Research-Stack/6-Documentation/docs/semantics/candidate_theorems_565_plus.md

Candidate Theorems 182+ (Signal Analysis Swarm Output)

Generated: 2026-04-17 (Template - Run swarm to populate) Status: Placeholder - execute .windsurf/swarm/signal_analysis/run.sh to generate

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Swarm Configuration

Target Corpus: 30+ ChatGPT files (~5MB) Current MATH_MODEL_MAP: 181 models Agents: A1 (Pattern Matcher), A2 (Novelty), A3 (Classifier), A4 (Validator)

Priority Targets:

1. chat-tardygrada-patent-session-20260404.md (2.7 MB)
2. chatgpt_4_10_2026.md (650 KB)
3. chatgpt_4_11_2026.md (547 KB)
4. chatgpt_ingest1.md (397 KB)
5. chat-organoid-lambda-calibration-20260404.md (28 KB)

Expected Output: 10-20 new theorems (Models 182-200)

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Execution

cd /home/allaun/Research\ Stack
./.windsurf/swarm/signal_analysis/run.sh

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Placeholder Results (Example Format)

Model 565: Waveprobe Baseline Timing

Equation: t_baseline = 500ms · (1 + ε_field)

Purpose: Electromagnetic field correction to waveprobe temporal baseline

TTM Layer: K (Signal) — confidence: 0.92

Novelty: 0.85

Source: chat-tardygrada-patent-session-20260404.md

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Model 566: Microvoxel Spatial Address

Equation: addr(x,y,z,Γ) = (x·N² + y·N + z)·|Γ| + Γ_idx

Purpose: 4D spatial indexing with material type Γ

TTM Layer: I (Encoding) — confidence: 0.88

Novelty: 0.91

Source: chatgpt_ingest1.md

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Model 567: Soliton Path Curvature

Equation: κ_path = ∮_γ ∇²φ · ds / L_γ

Purpose: Mean curvature of soliton trajectory through n-manifold

TTM Layer: C₁ (Topology) — confidence: 0.87

Novelty: 0.78

Source: chat-soliton-nspace-path-trace-20260404.md

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Model 568: Codon Optical Coupling

Equation: η_coupling = |⟨ψ_in|E_field|ψ_out⟩|² / (ħω·A_cross)

Purpose: Quantum efficiency of optical codon state transfer

TTM Layer: G (Energy) — confidence: 0.85

Novelty: 0.82

Source: chat-engram-codon-optical-decompressor-20260404.md

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Model 569: Hypercube Engram Capacity

Equation: C_engram = 2^{d_h} · B · log₂(S/B + 1)

Purpose: Shannon capacity of d_h-dimensional hypercube memory

TTM Layer: A (Compression) — confidence: 0.90

Novelty: 0.88

Source: chat-connection-machine-hypercube-engram-topology-20260404.md

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Model 570: SAE Feature Frequency Lock

Equation: f_lock = argmax_f |FFT(φ_SAE(f))|² · 1_{|f - f_target| < δ}

Purpose: Frequency-domain feature extraction from sparse autoencoder

TTM Layer: K (Signal) — confidence: 0.89

Novelty: 0.79

Source: chat-sae-feature-frequency-analysis-20260405.md

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Model 571: Organoid Lambda Calibration

Equation: λ_cal = λ_nominal · (1 + α_thermal·ΔT + β_field·B²)

Purpose: Wavelength correction for organoid photonic substrate

TTM Layer: G (Energy) — confidence: 0.84

Novelty: 0.86

Source: chat-organoid-lambda-calibration-20260404.md

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Model 572: Janus Number System Projection

Equation: π_Janus(n) = (n mod p₁, n mod p₂, ..., n mod p_k)

Purpose: CRT-based multi-base representation for Piet connector addressing

TTM Layer: H (Algebra) — confidence: 0.91

Novelty: 0.93

Source: chat-janus-number-systems-piet-connectors-20260402.md

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Model 573: Mu-Seed Activation Threshold

Equation: θ_activation = E_binding / (k_B·T) · ln(τ_observation/τ_0)

Purpose: Thermodynamic threshold for μ-seed state transition

TTM Layer: F (Control) — confidence: 0.86

Novelty: 0.81

Source: chat-tardygrada-patent-session-20260404.md

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Model 574: Braid Strand Tension Equilibrium

Equation: Σ_i T_i · ∇_i σ = 0 ∀ σ ∈ {a,t,g,c}

Purpose: Force balance at braid crossing for ATGC sequence

TTM Layer: C₂ (Braid) — confidence: 0.88

Novelty: 0.77

Source: chatgpt_4_11_2026.md

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Integration Checklist

After running swarm and populating this file:

• Review all candidate equations for validity
• Assign final model numbers (182-200 range)
• Update MATH_MODEL_MAP.md with new entries
• Update MATH_MODEL_MAP_BY_DOMAIN.md layer sections
• Add proof templates to missingproofs/AVMR_Theorems.lean
• Run lake build to verify compilation
• Update model count totals (currently 181)

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Next Steps

1. Execute swarm: ./.windsurf/swarm/signal_analysis/run.sh
2. Review output: This file will be overwritten with actual results
3. Validate: Check equation syntax and theorem coherence
4. Integrate: Add approved theorems to MATH_MODEL_MAP
5. Formalize: Move to Lean implementation where appropriate

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Document ID: CANDIDATE_THEOREMS_182_PLUS Status: TEMPLATE — awaiting swarm execution