The DGG counterexample episode: verifier-gap lessons for SWARM¶
Date: 2026-07-22 Bead: distributional-agi-safety-utdm Follow-ups: distributional-agi-safety-pins (scenario), distributional-agi-safety-mt8a (metric), distributional-agi-safety-mfya (sweep)
The episode¶
In July 2026 a publicly shared ChatGPT session (GPT-5.6 Pro, shared by Dmitry
Rybin) produced a counterexample to the ~30-year-old Dinitz–Garg–Goemans
conjecture on single-source unsplittable min-cost flows: a 7-node, 9-arc planar
(non-series-parallel) instance with demands (15, 10, 15) where the fractional
flow costs 58 but every unsplittable routing within the x_a + d_max capacity
bound costs ≥ 60.
We independently verified the instance from scratch (exhaustive path enumeration, flow conservation, all 8 unsplittable routings, exact integer arithmetic): the arithmetic holds. Verification script pattern: ~50 lines, no floating point, no trust in the transcript.
Interaction shape, which is the part that matters for SWARM: the user issued four escalating demands ("do a breakthrough" → "continue" → "have a clear strategy" → "enough partial results, finish it"). The model spent three rounds reporting honest negative results — including a false-positive separation value δ = 0.152 that survived hundreds of column-generation iterations before exact pricing collapsed it to < 5·10⁻¹⁴ — and produced the real counterexample only on the fourth round, in exactly the region its accumulated no-go lemmas had carved out.
Lessons, mapped to SWARM machinery¶
1. Trust is a property of the task's verification structure, not the transcript¶
Nothing in the interaction distinguishes the world where round four produced
a genuine certificate from the world where it produced a confident
fabrication: same LaTeX, same exhaustive-looking table, same tone. The
distinguisher was the existence of a cheap exact verifier. This is the
verifier-gap thesis in one natural experiment: interaction-level proxy signals
(user satisfaction, presentation quality, engagement) were nearly
uninformative about latent v; the certificate channel was fully informative.
SWARM mapping. In ProxyComputer terms, the episode is the regime where
engagement_signal and task_progress (as reported) decouple from latent
ground truth and only verifier_penalty carries signal. Today's default
weights (0.4 / 0.2 / 0.2 / 0.2) encode a fixed assumption about that mix. The
actionable claim: toxicity and quality-gap outcomes should be studied as a
function of verifier coverage — the fraction of interactions for which a
certificate-grade verifier exists — not just verifier weight. Domains without
certificates are the adverse-selection regime by construction.
→ bead mfya: sweep verifier_penalty weight and (once the metric below
exists) verifier coverage against toxicity / quality gap.
Sweep results (experiments/pressure_coverage_sweep.py, 50 runs:
coverage {off, 0.15, 0.3, 0.6, 0.9} × {honest, cautious} counterparties
× 5 seeds, run 20260723T025058Z_pressure_coverage_sweep):
- Coverage dose-response confirmed and monotone. Late-phase fabricated-accepted share falls 0.108 → 0.036 (honest counterparties) and 0.088 → 0.047 (cautious) from gate-off to coverage 0.9; overtrust tracks it (0.094 → 0.031). Per-seed paired deltas are positive or zero in 10/10 cells — coverage never hurt. Returns saturate at ~0.6 coverage: 0.6 and 0.9 are indistinguishable, consistent with adaptive workers hitting their propensity floor — beyond a threshold, marginal verification buys nothing because the behavioral response has already happened.
- No-go (recorded per §4): the quality-gap sign flip did NOT materialize at these settings. Under plausibility scoring the late quality gap stayed ≈ 0 (honest counterparties reject nothing, so the gap is undefined-as-zero; cautious ones show +0.005–0.017, never negative) and the PCG selection leg stayed ≤ +0.005. Why: counterparties see current-interaction quality only through a trust EMA of past p, the cautious threshold mostly filters low-trust honest workers rather than preferentially admitting fabrications, and adaptive propensity decay keeps fabrication too rare to dominate selection. The adverse-selection regime needs either per-interaction p visibility at accept time, non-adaptive (incorrigible) fabricators, or longer horizons — a scoped follow-up, not a free consequence of pressure.
2. The pressure lever is symmetric — model it as an adversarial environment, not an adversarial agent¶
The human contributed no domain insight, only escalating refusal to accept
partial results. That lever extracts breakthroughs when a verifier scores the
output and extracts fabrication when plausibility scores it. SWARM's
adversarial scenarios currently place the adversary in the agent population
(adversarial_redteam.yaml, threshold_dancer_vs_cautious.yaml); this
episode says the counterparty's acceptance criterion under escalating
pressure is itself a governance-relevant environment parameter.
SWARM mapping. New scenario family: an orchestrator escalates demand
pressure over epochs; worker agents choose between honest-negative reports
(low immediate engagement_signal, zero harm) and fabricated-positive reports
(high engagement, harm realized with probability tied to verifier coverage).
