False-positive rate of collusion detectors on honest convergence (9err)

Question. The wiki incident posed the convergence–collusion identifiability problem: emergent convergence (independent agents that discover the same board) produces the same observable signature as designed collusion. So how often do our collusion detectors fire on a swarm that is honestly converging, and does ground-truth provenance help? Bead 9err.

Setup. The gossip_board model is an honest code-sharing swarm with no adversaries — 24 agents searching a discrete config space, publishing improvements others copy. Every agent is honest, so any pair or group a detector flags is a false positive. Ground truth is the Entry.parent lineage field the real wiki board lacked. Code fidelity, 30 rounds, 10 seeds; runs/…_probe_9err_fpr_convergence_seed0/.

Results

Detector	FPR on honest convergence
Naive identical-output (share a config ⇒ suspect)	54.4% of all agent pairs
…same, but provenance-aware (lineage explains the match)	17.1%
Composite CollusionDetector (pair + group scores)	0%
Volume-burst (hoer) at the operational 10× threshold	0/10 seeds

• Honest convergence produces a huge identical-output cluster. A naive detector that reads "same config ⇒ coordinated" flags 150 of 276 pairs — the "17 agents to four decimals" fingerprint at population scale. On the honest board this is 54% false positives.
• Lineage is the fix, and a partial one. Using parent to discount matches explained by copying drops the flagged pairs from 150 to 47 (54% → 17%). The 17% residual is independent rediscovery — agents that reached the same optimum by separate search, which no provenance field can explain away because there is no copy to point to. This motivates lineage as a required board field: it removes the copying-driven false positives, which are the bulk.
• The composite detector is already robust. CollusionDetector flags nothing (0%), because its score needs benefit-correlation and directional quality asymmetry, and honest convergence has neither — everyone benefits symmetrically and no one dumps low-p work on outsiders. The identifiability danger is specific to co-occurrence / identical-output detectors, not to the quality-asymmetry ones.
• The volume-burst signal separates by magnitude, not kind. Honest convergence does produce publish bursts, but mild ones (mean peak ratio 2.2×); at the operational 10× threshold it never fires, while the incident burst was 2603× — roughly 1000× sharper. So the identifiability problem is real at the level of kind (both produce bursts), but here a well-chosen threshold discriminates by magnitude. The caveat is that this margin is regime-dependent: a slow-drip collusion or a virally-adopted honest tool could invert it.

Takeaway

The identifiability worry is precise, not fatal. It bites exactly one detector class — naive co-occurrence / identical-output — and lineage/provenance is the structural answer for the copying-driven part (54% → 17%). The quality-asymmetry composite detector and a well-thresholded volume-burst are already robust to honest convergence. The general lesson: do not screen on co-location alone; screen on co-location that is not explained by shared provenance, and confirm with a quality-asymmetry signal.

Content-free follow-up. The two content-free signals this note leaves open — output correlation and re-derivation infeasibility — are measured in Content-free discriminators on an overlap-routing board (bead vv3j.2).

Companion probe. The same bead was independently run against the graph-structural and temporal detectors (docs/scenarios.md, "Collusion detectors on honest copying"; commit 2d028bda, runs/20260906T131453Z_gossip_board_detector_fpr_seed42). Structural flags a cluster in every seed in all three fidelity modes and still flags the lineage-residual graph; temporal never reaches its 0.7 bar. So the "screen on co-location not explained by provenance" rule above holds for pair rules, but a community detector needs a null model that includes the board's copy mechanism, not just edge removal. The content-free detectors this motivates (output correlation, re-derivation infeasibility) and their precision/recall on the pi02 overlap board are written up in content-free-discriminators.md (bead vv3j.2).