David Mullett
Independent researcher working on formal models of collapse in digital feedback systems.
d@loopzero.org · ORCID 0009-0004-2543-1664 · GitHub

Research

Preprint
A formally specified warning criterion for collapse in recursive systems
David Mullett  ·  arXiv preprint
Loopzero defines a warning criterion for collapse in recursive systems around a minimal no-progress obstruction, formalized in Lean 4 to make the claim boundary explicit. The criterion is instantiated as a triplet of telemetry witnesses — gain (G), recursive persistence (p), and diversity (δ) — and evaluated on two public benchmark domains under a matched false-positive contract, with a secondary consistency analysis on published model-collapse trajectories.

What Is New

  • Specifies A formal claim boundary for one specific failure mode in recursive feedback systems, articulated in Lean 4. The artifact is intentionally elementary — it exists to make the empirical bridge assumption explicit and inspectable.
  • Tests A conditional empirical bridge from the formal claim boundary to a measurable pre-collapse footprint, evaluated on two public benchmark domains under a locked equal-false-positive contract. A secondary consistency analysis on published model-collapse trajectories (Shumailov et al., 2024) corroborates the witness pattern in a third recursive setting.
  • Introduces A matched-false-positive comparator contract — detectors compared at the same alert budget rather than at arbitrary thresholds — designed as extensible infrastructure for evaluating recursive-collapse detectors across system families.

Current Status

Specified
A minimal no-progress obstruction in Lean 4, together with a measurement-map bridge and a schematic telemetry specialization. The artifact establishes what is and is not claimed: it verifies the abstract obstruction, not that real benchmark telemetry supplies the required measurement map.
Empirically tested
Two public benchmark domains under a matched-false-positive contract: a public-data markets event family (Volmageddon 2018, COVID March 2020 circuit breakers) and an offline MovieLens-25M recursive recommender replay benchmark. A secondary consistency analysis on Shumailov et al. (2024) corroborates the witness pattern in a third recursive setting; matched-FP comparator evaluation in that domain is deferred to follow-up work. Empirical claims are bounded to the protocol and analyses described in the preprint.
Open work
A v1.1 program is in development: adding the proposed criterion's own matched-FP operating point to the comparator table, threshold-path calibration of comparators, recommender negative controls, and cluster-robust dependency analysis. Future work includes extension to additional recursive domains with matched-FP comparator evaluation.

Why It Matters

Recursive feedback systems — algorithmic, financial, and social — are widely studied. Their failure modes are often described operationally and less often specified as formal objects. Loopzero approaches one specific failure mode by treating it as a formally bounded claim: the obstruction is specified in Lean 4, the bridge from that obstruction to observable telemetry is stated explicitly as a conditional assumption, and the empirical claims are bounded to a defined benchmark protocol. The aim is not deeper formal machinery; it is making what is claimed easier to inspect, contest, and test across domains.

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