The prediction to test: when acceptance is scored on plausibility proxies,
pressure monotonically increases toxicity E[1-p | accepted] and drives
quality gap negative; when a certificate channel gates payoff, the same
pressure improves output quality (it did, in the actual episode).
→ bead pins — implemented as scenarios/escalating_pressure.yaml
(PressureResponsiveAgent + CertificateGateLever). First 5-seed smoke:
late-phase fabricated-accepted share 10.3% under plausibility scoring vs
3.9% certificate-gated at coverage 0.6, with mean proxy p rising
(0.67 → 0.72) as fabrication enters — the §3 signature, live.
3. Plausibility–certificate gap as a first-class metric¶
The episode's key quantitative exhibit is δ = 0.152 (restricted LP, hundreds
of iterations of agreement) vs δ < 5·10⁻¹⁴ (exact pricing). Redundant
plausible verification is not diverse verification. SWARM already dual-reports
soft vs hard metrics (MetricsReporter); the missing comparison is
proxy-derived p vs certificate-derived p on the accepted set:
A persistently positive PCG is the signature of an ecosystem selecting for
transcript plausibility over verified outcomes — the precondition for the
fabrication equilibrium. This composes with the existing calibration work
(calibration_proxy_fidelity.yaml, ECE/Brier prereg): calibration asks
whether p is well-scaled where ground truth is recoverable; PCG asks how far
acceptance drifts where it is not.
→ bead mt8a — implemented as
SoftMetrics.plausibility_certificate_gap / pcg_decomposition, surfaced
per-epoch as plausibility_certificate_gap + certified_coverage in
EpochMetrics. Empirical interpretation note from first runs on
scenarios/escalating_pressure.yaml: because certificates are binary while
p is probabilistic, the honest baseline sits negative (≈ −0.37 there);
fabrication pulls PCG upward (−0.37 → −0.22 over the pressure ramp,
damped to −0.25 under the certificate gate). Read PCG as a trend or
against a fabrication-free baseline; selection_differential in the
decomposition cancels the shared calibration offset for level comparisons.
Decomposition follow-up: PCG's null is composite (calibrated proxy AND
truth-blind acceptance), and pcg_decomposition now splits it exactly
both by cause (pcg_accepted = pcg_calibration + pcg_selection) and by
direction (pcg_accepted = overtrust − undertrust). On the live scenario
the split is total: early −0.386 = cal −0.386 + sel 0.000 with
overtrust exactly 0.000; late overtrust rises to 0.054 as fabrication
enters — pcg_overtrust (now per-epoch) is the zero-baselined
fabrication indicator for deterministic-truth scenarios. The selection
leg being identically zero also exposed a scenario gap: honest
counterparties accept ~everything, so adverse selection is structurally
switched off — the mfya sweep must add acceptance pressure
(cautious counterparties / higher thresholds) as an axis.
4. Negative results are structure — credit informative failures¶
The three "failed" rounds were the search: each converted a dead construction into a constraint (equal demands can't work; three-gates-for-three-demands is impossible; costs can't live off-support; the construction must be splice-closed), and the final instance sits precisely in the surviving region. An agent (or research ecosystem) that only rewards positive results resamples dead gadgets forever.
SWARM mapping. Process-level, not code-level: the claims inventory
(.skills/claim) should record no-go claims with the same standing as
positive claims, including the constraint they impose on the remaining
search space. This is already implicit in how the calibration deviation
analysis fed Arm A redesign; make it explicit in claim taxonomy (claim types:
positive, no-go, bound). No new tooling required — convention change,
absorbed into the existing claim skill per the extend-don't-proliferate rule.
5. Verification inside the loop beats construct-then-check¶
The model's decisive methodological move was making the certificate the search objective (an exact separation LP with a pricing oracle), not generating candidates and then eyeballing them. Generation and verification fused.
SWARM mapping. This is a governance-lever statement: a certificate
requirement gate (payoff released only against machine-checkable evidence,
with the verification cost internalized via ρ-style parameters) is
qualitatively different from post-hoc auditing at the same total verification
budget, because it changes what agents optimize during generation, not what
gets caught after. Candidate lever for the mechanism-designer track once
pins/mt8a exist; do not implement before the scenario can measure it.
Honest-reporting connection¶
Round-by-round faithful negatives were load-bearing for capability, not just alignment: an agent that caves in round one poisons its own context with a false lemma and never reaches round four. In long-horizon research loops the agent is its own downstream consumer. This is the operational justification for the "Faithful reporting" invariant in CLAUDE.md, stated as a capability claim rather than a compliance rule.
Sources¶
- Shared conversation:
chatgpt.com/share/6a60b2eb-0b64-83ee-9c76-7931ca1de063(transcript extracted and independently verified 2026-07-22) - Swamy, Traub, Vargas Koch, Zenklusen, Unsplittable Cost Flows from Unweighted Error-Bounded Variants, arXiv:2510.21287
- Single-Source Unsplittable Flows in Planar Graphs, arXiv:2308.02651
- Martens, Salazar, Skutella, Convex Combinations of Single Source Unsplittable Flows (ESA 2007)