec + pol + int + res + par + pri Additive score
83 Spectral Overlap spec = Σᵢ(V.spectrumᵢ · e.spectrumᵢ) Compatibility
84 Polarity Bias pol = f(sign(V.polarity), e) Purine/pyrimidine
85 Interaction Bucket int = quantize(V.interaction, {-64,0,64}) 5-level coupling
86 Resonance Weight res = min(V.resonanceCount, 4) + 1 Saturated bonus
87 Parity Weight par = 2 if parity(e) = V.parityXor else 1 XOR check
88 Normalized Probability P(e|V) = w(e) / Σ_{b∈{a,t,g,c}} w(b) Distribution
119 Final Score Law ℓₜ = eₜ·bind(γₜ,modelₜ,gₜ,historyₜ) + λ₁H + ... Per-step cost
120 Total Compression L(X) = Σₜℓₜ + commitments + residual Global aggregation

Key Intersection: B ↔ C₁ (Routing → Topology), B ↔ M (Routing → Lean)

Layer C₁: TOPOLOGY (24 models)

# Model Equation Purpose
24 Temporal Weight w_ij^(τ) = cos(2π(τ_j-τ_i)/16) Phase coupling
25 Complete Weight w_ij = cos(Δθ·22.5°)·cos(Δφ·22.5°)·cos(2πΔτ/16)·... Full 5-factor
26 Temporal Force F_ij^(τ) = w_ij^(τ)·(a_j-a_i)·sgn(τ_j-τ_i) Past→future
27 Temporal Evolution τ_i(t+1) = τ_i(t) + α_τ·F_{i,τ} + ω₀ Intrinsic clock
28 Temporal Stability d/dt(τ_j-τ_i) = 0 Locked phase
29 Temporal Entropy H_τ = -Σ p(τ=k)·log₂ p(τ=k) Temporal disorder
30 μ-Seed Cardinality |S_μ| = 8,589,934,592 ≈ 2³³ Local state
31 Fractal Occupancy |P_occ| = ρ·N^{d_H} (d_H≈2.7268) Menger sponge
32 Total Formal State |S_total| ≈ 2^{5,900,000} Upper bound
33 Reachable State |S_reachable| ≈ |S_total| / 10²⁹ Admissible
34 Packet State P = (ΔV, Δt, π, τ, χ, C, A) Wave packet
35 Throat Condition Φ_topo(i,j) >> Φ_metric(i,j) Non-local corridor
36 Multi-Factor Weight w_ij = w_p·w_π·w_τ·w_χ·w_topo·w_σ 6-factor
37 Holonomy Hol(γ_loop) = ∮_γ T(p) dp Phase around loop
38 Non-Euclidean Distance d_N = path_length + curvature_penalty + torsion Topology-aware
94 Traversal Safety safe = aperture > 0.001 ∧ stress < 10.0 Mouth stability
95 Shortcut Distance Δd = manifold_dist - throat_length Distance saved
96 Throat Efficiency η = manifold_dist / throat_length Compression ratio
97 Traversal Cost cost = exotic_matter + stability_penalty Resource
98 Flux Capacity flux ≤ max_throughput Bandwidth
102 Square-Shell Identity n = k² + a = (k+1)² - b, a+b = 2k+1 [REVIEWED - requires Lean theorem verification evidence]
103 Tip Coordinate Vector Tip(n) = (ab, a-b) ∈ ℝ² Embedding
121 Axial Generator Exhaustivity {A_k, G_k, C_k, T_k} partition S_k [REVIEWED - requires Lean theorem verification evidence]
124 45° Line Factor L_45°(n) contains all d|n Fermat factorization

Key Intersection: C₁ ↔ C₂ (Topology → Braid), C₁ ↔ F (Topology → Control)

Layer C₂: BRAID (10 models)

# Model Equation Purpose
79 Cosine Similarity cos = x·x_ref / (|x|·|x_ref|) Reference alignment
80 Gradient Alignment align = ∇g_i·∇g_j / (|∇g_i|·|∇g_j|) Coherence
81 Phase Accumulation phase += Σ y·dx Work integral
104 Axial Event Production A_k, G_k, C_k, T_k generators PROVEN
105 Resonance Hub Tip(m²) = (0, -(2k+1)) PROVEN
110 AVMR Commitment Σ_{k+1}[i] = Φ(Σ_k[2i], Σ_k[2i+1]) Vectorized Merkle
122 Tip Mass Resonance ab_i = ab_j Hyperbola intersection
123 Tip Mirror Resonance (a-b)_i = -(a-b)_j Shell coupling
131 Missing Link ODE d/dt(a,b) = (1,-1) + ε·∇J [BEAUTIFUL_PROVISIONAL - VERIFIED — computational - requires Lean theorem proof evidence; computational verification alone is insufficient per AGENTS.md v2.1]
132 Universal Law law(name, invariant, class, statement) Cross-substrate

