Narya Proofs Skill Skill

Narya Proofs Skill

Unified verification for event-sourced systems using JSONL interaction logs. Generates cryptographic proof certificates with GF(3) conservation guarantees.

Four Verifiers with GF(3) Assignments

| Verifier | Trit | Role | Color Range | |----------|------|------|-------------| | queue_consistency | -1 | MINUS validator | Cold (180-300°) | | non_leakage | -1 | MINUS validator | Cold (180-300°) | | replay_determinism | 0 | ERGODIC coordinator | Neutral (60-180°) | | gf3_conservation | +1 | PLUS generator | Warm (0-60°, 300-360°) |

GF(3) Meta-Balance: Sum = -1 + -1 + 0 + 1 = -1 ≡ 2 (mod 3). Runner adds meta-trit +1 → 0 ≡ 0 (mod 3) ✓

Denotation

This skill generates cryptographic proof certificates for event-sourced systems, verifying that all invariants hold and ensuring consistency across distributed systems via mechanically checked proofs.

ProofBundle = ∏_{verifier} (Events → VerifierResult)
Certificate = sha256(Merkle(ProofBundle))
Verdict: VERIFIED ⟺ ∀ verifier: passed = true

Invariant Set

| Invariant | ID | Definition | Verifier | |-----------|-----|------------|----------| | QueueConsistency | INV-001 | No duplicate event IDs, monotonic timestamps | queue_consistency | | ReplayDeterminism | INV-002 | Same seed → same content hash | replay_determinism | | NonLeakage | INV-003 | No PII/secrets in event content | non_leakage | | GF3Conservation | INV-004 | Context trit sum ≡ 0 (mod 3) | gf3_conservation | | ProofIntegrity | INV-005 | Certificate hash covers all verifier outputs | Hash verification |

GF(3) Typed Effects

| Verifier | Trit | Effect Type | Description | |----------|------|-------------|-------------| | queue_consistency | -1 | VALIDATOR | No state mutation, validates structure | | non_leakage | -1 | VALIDATOR | No state mutation, validates schema | | replay_determinism | 0 | COORDINATOR | Ensures deterministic replay coordination | | gf3_conservation | +1 | GENERATOR | Generates proof of conservation |

Narya Compatibility

| Field | Definition | |-------|------------| | before | Initial event log (JSONL) | | after | Proof bundle with all verifier results | | delta | Proof of state transition (certificate) | | birth | Empty event log | | impact | 1 if any verifier fails (state change from VERIFIED to FAILED) |

Condensation Policy

Trigger: When all 4 verifiers pass for 3 consecutive verification cycles.

Action: Archive event log segment, emit condensed proof certificate.

Proof Objects and Certificates

from dataclasses import dataclass

@dataclass
class VerifierResult:
    name: str           # Verifier name
    trit: int           # GF(3) assignment {-1, 0, +1}
    passed: bool        # Verification passed
    details: dict       # Violation details

@dataclass
class ProofBundle:
    log_path: str           # Source JSONL file
    events_total: int       # Total events processed
    verifiers: dict         # Results per verifier
    overall: str            # "VERIFIED" or "FAILED"
    proof_hash: str         # sha256:... certificate
    gf3_meta: dict          # Trit conservation metadata

Narya JSONL Log Format

Each line is a JSON object representing an event:

{"event_id": "e1", "timestamp": 1735084800.0, "thread_id": "t1", "trit": -1, "context": "workflow-A", "delta": {"type": "queue_item", "queue_id": "q1", "agent_of": 1, "item_of": "i1", "route": 1}, "content": {"action": "enqueue"}}
{"event_id": "e2", "timestamp": 1735084801.0, "thread_id": "t1", "trit": 0, "context": "workflow-A", "delta": {"type": "route_update", "interaction_id": "i1", "agent_id": 1}, "seed": 42}
{"event_id": "e3", "timestamp": 1735084802.0, "thread_id": "t1", "trit": 1, "context": "workflow-A", "delta": {"type": "agent_assignment", "queue_id": "q1", "agent_id": 1}}

