The cricket-Laws paper reaches its 'phase-transition'/'punctuated' framing independently via condensed-matter physics, not by citing the punctuated-equilibrium literature

A full-text read of Chia et al. (2026), "Three Centuries of the Laws of Cricket Reveal Core Principles of the Evolution of Regulatory Mechanisms" (arXiv:2607.05586), resolves how the paper's discontinuous-restructuring language relates to the punctuated-equilibrium lineage: it does not. The connection the vault's earlier cricket notes drew is the vault's own cross-domain overlay, not a link the authors make.

The negative finding. Every in-text citation number was cross-checked against the paper's 54-item numbered reference list. None is Eldredge & Gould (1972), any Ernst Mayr work, Gersick (1991), or Tushman & Romanelli — the four anchor citations of the vault's punctuated-equilibrium cluster (claim-punctuated-equilibrium-derives-from-mayr-peripatric-speciation, claim-gersick-1991-punctuated-equilibrium-deep-structure, claim-tushman-romanelli-1985-reorientation-exogenous-trigger). The phrase "punctuated equilibrium" appears nowhere in the document. The word "punctuated" appears twice, both uncited and both in statistical-physics framing rather than biological: "the rule hierarchies evolve with punctuated events delineating periods of smooth structural change" and "the punctuated and discontinuous nature of the evolution of the Laws of Cricket" — ordinary English for "in bursts," not invocations of Eldredge & Gould's technical term.

The positive ancestry. The paper's headline structural result — a 1939 discontinuity in the rule tree's average branching factor — is explicitly typed as a physics phase transition and cited to condensed-matter physics: a "first-order dynamical phase transition [39, 40]—defined by the presence of discontinuities in an order parameter as a system evolves in time, which in our case is the branching factor of the rule tree." References [39] and [40] are Canovi, Werner & Eckstein (Phys. Rev. Lett. 2014) and Budich & Heyl (Phys. Rev. B 2016) — both non-equilibrium condensed-matter physics. So "phase transition" here is load-bearing physics (a named order parameter, an observed discontinuity in time), not borrowed vocabulary — which settles the second half of the question at question-verify-cricket-laws-cites-biological-punctuated-equilibrium.

The one biology the paper does reach for is a different subfield entirely: the Discussion compares its 1939 transition to the prokaryote-to-eukaryote increase in gene-regulatory depth (enhancers, chromatin, CTCF insulators), citing gene-regulatory-network work (Davidson 2010; Erwin & Davidson 2009), not the macroevolutionary tempo-and-mode literature to which punctuated equilibrium belongs.

This directly qualifies claim-cricket-laws-268-years-abrupt-regulatory-phase-transitions and claim-cricket-laws-paper-extends-sfi-universal-scaling-to-regulation, whose [unverified] punctuated-equilibrium flag this note discharges: the cricket paper belongs to the vault's punctuated-equilibrium cluster (moc-schema-change-and-restructuring) as an analogical third domain the vault itself supplied, not as a citation-linked lineage member.