# 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

```bash
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

---

### 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

---

### 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

---

### 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