Required fields: event_id Optional fields: timestamp, thread_id, trit, context, delta, content, seed, before_hash, after_hash

1. Queue Consistency (Diagram Commutativity)

Claim: agent_of(q) = route(item_of(q)) always holds.

        agent_of
Queue q ────────────► Agent a
    │                    ▲
    │ item_of            │ route
    ▼                    │
Interaction i ───────────┘

Verifies that the diagram commutes for every event touching agent_of, item_of, or route.

from src.narya_proofs.queue_consistency import (
    QueueConsistencyVerifier,
    generate_proof_certificate,
    NaryaEvent
)

verifier = QueueConsistencyVerifier(seed=1069)
log = [
    NaryaEvent(event_id="e1", before_hash="000", after_hash="abc",
               delta={"type": "queue_item", "queue_id": "q1", 
                      "agent_of": 1, "item_of": "i1", "route": 1})
]
summary = verifier.verify_log(log)
cert = generate_proof_certificate(log, seed=1069)
# cert["verdict"] == "VERIFIED"

2. Replay Determinism (Hash Replay, Time-Travel)

Claim: Events with the same seed produce identical content hashes.

Verifies that replay is deterministic—running the same seed produces identical outputs regardless of execution order or timing.

from src.narya_proofs.runner import replay_determinism

events = [
    {"event_id": "e1", "seed": 42, "content": {"value": "hello"}},
    {"event_id": "e2", "seed": 42, "content": {"value": "hello"}},  # Same seed → same hash ✓
    {"event_id": "e3", "seed": 99, "content": {"value": "world"}},
]

result = replay_determinism(events)
# result.passed == True
# result.details["hash_matches"] == 2

3. Non-Leakage (Schema Conformance, PII Detection)

Claim: No secrets or PII appear in event content.

Detects:

Email addresses
SSNs (\d{3}-\d{2}-\d{4})
Credit card numbers (16 digits)
Redaction markers [REDACTED:...]
Credentials (password=, api_key=, etc.)

from src.narya_proofs.runner import non_leakage

events = [
    {"event_id": "e1", "content": {"user": "alice"}},  # Clean ✓
    {"event_id": "e2", "content": {"email": "alice@example.com"}},  # Leak! ✗
]

result = non_leakage(events)
# result.passed == False
# result.details["leak_details"][0]["types"] == ["email"]

4. GF(3) Conservation (Workflow Law)

Claim: In any closed workflow context, sum of trits ≡ 0 (mod 3).

from src.narya_proofs.gf3_conservation import (
    GF3ConservationVerifier,
    Event,
    create_triadic_cycle
)

# Create verifier
verifier = GF3ConservationVerifier(auto_close=True)

# Valid triadic cycle (sum = -1 + 0 + 1 = 0)
events = [
    Event("e1", "ctx-alpha", trit=-1),
    Event("e2", "ctx-alpha", trit=0),
    Event("e3", "ctx-alpha", trit=1),
]

for e in events:
    verifier.add_event(e)

proof = verifier.verify_context_closure("ctx-alpha")
# proof.conserved == True
# proof.qed == True

ASCII Visualization

─── Trit Flow: ctx-alpha ───

  Event   │ Trit │ Running Sum │ Visualization
──────────┼──────┼─────────────┼────────────────────────────────
  e1      │ [-1] │    -1 (2)   │ ◀── █████████████████████│
  e2      │ [ 0] │    -1 (2)   │ ─●─ █████████████████████│
  e3      │ [+1] │     0 (0) ◆ │ ──▶                     │
──────────┴──────┴─────────────┴────────────────────────────────
  Final: Σ =   0, ✓ CONSERVED (mod3=0)

