narya-proofs

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": "[email protected]"}},  # 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.