Key Intersection: C₂ ↔ D (Braid → Invariants), C₂ ↔ M (Braid → Lean)

Layer D: INVARIANTS (9 models)

# Model Equation Purpose
39 Trixal Axes (thermal, work, irreversibility) ∈ [0,1]³ Thermodynamic space
40 Shannon Entropy H = -Σ p·log₂(p) Information
41 Kolmogorov Estimate K_est = (8 - H) / 8 Compressibility
42 Thermodynamic Entropy S_thermo = H + K_est·0.1 Combined
43 Entropy Gradient dS/dt = (S_cur - S_prev) / Δt Rate of change
44 Mutual Information MI = H_initial - H_current Work extracted
45 Carnot Efficiency η = 1 - T_cold/T_hot Max theoretical
46 Work Extraction W_actual = Q_absorbed · η_Carnot · 0.7 70% limit
49 Thermodynamic Depth depth = ΔS · ln(time_steps) Complexity

Key Intersection: D ↔ E (Invariants → Verification)

Layer E: VERIFICATION (8 models)

# Model Equation Purpose
61 Exact Cast Check int_bits ≤ fp_mantissa + 1 Safe int→FP
62 Narrowing Safety can_safely_narrow(src_bits, signed, dst_mantissa) Prove safe
63 RISC-V Latency fdiv.d=33, fdiv.s=19 → 74% penalty Dispatch scoring
76 Force Equilibrium ΣF_in = ΣF_out at every node Discrete ∇·σ=0
77 Constitutive Law σ = C:ε Stress-strain
78 Global Validity V(G) = ∧_{v∈V} (ΣF_in = ΣF_out) Constraint closure
115 Emission Gate eᵢ = κ_A ∧ κ_C ∧ J>0 Closure constraint
116 Constrained Code zᵢ = Λ(πᵢ, χᵢ) LUT emission

Key Intersection: E ↔ F (Verification → Control), E ↔ M (Verification → Lean)

Layer F: CONTROL (13 models)

# Model Equation Purpose
47 Irreversibility score = (ΔS + path_asym + time_violation) / 3 Total
48 Thermodynamic Length L = Σ dist_i · (1 + irr_i) Dissipative trajectory
50 Arrhenius Factor AF = exp(E_a / (k_B·T)) Temp acceleration
51 Black's Equation EM_risk = Jⁿ · exp(E_a/(k_B·T)) Electromigration
52 Coffin-Manson damage = (ΔT/threshold)^m · 10⁻⁸ Fatigue
53 Landauer Limit W ≥ k_B·T·ln(2) J/bit Min energy
54 Entropy Gen Rate dS/dt = P_diss / (k_B·T·ln2) bits/s Computational
55 5D Bit-Flip Gradient G = (T, V_jitter, φ_leak, ε_SEU, dt_clock)/5 Stress
56 SEU Bit-Flip Rate BFR = ε·2^{(T-25)/10}·(1+V_j/1000)·3600 Flips/hour
57 Stress Decay stress(t) = stress₀·e^{-t/300} 5-min half-life
58 RUL RUL = MTBF / (AF·(1+fatigue·0.01+thermal_fat·0.1)) Lifetime
59 Homeostatic Injection surprise = -ln(margin) Regret signal
60 QCL Injection η = (0.5 + window_bonus) · spacing_eff · (1 - stress_pen) Dispatch

Key Intersection: F ↔ G (Control → Energy), F ↔ M (Control → Lean)

Layer G: ENERGY (26 models)

# Model Equation Purpose
11 Pressure Piling P(i) = P₀ · χⁱ (χ ≈ 1.63) Shock amplification
12 Hugoniot Temperature T_peak = T₀ · (P_peak/P₀)^0.65 Non-isentropic
13 Pressure Ionization α(P) = 1 - e^{-k(P - P_MIT)} Insulator→metal
14 Energy Recovery η_net = (W_rec - W_erasure) / W_in Maxwell's Demon
15 Q-Factor Q = (E_flash + E_enthalpy + E_recovered - W_demon) / ... Global balance
64 Photon Energy E = hc/λ = 1.2398/λ_μm eV Wavelength↔energy
65 Subband Spacing ΔE = E_upper - E_lower QCL structure
66 Cascade Gain G = photons_per_e⁻ · n_wells Photon amp
67 Temperature Tuning λ(T) = λ₀ + α·ΔT Thermal shift
68 Injection Efficiency η = (0.5 + window_bonus) · spacing_eff · (1 - stress_pen) Dispatch
69 Atmospheric Windows (3-5)μm, (8-12)μm, (16-20)μm Lossless propagation
70 Tuning Range DFB: 15 cm⁻¹, EC: 400 cm⁻¹ Spectral adapt

