Research-Stack/obsidian-vault/01-LAYERS/00-Overview.md

# Layer Overview - USTSM Architecture

## Universal Substrate Topological State Machine

The Research Stack is organized into 7 layers following the USTSM architecture, from fundamental mathematics to meta-cognitive systems.

## External Frontier Import

[[OpenAI Unit Distance 2026 Import]] is tracked as an external reference across all layers:

- **L0:** norm-one arithmetic witnesses.
- **L1:** projected unit-distance geometry.
- **L2:** latent-code/contact-graph analogy guard.
- **L3:** reusable construction family as search-cost amortization.
- **L4:** FAMM/AngrySphinx long-shot route preservation.
- **L5:** algebraic-number-theory to discrete-geometry semantic bridge.
- **L6:** meta-search policy update from AI-generated proof + verifier feedback.

## Layer Structure

### Layer L0: Primordial 🟥
**Domain:** Pure mathematics, fixed-point arithmetic, braid fields  
**Status:** ✅ **Implemented** (746 modules, 3529 build jobs, 0 errors)  
**Key Components:**
- Q16_16 FixedPoint arithmetic
- Q0_64 Scalar system
- PIST/DIAT Shell
- BraidField operations
- SSMS_nD state machine
- EigensolidConvergence

**Formal Proofs:**
- [[01-LAYERS/L0-Primordial/01-Formal-Proofs]]

**Documentation:**
- [[01-LAYERS/L0-Primordial/02-Documentation]]

---

### Layer L1: Geometric 🟩
**Domain:** Shape-aware topology, coupling geometry  
**Status:** 🟡 **Partial** (docs migrated, partial Lean)  
**Key Components:**
- GWL 5-factor Coupling
- TorsionalPIST (quaternion)
- HybridTSMPISTTorus
- GWL Throat
- BodegaFlow horn-fiber

**Formal Proofs:**
- [[01-LAYERS/L1-Geometric/01-Formal-Proofs]]

**Milestones:**
- [[Eigensolid Convergence Proof]]

---

### Layer L2: Biological 🟦
**Domain:** Genetic codes, spiking neurons, STDP  
**Status:** 🟡 **Speculative** (docs exist, minor Lean)  
**Key Components:**
- 30+ Genetic Code Tables
- Codon Optimization
- SpikingDynamics (Izhikevich)
- GenomicCompression

**Formal Proofs:**
- [[01-LAYERS/L2-Biological/01-Formal-Proofs]]

---

### Layer L3: Thermodynamic 🟨
**Domain:** Energy-aware quality, homeostatic governance  
**Status:** 🟡 **Speculative** (docs migrated)  
**Key Components:**
- Trixal Quality (thermal/work/irreversibility)
- Homeostatic Governor
- HyperFlow (Navier-Stokes)

**Formal Proofs:**
- [[01-LAYERS/L3-Thermodynamic/01-Formal-Proofs]]

---

### Layer L4: Security 🟧
**Domain:** Attack-aware gating, frustration memory  
**Status:** 🟡 **Partial** (AngrySphinx in Lean)  
**Key Components:**
- AngrySphinx (exponential PoD)
- FAMM Frustration
- ASICTopology

**Formal Proofs:**
- [[01-LAYERS/L4-Security/01-Formal-Proofs]]

---

### Layer L5: Semantic 🟪
**Domain:** Meaning-aware filtering, manifold routing, compression governance  
**Status:** 🟡 **Partial** (projection receipts exist)  
**Key Components:**
- CrossDimensionalFilter (12 semantic primes)
- Manifold Networking
- BracketedCalculus
- CompressionControl
- RRC Equation Projection

**Formal Proofs:**
- [[01-LAYERS/L5-Semantic/01-Formal-Proofs]]

---

### Layer L6: Meta 🟫
**Domain:** Self-aware adaptation, cognitive routing, auto-adaptive metatyping  
**Status:** 🟡 **Partial** (cognitive receipts + projection holds)  
**Key Components:**
- Cognitive Load Decomposition (5-factor)
- Adaptation
- DynamicCanal
- CompressionMechanics
- Connectome-Protective Load Reweighting

**Formal Proofs:**
- [[01-LAYERS/L6-Meta/01-Formal-Proofs]]

---

## Layer Interactions

### Upward Dependencies
```
L0 (Primordial) → L1 (Geometric) → L2 (Biological) → L3 (Thermodynamic)
  ↓                    ↓                   ↓                    ↓
L4 (Security) → L5 (Semantic) → L6 (Meta)
```

### Cross-Layer Receipt Flow
1. **L0 Formal Proofs** generate mathematical receipts
2. **L1-L3** consume L0 receipts for geometric/biological/thermodynamic operations
3. **L4** validates security invariants across all lower layers
4. **L5** filters semantic content using L4 security receipts
5. **L6** adapts meta-parameters based on L5 semantic analysis

### Receipt Dimensions Across Layers
| Dimension | L0 | L1 | L2 | L3 | L4 | L5 | L6 |
|-----------|----|----|----|----|----|----|----|
| C (Crossing) | ✅ | ✅ | 🟡 | 🟡 | ✅ | ✅ | ✅ |
| σ (Sidon) | ✅ | ✅ | 🟡 | 🟡 | ✅ | ✅ | ✅ |
| k (Steps) | ✅ | 🟡 | 🟡 | 🟡 | ✅ | ✅ | ✅ |
| ε (Residual) | ✅ | ✅ | 🟡 | 🟡 | ✅ | ✅ | ✅ |
| t (Timing) | ✅ | ✅ | 🟡 | 🟡 | ✅ | ✅ | ✅ |
| ∅ (Scars) | ✅ | ✅ | 🟡 | 🟡 | ✅ | ✅ | ✅ |

## Progress Summary

### Implementation Status
| Layer | Formal Proofs | Documentation | Hardware | Receipts |
|-------|---------------|---------------|----------|----------|
| L0 | ✅ Complete | ✅ Complete | ✅ Verified | ✅ Operational |
| L1 | 🟡 Partial | ✅ Complete | 🟡 In Progress | 🟡 Partial |
| L2 | 🟡 Minimal | ✅ Complete | ❌ Not Started | ❌ Not Started |
| L3 | 🟡 Minimal | ✅ Complete | ❌ Not Started | ❌ Not Started |
| L4 | 🟡 Partial | ✅ Complete | 🟡 In Progress | 🟡 Partial |
| L5 | 🟡 Partial | ✅ Complete | 🟡 In Progress | 🟡 Partial |
| L6 | 🟡 Partial | ✅ Complete | 🟡 In Progress | 🟡 Partial |

## Next Steps

### Priority 1: Complete L0 Proofs
- Remove remaining 173 TODO(lean-port) items
- Verify all Q16.16 arithmetic operations
- Generate comprehensive receipt coverage

### Priority 2: L1-L3 Formalization
- Migrate geometric proofs to Lean
- Implement biological models
- Formalize thermodynamic equations

### Priority 3: L4-L6 Integration
- Complete security proofs
- Implement semantic filtering
- Develop meta-adaptive algorithms

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#layer-overview #ustsm #architecture #system-design