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GF3_CONSERVATION_QUICK_REFERENCE.md

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GF(3) Conservation: Quick Reference

What is GF(3)? Galois Field with 3 elements: {-1, 0, +1}, addition mod 3

Conservation Law:

causality_trit + ergodic_trit + minus_trit ≡ 0 (mod 3)
    +1        +      0       +      -1    = 0 ✓

The Three Agents and Their Trits

Agent Trit Role What It Does
causality +1 PLUS (Generation) Generates candidate moves, explores possibilities
2-monad 0 ERGODIC (Coordination) Routes moves, filters, maintains rhythm
amp -1 MINUS (Constraint) Verifies moves, enforces safety, gates expansion

What Each Agent Conserves

PLUS (+1): Generative Energy

  • Prevents infinite loops
  • Provides novelty and exploration
  • Must be balanced by MINUS
  • If unchecked: White Hole (explosion, incoherent)

ERGODIC (0): Coordinating Capacity

  • Routes between PLUS and MINUS
  • Maintains timing and rhythm
  • Holds context window
  • If bottlenecked: System gridlocks, timing skew

MINUS (-1): Constraining Power

  • Verifies coherence
  • Enforces invariants
  • Prevents corruption
  • If exhausted: System accepts invalid moves, enters BH

The JSON RPC Protocol Error Explained

Error: jsonrpc2: protocol error: read |0: file already closed

Root Causes (in probability order):

  1. PLUS Overflow (Most Likely)

    • causality generating faster than 2-monad routing
    • Indicator: Memory/queue pressure signals
    • Fix: Strategy B (throttle PLUS) or Strategy A (boost ERGODIC)

  2. ERGODIC Starvation

    • 2-monad routing slower than causality rate + amp processing
    • Indicator: Growing latency from 2-monad
    • Fix: Strategy A (increase 2-monad workers/queue)

  3. MINUS Exhaustion

    • amp verification budget depleted
    • Indicator: Verification failure signals
    • Fix: Strategy C (increase amp budget)

  4. Semantic Violation

    • One skill violates Bridge Type coherence
    • Indicator: Neighbor-awareness constraints fail
    • Fix: Debug specific skill, reduce strictness, or Strategy D (rebalance)

The Four Fix Strategies

Strategy A: Increase ERGODIC Capacity

{
  "2-monad": {
    "workers": 4,         // 2→4
    "queue_depth": 1000,  // 500→1000
    "filter_timeout_ms": 200  // 100→200
  }
}

Use when: latency from 2-monad is growing Cost: More memory, slightly higher latency

Strategy B: Throttle PLUS Generation

{
  "causality": {
    "generation_rate": 5,  // 10→5
    "batch_size": 5,       // 10→5
    "backpressure_enabled": true  // false→true
  }
}

Use when: Memory/queue overflow detected Cost: 2x slower total time, natural rhythm restored

Strategy C: Increase MINUS Budget

{
  "amp": {
    "verification_budget": 500,     // 100→500
    "parallel_verifiers": 4,        // 2→4
    "proof_cache_size": 10000       // 1000→10000
  }
}

Use when: Verification failures from amp detected Cost: Higher CPU, larger memory for proof cache

Strategy D: Balanced Reweighting

{
  "causality": {"generation_rate": 8, "batch_size": 8},
  "2-monad": {"workers": 3, "queue_depth": 750},
  "amp": {"verification_budget": 300, "parallel_verifiers": 3}
}

Use when: Multiple agents showing issues Cost: Moderate across all dimensions

Diagnostic Workflow (5 Minutes)

# Step 1: Run diagnostic
./scripts/diagnose_gf3_protocol_error.sh .local/share/ies/logs/crush_latest.log

# Step 2: Look for root cause
# Output will show one of:
# - "PLUS OVERFLOW" → Use Strategy B or A
# - "ERGODIC STARVATION" → Use Strategy A
# - "MINUS EXHAUSTION" → Use Strategy C
# - "SEMANTIC VIOLATION" → Use Strategy D or debug skill

# Step 3: Apply fix
cp .claude/mcp-gf3-fixes.json#strategy_X .claude/mcp.json

# Step 4: Retest
npx ai-agent-skills install plurigrid/asi --agent crush

# Step 5: Verify success
grep "protocol error\|json" .local/share/ies/logs/crush_latest.log
# (Should be empty if successful)

Operational GF(3) Signatures

✓ Coherent System

  • Monotonic progress: 0 → 315 skills
  • No backpressure signals
  • No memory/queue warnings
  • Consistent latency across agents
  • No protocol errors
  • Symmetry: generation ≈ verification + routing

✗ Incoherent System (GF(3) Violated)

  • Stalled progress (stuck at skill N)
  • Memory/queue warnings
  • Growing latency
  • Backpressure signals
  • Protocol error drops connection
  • Asymmetry: generation >> verification (or vice versa)

Before/After Formalization

Before Phase A.0 (Current State)

  • System crashes at skill ~N with protocol error
  • Cannot prove Bridge Type because system doesn't reach 315 skills
  • Formalization would be meaningless

After Phase A.0 (After Fix & Verification)

  • System successfully reaches 315 skills
  • All 315 skills installed, verified, coherent
  • GF(3) conservation maintained throughout
  • Ready for Phase A.1: Formalize the working system

After Phase A.1-D (Full Implementation)

  • Bridge Type formally proven in Lean 4
  • Ecosystem proven to satisfy Bridge Type
  • Three mechanisms formalized (Valve/Filter/Resurrector)
  • Deployed in music-topos, emmy-sicm, UNWORLD federation

The Conservation Equation

In terms of rates (per second):

rate(causality generates moves)
- rate(amp verifies moves)
= rate(2-monad routes moves)

10 moves/sec - 7 verified/sec ≈ 3 routed/sec (balanced)

If 10 - 0 = 10 → queue grows unbounded → PLUS OVERFLOW
If 10 - 7 = 3 but 2-monad can only route 2 → ERGODIC bottleneck
If 0 - 0 = 0 but nothing happens → MINUS exhausted or skill complete

Success Checklist for Phase A.0

  • Diagnostic script executed successfully
  • Root cause identified (PLUS/ERGODIC/MINUS/Semantic)
  • Appropriate fix strategy chosen
  • MCP configuration updated
  • crush validation rerun
  • All 315 skills installed without error
  • No protocol error in logs
  • GF(3) conservation verified (trit sum = 0 throughout)
  • Operational metrics documented
  • Commit success report
  • Ready for Phase A.1 (formal Lean 4)

Key Insight

GF(3) conservation is the operational manifestation of Bridge Type coherence.

  • Theoretically: Bridge Type = verified transition between extremes
  • Operationally: GF(3) = balance that prevents White Hole (PLUS excess) and Black Hole (MINUS excess)
  • When GF(3) is conserved, the system stays alive (rhythmic pulsing)
  • When GF(3) is violated, the system dies (protocol error drops connection)

Phase A.0 restores operational life. Phase A.1 formalizes why it works.