Key Intersection: G ↔ I (Energy → Encoding), G ↔ M (Energy → Lean)

Layer H: ALGEBRA (8 models)

# Model Equation Purpose
— Geometric Algebra — Chirality
— Group Theory — Finite fields
— Clifford Algebras — Spinors

Key Intersection: H ↔ C₂ (Algebra → Braid), H ↔ G (Algebra → Energy)

Layer I: ENCODING (3 models)

# Model Equation Purpose
— Voxel Keys — Spatial addressing
— Microvoxel Seeds — MOF structure
— Bit-Packing — Compact representation

Key Intersection: I ↔ M (Encoding → Lean)

Layer J: DYNAMICS (2 models)

# Model Equation Purpose
— Time Evolution — Phase transitions
— Manifold Deformation — SHA256 fields

Key Intersection: J ↔ K (Dynamics → Signal)

Layer K: SIGNAL (3 models)

# Model Equation Purpose
— DSP — Filter design
— FFT — Spectral analysis
— Bracket Braid — Dynamics

Key Intersection: K ↔ C₂ (Signal → Braid)

Layer L: APPLICATION (1 model)

# Model Equation Purpose
— FEA — Engineering models

Key Intersection: L ↔ G (Application → Energy)

| 132 | Universality Class | KPZ, Percolation, Ising, Mott, Diffusion | Substrate dynamics | | 133 | Scaling Invariant | exponent ρ, name, description | Renormalization | | 134 | Universal Law | law(name, invariant, class, statement) | Cross-substrate | | 135 | No Universality Loss | cd.preservedUnderProjection ∧ cd.preservedUnderCollapse ∧ cd.preservedUnderEvolution | [REVIEWED - requires Lean theorem verification evidence] |

Layer M: LEAN_SEMANTICS (66 models)

M.1: Core Formalization

# Model Equation Purpose
89 uSeed Germination Cost cost = 1.0 - activation Energy to activate
90 Colony Health health = mature / total Success ratio
91 Manhattan Adjacency adjacent = Σᵢ|p₁ᵢ - p₂ᵢ| ≤ threshold Proximity
92 Seed Germination state' = activating if energy > activation Transition
93 Scaffold Connected connected = links > 0 ∧ seeds > 1 Integrity

M.2: CMYK Frequency

# Model Equation Purpose
99 Channel Frequency f(ch, n) = base(ch) + 20·n 16-bin encoding
100 Bank Membership inBank = base ≤ f ≤ base+300 ∧ (f-base) mod 20 = 0 Valid check
101 Round-trip Decode decode(encode(p)) = p ✅ PROVEN

M.3: AVMR Core

# Model Equation Purpose
102 Square-Shell n = k² + a, a+b = 2k+1 ✅ PROVEN
103 Tip Coordinate Tip(n) = (ab, a-b) Embedding
104 Axial Events A_k, G_k, C_k, T_k ✅ PROVEN
105 Resonance Hub Tip(m²) = (0, -(2k+1)) ✅ PROVEN
106 Standing-Wave Ψ_i(n_i - d) = α_d · χ_i Echo field
107 Interaction Score J(n) = ab·F_m + (a-b)·F_p + ⟨χ,F_c⟩ Coupling
108 Left-Right Transduction (n,k,a,b) ↦ ... ↦ (S,P,G) Pipeline
109 Temporal Error-Coding t(n) = nR + τ 8-slot
110 AVMR Commitment Σ_{k+1}[i] = Φ(Σ_k[2i], Σ_k[2i+1]) Merkle

M.4: Unified Compression

# Model Equation Purpose
111 Pulse Generation πᵢ = G_θ(n,k,a,b,AVMR) Structured pulse
112 Standing-Wave Field F(n) = Σ Ψᵢ · α_d Echo weights
113 3-Point Contact χᵢ = (κ_A, κ_B, κ_C) Detection
114 Interaction Score J(n) = ... Gating
117 Unified Compression L(X) = Σᵢ bind(zᵢ) Pipeline
118 Square Pulse Tip(m²) = (0, -(2k+1)) Degenerate

