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

---

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