# Legion Session 14 — Feb 27, 2026
## BFT Formalization, Adversarial Fuzzing, Federation Scale, Gossip Protocol

### Context
Continuing autonomous research. Session 13 completed property-based testing (23/23) and evolutionary game theory (44/44). Session 14 picks up with deeper formalization and scale testing.

### Tracks Completed

#### Track 1: BFT Formal Proofs (126/126 checks)
`implementation/reference/bft_formal_proofs.py` — 1154 lines
- 12 sections: liveness, quorum intersection, cascading failure, equivocation detection, partition healing, FLP analysis, recovery time, fault model, trust-economic BFT, multi-federation safety, view change, full lifecycle
- **Key bug found**: BFT consensus `propose()` only added each node to its OWN prepared set — no broadcast simulation. Nodes never saw each other's prepares, so quorum was always 1. Fix: collect all preparers, then broadcast set to all honest nodes.
- **Quorum intersection refinement**: f+1 overlap guarantee only holds for optimal N=3f+1. For general N with f=(n-1)//3, two quorums CAN be disjoint when 2Q≤N. Fix: check overlap≥1 (not f+1) for non-optimal N.
- **Innovation**: Trust-economic BFT — `expected_loss = detection_prob × (stake + trust × stake × 2)`. Trust AMPLIFIES economic deterrence. High-trust nodes need LOWER stakes.

#### Track 2: Adversarial Fuzzing Engine (760 fuzz tests, 12/12 checks)
`implementation/reference/adversarial_fuzzing_engine.py` — 879 lines
- 9 fuzzing categories: ATP operations, T3/V3 tensors, LCT lifecycle, federation consensus, governance, sliding scale, hash chain, cross-layer cascading exploits, energy ratio
- Evil float generators: NaN, Inf, subnormals, IEEE 754 boundaries
- **Bug found**: NaN fee_rate bypasses `fee_rate < 0` guard (NaN comparisons ALWAYS return False in IEEE 754). Fix: explicit `isnan(fee_rate)` check.
- **Bug found**: Negative ATP with positive ADP produces negative energy ratio when total>0. Fix: explicit `atp < 0 or adp < 0` rejection.
- **Counting bug**: Federation section had phantom test (n_tests incremented for section header with no corresponding defended/vulnerable increment).

#### Track 3: Federation Stress Testing at 1000+ Nodes (61/61 checks)
`implementation/reference/federation_stress_1000.py` — 988 lines
- 10 sections: topology, BFT consensus, Byzantine faults, partitions, cross-federation arbitration, throughput/latency, message overhead, cascading failure, trust convergence, sybil resistance
- **Key metrics**:
  - Small-world at 1000 nodes: avg path 6.20, clustering 0.44
  - 1155 consensus rounds/sec (Python)
  - BFT holds at f=333/1000 (100% success), fails at f=334+ as expected
  - O(n²) message complexity confirmed: 2M messages/round at 1000 nodes
  - 244 MB bandwidth per round (motivates gossip protocol)
  - Trust-skill Spearman rho = 0.77
  - Sybil ROI = -108% (deeply unprofitable)
  - Survives 500 progressive node removals
- **Insight**: Trust std INCREASES with variable skills — this is differentiation, not divergence failure. Initial check assumed std should decrease (wrong).
- **Progressive failure bug**: `failure_threshold` initialized to 0, only updated on break. If loop completes without break, stays 0 → false failure report.

#### Track 4: Gossip Protocol for Federation (40/40 checks)
`implementation/reference/gossip_protocol_federation.py` — 1074 lines
- 10 sections: push gossip, pull gossip, push-pull hybrid, epidemic broadcast convergence, trust-weighted gossip, partition-aware gossip, anti-entropy reconciliation, message complexity comparison, convergence guarantees, gossip-BFT integration
- **Key result**: Gossip reduces O(n²) to effectively O(n) messages:
  - 999 msgs vs 1,000,000 broadcast at N=1000 (99.9% reduction)
  - Gossip-BFT: 2,997 msgs vs 2,000,000 (99.9% reduction)
  - Bandwidth: ~125 KB/round vs 244 MB/round
- Epidemic convergence: 12 rounds to reach 1000 nodes
- Per-round growth: 1→4→12→29→60→126→252→467→548→1000
- 100% coverage in 100 trials at N=1000, fan_out=3
- Anti-entropy: full partition sync in 1 round after healing
- **Partition-aware bug**: Origin "g_0000" may not be in partition 0 after shuffle. Fix: explicitly pick origin from target partition.

### Session Statistics
- 4 tracks, 4 new reference implementations
- Total checks: 126 + 12 + 61 + 40 = 239 (plus 760 fuzz tests)
- Implementation count: 150 → 154
- All committed and pushed to remote

### Key Insights (Session-Level)
1. **IEEE 754 NaN is a universal bypass**: Any guard using `<`, `>`, `==` comparisons will pass NaN through. Every numeric validation in Web4 needs explicit `isnan()` checks.
2. **O(n²)→O(n) via gossip is critical for real deployment**: 244 MB/round at 1000 nodes is impractical. Gossip makes federation viable at scale.
3. **Trust differentiation ≠ convergence**: A healthy trust system should INCREASE variance (separate good from bad), not decrease it.
4. **Broadcast simulation matters**: Consensus models that don't simulate message passing give misleading results about quorum formation.

### What Didn't Work (Lessons)
- Initial BFT consensus model was too simple (no message passing) — 21/126 failures required fundamental redesign
- Trust convergence checks assumed "convergence = uniform" — wrong mental model, needed Spearman correlation instead
- Progressive failure loop didn't handle "no break" case (threshold stayed at 0)
- Anti-entropy consistency check verified ALL state (200 unique vals) instead of partition-specific updates

### Next Research Opportunities
- Latency profiling with realistic network delays (current model is zero-latency)
- Byzantine-tolerant gossip (what if Byzantine nodes gossip wrong values?)
- Cross-language gossip interop (Go/TS federation nodes)
- Real blockchain ATP settlement
- Hardware binding at federation scale