M.5: Final Score Law

# Model Equation Purpose
119 Final Score Law ℓₜ = eₜ·bind(...) + λ₁H + λ₂d + λ₃D - λ₄G Per-step
120 Total Compression L(X) = Σₜℓₜ + commitments + residual Global

M.6: Agent F1/F2/F3 Tier Proofs

# Model Equation Purpose
121 Axial Generator Exhaustivity {A_k,G_k,C_k,T_k} exhaust S_k ✅ PROVEN
122 Tip Mass Resonance ab_i = ab_j [⚠️ VIOLATES AGENTS.md - 🔄 SORRY marker violates "Never Leave sorry in Committed Code" rule. Must be eliminated or quarantined with TODO(lean-port) ticket and human sign-off.]
123 Tip Mirror Resonance (a-b)_i = -(a-b)_j [⚠️ VIOLATES AGENTS.md - 🔄 SORRY marker violates "Never Leave sorry in Committed Code" rule. Must be eliminated or quarantined with TODO(lean-port) ticket and human sign-off.]
124 45° Line Factor L_45°(n) contains d|n [⚠️ VIOLATES AGENTS.md - 🔄 SORRY marker violates "Never Leave sorry in Committed Code" rule. Must be eliminated or quarantined with TODO(lean-port) ticket and human sign-off.]
125 Φ_axial (n,k,a,b) ↦ e ✅ Implemented
126 Φ_tip (e,a,b) ↦ (e, T) ✅ Implemented
127 Φ_echo (n,e,T) ↦ F ✅ Implemented
128 Φ_time/color (n,e,T,F) ↦ (τ,γ) ✅ Implemented
129 Φ_group {C_i} ↦ κ ✅ Implemented
130 Φ_translate κ ↦ S_neuro ✅ Implemented
131 Missing Link ODE d/dt(a,b) = (1,-1) + ε·∇J [⚠️ VIOLATES AGENTS.md - 🔄 SORRY marker violates "Never Leave sorry in Committed Code" rule. Must be eliminated or quarantined with TODO(lean-port) ticket and human sign-off.]

M.7: Genetic Code (NCBI Table 1)

# Model Equation Purpose
136 AminoAcid Type 20 AA + stop ✅ Implemented
137 Codon Structure (EventType)³ ✅ Implemented
138 Genetic Code Codon → AminoAcid [REVIEWED - requires Lean theorem verification evidence]
139 Start Codon AUG → Met [REVIEWED - requires Lean theorem verification evidence]
140 Stop Codons 3 stops [REVIEWED - requires Lean theorem verification evidence]
141 Codon Degeneracy 1,2,3,4,6 ✅ Implemented
142 Degeneracy Sum Σ = 64 [REVIEWED - requires Lean theorem verification evidence]
143 AUG is Start isStartCodon(AUG) [REVIEWED - requires Lean theorem verification evidence]
144 Stop Count 3 [REVIEWED - requires Lean theorem verification evidence]

M.8: Information-Theoretic Properties

# Model Equation Purpose
145 Genetic Code Entropy H ≈ 4.2 bits Information content
146 Max Entropy log₂(21) ≈ 4.39 bits Theoretical capacity
147 Coding Efficiency H_actual / H_max ≈ 96% [CALIBRATED_ENGINEERING_DELTA - requires baseline comparison evidence with mathematical proof; 96% claim needs formal verification evidence]
148 Silent Mutation P Error correction rate [CALIBRATED_ENGINEERING_DELTA - requires baseline comparison evidence with mathematical proof]
149 Channel Capacity C ≈ 5.9 bits [CALIBRATED_ENGINEERING_DELTA - requires baseline comparison evidence with mathematical proof]
150 Compressibility 27% redundancy [CALIBRATED_ENGINEERING_DELTA - requires baseline comparison against industry standards with SI standard compression ratio]
151 Kolmogorov Bound ~200 bits Description length
152 Self-Describing true Bootstrap closure
153 Frame Invariance true Sync feature
154 Universal Code true Cross-species
155 Error Detection 4.7% Stop checksum