Unified Runner with CLI

# Run all verifiers on a JSONL log
python -m src.narya_proofs.runner path/to/events.jsonl

# Output to file
python -m src.narya_proofs.runner events.jsonl -o proof.json

# With custom seed
python -m src.narya_proofs.runner events.jsonl --seed 42

# Quiet mode (JSON only)
python -m src.narya_proofs.runner events.jsonl -q

Programmatic Usage

from src.narya_proofs import NaryaProofRunner

runner = NaryaProofRunner(seed=1069)
runner.load_log("events.jsonl")
runner.run_all_verifiers()

bundle = runner.generate_proof_bundle()
print(bundle.overall)      # "VERIFIED" or "FAILED"
print(bundle.proof_hash)   # "sha256:abc123..."
print(runner.to_json())    # Full JSON certificate

Example Verification Output

{
  "log_path": "/path/to/events.jsonl",
  "events_total": 150,
  "verifiers": {
    "queue_consistency": {
      "passed": true,
      "events_checked": 150,
      "violations": 0,
      "violation_details": []
    },
    "non_leakage": {
      "passed": true,
      "clean": 150,
      "leaked": 0,
      "leak_details": []
    },
    "replay_determinism": {
      "passed": true,
      "hash_matches": 45,
      "total_seeds": 45,
      "mismatches": []
    },
    "gf3_conservation": {
      "passed": true,
      "contexts": 5,
      "conserved": 5,
      "violated": 0,
      "total_trit_sum": 0,
      "total_mod3": 0
    }
  },
  "overall": "VERIFIED",
  "proof_hash": "sha256:8a4f2e1b3c5d7e9f...",
  "gf3_meta": {
    "verifier_trits": {
      "queue_consistency": -1,
      "non_leakage": -1,
      "replay_determinism": 0,
      "gf3_conservation": 1
    },
    "verifier_trit_sum": -1,
    "meta_trit": 1,
    "total_sum": 0,
    "conserved": true
  }
}

Reference Files

runner.py — Unified runner, CLI, all 4 verifiers
queue_consistency.py — Diagram commutativity, Čech cohomology integration
gf3_conservation.py — Context tracking, triadic cycles
non_leakage.py — PII detection patterns
replay_determinism.py — Seed→hash verification

GF(3) Triadic Integration

Forms valid triads with complementary skills:

narya-proofs (-1) ⊗ ordered-locale (0) ⊗ gay-mcp (+1) = 0 ✓
narya-proofs (-1) ⊗ bisimulation-game (-1) ⊗ gf3_conservation (+1) = -1 ≡ 2 (mod 3)
sheaf-cohomology (-1) ⊗ narya-proofs (-1) ⊗ topos-generate (+1) + meta(+1) = 0 ✓

Commands

# Run verification demo
just narya-verify events.jsonl

# Generate proof certificate
just narya-cert events.jsonl -o cert.json

# Queue consistency only
just narya-queue-check events.jsonl

# GF(3) conservation report (ASCII visualization)
just narya-gf3-report events.jsonl

Skill Name: narya-proofs
Type: Formal Verification / Proof Generation / Event Sourcing
Trit: -1 (MINUS - overall validator role)
GF(3): Conserved via meta-trit balancing
Proof Hash: SHA-256 Merkle root over all proof objects

Scientific Skill Interleaving

This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem:

Graph Theory

networkx [○] via bicomodule
- Universal graph hub

Bibliography References

cryptography: 1 citations in bib.duckdb

Cat# Integration

This skill maps to Cat# = Comod(P) as a bicomodule in the equipment structure:

Trit: 0 (ERGODIC)
Home: Prof
Poly Op: ⊗
Kan Role: Adj
Color: #26D826

GF(3) Naturality

The skill participates in triads satisfying:

(-1) + (0) + (+1) ≡ 0 (mod 3)

This ensures compositional coherence in the Cat# equipment structure.

Agent Skills: Narya Proofs Skill

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Skill Files