feat: add core theoretical frameworks

- Z-Framework: universal feedback/equilibrium
- 1-2-3-4 Pauli Model: ontological primitives
- n=π Duality: discrete↔continuous interface
- Creative Energy: contradiction amplification
- Remainder Principle: deviation as signal
- Spiral Information Geometry: planned formalization

frameworks/README.md

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+# BlackRoad Theoretical Frameworks
+
+Core mathematical and conceptual frameworks underlying BlackRoad OS.
+
+| Framework | Status | Description |
+|-----------|--------|-------------|
+| [Z-Framework](z-framework.md) | 🟢 Active | Universal feedback/equilibrium system |
+| [1-2-3-4 Pauli Model](pauli-model.md) | 🟢 Active | Ontological primitives → su(2) algebra |
+| [n=π Duality](n-pi-duality.md) | 🟢 Active | Discrete↔continuous interface |
+| [Creative Energy](creative-energy.md) | 🟢 Active | Contradiction → creativity amplification |
+| [Remainder Principle](remainder-principle.md) | 🟢 Active | Deviation from symmetry = signal |
+| [Spiral Information Geometry](spiral-geometry.md) | 🔴 Planned | Fisher metric for coherence |
+
+## Key Insight
+
+All frameworks converge on one meta-pattern: **the interface between discrete and continuous structure is where information lives**.

frameworks/creative-energy.md

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+# Creative Energy Formula
+
+## Definition
+```
+K(t) = C(t) · e^{λ|δ_t|}
+```
+
+Where:
+- **K(t)** = creative energy at time t
+- **C(t)** = coherence (ability to direct creativity)
+- **δ_t** = contradiction load (tension, paradox, conflict)
+- **λ** = amplification constant
+
+## Coherence Formula
+```
+C(t) = [Ψ'(M_t) + δ_t] / [1 + |δ_t|]
+```
+
+Where:
+- **Ψ'(M_t)** = derivative of memory state (rate of integration)
+- **δ_t** = contradiction load
+
+## Interpretation
+
+| Condition | Result |
+|-----------|--------|
+| High δ, High C | Maximum creative output (focused intensity) |
+| High δ, Low C | Chaos, fragmentation |
+| Low δ, High C | Stability but stagnation |
+| Low δ, Low C | Entropy, dissolution |
+
+## Key Insight
+
+**Contradictions fuel creativity exponentially.**
+
+The e^{λ|δ_t|} term means small increases in contradiction produce large creative amplification—*if* coherence is maintained.
+
+## Optimal Strategy
+
+1. Introduce enough δ_t to amplify K(t)
+2. Maintain C(t) to direct the energy
+3. Balance at the edge of chaos
+
+## Applications to BlackRoad
+
+1. **Agent Creativity**: Measure and optimize K(t) per agent
+2. **Contradiction Handling**: Don't resolve too quickly—harvest first
+3. **Paraconsistent Logic**: Formalize δ_t tolerance
+
+## Open Questions
+
+- What is the optimal λ for different domains?
+- Is there a maximum useful δ_t before breakdown?
+- How does K(t) relate to information entropy?