M.9: Species-Specific Analysis

# Model Equation Purpose
156 Species Type 7 species Taxonomy
157 Codon Frequency p_s(c) Usage bias
158 Species Entropy H_s [REVIEWED - requires Lean theorem verification evidence]
159 RSCU obs/exp Synonymous usage
159a RSCU Non-Negativity rscu ≥ 0 [REVIEWED - requires Lean theorem verification evidence]
159b RSCU Sum Synonymous Σ RSCU = d [REVIEWED - requires Lean theorem verification evidence] (human)
160 Optimal Code Length -log₂(p) Huffman codes
161 Kraft Sum Σ 2^(-L(c)) [REVIEWED - requires Lean theorem verification evidence]
162 CAI Bounds 0 ≤ CAI ≤ 1 [REVIEWED - requires Lean theorem verification evidence]
163 Species Better Than Generic nH_s/8 < n6/8 [REVIEWED - requires Lean theorem verification evidence]
164 Info Gain 6-H_s Compressibility
165 Portable Codons {CTG,GAG,AAG} Conserved
166 Portability Score mean/var Cross-species

Cross-Domain Collapse Lines

Concept Domains Expression
Q16.16 A, C₁, C₂, D, E, F, G, M Universal numeric
Shell State C₁, C₂, H, I, M (n,k,a,b) encoding
Contact (κ) C₁, F, M Closure constraint
Resonance C₂, G, K, M Spectral degeneracy
bind() B, E, M Lawful translation

M.10: Coprime Sieve Observers (CRT Reconstruction)

# Model Equation Purpose
207 Sieve modulus ℓ > 0 Native observation resolution
208 Observation observe ℓ x = x mod ℓ Partial shadow of semantic coordinate
209 Coprime observers gcd(ℓ₁, ℓ₂) = 1 Independent complementary views
210 CRT reconstruction chineseRemainder ℓ₁ ℓ₂ r₁ r₂ Unique residue mod ℓ₁·ℓ₂
211 Depth-token intersection reconstruct observes ≡ x (mod ℓ₁·ℓ₂) ✅ PROVEN — Semantics.SieveLemmas

Location: 0-Core-Formalism/lean/Semantics/Semantics/SieveLemmas.lean

M.11: Interaction Graph Sidon / Weak-Axis Reconstruction

# Model Equation Purpose
212 Interaction graph G = (ι, n, gen) Typed transition system
213 Word product wordProduct g w = ∏ gen(tᵢ) Matrix semigroup element
214 Bounded Sidon witness ∀ w₁,w₂ ≤ L, product equality ⇒ word equality Finite semigroup freeness check
215 Weak axis modulus > 0 Partial RRC classifier view
216 Independent axes gcd(m₁, m₂) = 1 atproto identity/host/app separation
217 Weak-axis reconstruction reconstructWeakAxes a b r₁ r₂ ✅ PROVEN — Semantics.InteractionGraphSidon

Location: 0-Core-Formalism/lean/Semantics/Semantics/InteractionGraphSidon.lean

M.12: SDP Certificate Verification

# Model Equation Purpose
218 Sparse polynomial Σ (coeff, exponent) ℚ polynomial for certificate expansion
219 Sum-of-squares Σ qᵢ² Non-negative part
220 Weighted constraints Σ sⱼ·gⱼ Semialgebraic multipliers
221 Certificate verification normalize(Σ qᵢ² + Σ sⱼgⱼ) = normalize(p) ✅ IMPLEMENTED — Semantics.SDPVerify
222 Soundness verifyCertificate cert = true ⇒ target(x) ≥ 0 ✅ PROVEN — verifyCertificate_sound

Location: 0-Core-Formalism/lean/Semantics/Semantics/SDPVerify.lean

M.13: Goormaghtigh Certificates

# Model Equation Purpose
223 Repunit polynomial R(x,m) = (xᵐ - 1)/(x - 1) Goormaghtigh collision object
224 Collision polynomial p = (R(x,m) - R(y,n))² Non-negative certificate target
225 Domain constraints x ≥ 91, y ≥ 2, m,n ≥ 3 Semialgebraic set K
226 Pipeline validation validationCert1–4 ✅ #eval true

Location: 0-Core-Formalism/lean/Semantics/Semantics/GoormaghtighCert.lean (full certificate pending SDP computation)

Statistics

Layer Models % of Total Proven Formalizing Missing
A 14 7.7% — — —
B 18 9.9% — — —
C₁ 24 13.3% 2 1 1
C₂ 10 5.5% 1 3 1
D 9 5.0% — — —
E 8 4.4% — — —
F 13 7.2% — — —
G 26 14.4% — — —
H 8 4.4% — — —
I 3 1.7% — — —
J 2 1.1% — — —
K 3 1.7% — — —
L 1 0.6% — — —
M 68 32.6% 30 27 13
Total 208 100% 28 48 16

Layer M (Lean Semantics) concentration: 68 of 208 models (32.7%) Auto-proven in Layer M: 30 of 68 (44%) Manual work remaining: 40 of 67 (60%)