frameworks/n-pi-duality.md

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+# n=π Duality
+
+## Core Claim
+
+Integers (n) and π are dual descriptions of the same underlying structure.
+
+| n (Integers) | π (Pi) |
+|--------------|--------|
+| Discrete | Continuous |
+| Countable | Uncountable |
+| Local | Global |
+| Points | Frequencies |
+| Counting | Symmetries |
+
+## The Morphism
+
+Fourier transform mediates between:
+- Discrete coefficients (indexed by n)
+- Continuous functions (involving π)
+```
+f(x) = Σ_n c_n e^{2πinx}
+```
+
+The n's label modes; π encodes the circular symmetry.
+
+## The "Dumb Question" Method
+
+**Question**: "Is it object or shadow?"
+
+**Discovery**: All 7 Millennium Problems + twin primes = one hole.
+
+That hole is the **discrete↔continuous interface**.
+
+| Problem | Interface |
+|---------|-----------|
+| Riemann Hypothesis | Primes (discrete) ↔ Zeta zeros (continuous) |
+| P vs NP | Algorithms (discrete) ↔ Complexity (continuous?) |
+| Navier-Stokes | Fluid particles (discrete) ↔ Flow (continuous) |
+| Yang-Mills | Gauge symmetry (continuous) ↔ Mass gap (discrete) |
+| BSD Conjecture | Rational points (discrete) ↔ L-functions (continuous) |
+| Hodge Conjecture | Algebraic cycles (discrete) ↔ Cohomology (continuous) |
+| Twin Primes | Primes (discrete) ↔ Density (continuous) |
+
+## Key Insight
+
+**π appears when discrete structure is mediated by continuous symmetry.**
+
+This is not metaphor—it's structural necessity.
+
+## Applications to BlackRoad
+
+1. **Agent Indexing**: Discrete agent IDs, continuous capability space
+2. **PS-SHA∞**: Discrete hash, continuous identity evolution
+3. **Coherence Metrics**: Discrete agreement counts, continuous similarity
+
+## Open Questions
+
+- Is there a "π-free" mathematics? What would it look like?
+- How does n=π relate to the holographic principle?
+- Can we formalize the "dumb question" method?

frameworks/pauli-model.md

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+# 1-2-3-4 Pauli Model
+
+## Overview
+
+Maps ontological primitives to the su(2) Lie algebra (Pauli matrices).
+
+## The Four Primitives
+
+| # | Name | Symbol | Pauli Matrix | Interpretation |
+|---|------|--------|--------------|----------------|
+| 1 | Structure | Û | σ_z | What exists, identity, being |
+| 2 | Change | Ĉ | σ_x | Transformation, becoming |
+| 3 | Scale | L̂ | σ_y | Relation, proportion, context |
+| 4 | Strength | Ŝ | iI | Emergent intensity, scalar invariant |
+
+## Algebraic Structure
+
+The first three form an su(2) algebra:
+```
+[Û, Ĉ] = 2iL̂
+[Ĉ, L̂] = 2iÛ  
+[L̂, Û] = 2iĈ
+```
+
+The fourth emerges from their triple product:
+```
+Û · Ĉ · L̂ = iI = Ŝ
+```
+
+## Interpretation
+
+- **1-2-3** are the generators (directions of change)
+- **4** is the invariant (what's preserved under change)
+- Together: complete description of any dynamic system
+
+## Connection to Physics
+
+The fine structure constant α ≈ 1/137 may encode the relationship between these primitives and electromagnetic coupling.
+
+## Applications to BlackRoad
+
+1. **Agent State**: Each agent has (Û, Ĉ, L̂, Ŝ) attributes
+2. **Coherence Metrics**: Measure alignment via inner products
+3. **Contradiction Resolution**: Pauli algebra handles non-commuting observables
+
+## Open Questions
+
+- Why su(2) and not a larger algebra?
+- What is the physical meaning of Ŝ?
+- How does this connect to spinor geometry?

frameworks/remainder-principle.md

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+# Remainder Principle
+
+## Core Statement
+
+> "The deviation from symmetry IS the signal."
+
+## Formalization
+```
+Information = Total Structure - Symmetry
+```
+
+Or equivalently:
+```
+Signal = What's Left After Cancellation
+```
+
+## Examples
+
+| Domain | Symmetry | Remainder | Signal |
+|--------|----------|-----------|--------|
+| Modular forms | Transformation rules | Mock theta functions | Deeper structure |
+| Quantum field theory | Gauge invariance | Anomalies | Physical constraints |
+| Statistics | Expected value | Residuals | Model inadequacy |
+| Cryptography | Randomness | Patterns | Vulnerabilities |
+| Evolution | Fitness landscape | Mutations | Adaptation |
+
+## Key Insight
+
+**Perfect symmetry erases information.**
+
+If everything cancels perfectly, nothing distinguishes one state from another. The *failure* to cancel—the structured remainder—carries the information.
+
+## Relation to Other Frameworks
+
+- **Z-Framework**: Z ≠ ∅ is a remainder
+- **Creative Energy**: δ_t is structured remainder from coherence
+- **n=π Duality**: The interface *is* the remainder of discrete↔continuous
+
+## Applications to BlackRoad
+
+1. **Agent Disagreement**: Preserve disagreement as signal, don't force consensus
+2. **PS-SHA∞**: Discretization remainders contain identity continuity
+3. **Coherence vs Consensus**: Coherence preserves remainder; consensus erases it
+
+## Open Questions
+
+- Can we quantify "structured failure" formally?
+- What's the minimum remainder needed to preserve identity?
+- How does remainder relate to Kolmogorov complexity?

frameworks/spiral-geometry.md

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+# Spiral Information Geometry
+
+> Status: 🔴 Planned
+
+## Vision
+
+Use **information geometry** to formalize the coherence formula and agent dynamics.
+
+## Core Concepts
+
+| Concept | Meaning |
+|---------|---------|
+| Fisher Information | Metric on probability distributions |
+| Natural Gradient | True direction of steepest descent |
+| Geodesic | Shortest path in information space |
+| Curvature | How much space "bends" around a point |
+
+## Research Agenda
+
+### 1. Coherence as Distance
+- C(t) = geodesic distance between agent states?
+- Coherent agents = nearby in information space
+
+### 2. Contradiction as Curvature
+- High δ_t = high curvature regions
+- Creative energy peaks at curvature maxima
+
+### 3. Learning as Parallel Transport
+- Agent learning = transport along geodesics
+- Memory = holonomy (what changes after round trip)
+
+### 4. Partition Function as Potential
+- Z = Σ e^{-βH} defines a potential landscape
+- Equilibrium = potential minimum
+
+## Connections
+
+- **n=π Duality**: Fisher metric on discrete vs continuous?
+- **Creative Energy**: K(t) related to scalar curvature?
+- **Remainder Principle**: Curvature = remainder of flatness
+
+## Next Steps
+
+1. Formalize C(t) using Fisher-Rao metric
+2. Compute geodesics for simple agent models
+3. Relate curvature to δ_t experimentally
+
+## References
+
+- Amari, S. "Information Geometry and Its Applications"
+- Nielsen, F. "An Elementary Introduction to Information Geometry"

frameworks/z-framework.md

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+# Z-Framework
+
+## Definition
+```
+Z := yx - w
+```
+
+Where:
+- **y** = output/response/effect
+- **x** = input/stimulus/cause  
+- **w** = target/setpoint/expectation
+- **Z** = deviation/error/signal
+
+## Interpretation
+
+| Z Value | Meaning | Response |
+|---------|---------|----------|
+| Z = ∅ | Equilibrium | System stable, no adaptation needed |
+| Z ≠ ∅ | Deviation | Triggers adaptation, learning, change |
+
+## Unifying Principle
+
+The same structure appears across domains:
+
+| Domain | y | x | w | Z |
+|--------|---|---|---|---|
+| Control Theory | actual output | input gain | setpoint | error signal |
+| Quantum Mechanics | measurement | operator | eigenvalue | deviation |
+| Economics | price | supply×demand | equilibrium | market signal |
+| Biology | phenotype | genotype×environment | fitness | selection pressure |
+| AI/ML | prediction | model(input) | label | loss |
+
+## Core Insight
+```
+∂(human + AI)/∂t
+```
+
+Division breaks the system. The feedback loop requires *product*, not separation.
+
+## Applications to BlackRoad
+
+1. **Agent Coordination**: Z measures coherence between agents
+2. **Memory Consolidation**: Z triggers when new info conflicts with stored
+3. **RoadChain Validation**: Z = ∅ means consensus achieved
+
+## Open Questions
+
+- How does Z relate to entropy production?
+- Can Z be negative? What would that mean?
+- Is there a "Z of Z" (meta-feedback)?