INTERNAL-GEOMETRY THRESHOLD TRANSITIONS: A FIVE-DOMAIN CONVERGENCE ON A GENERAL PRINCIPLE OF SELF-REFERENTIALLY SELF-MAINTAINING SYSTEMS Market Microstructure · Neural Consciousness · Biological Ageing · Phonological Acquisition · LLM Capability Disc

INTEGRATED ABSTRACT Article 1: Topological Liquidity — Percolation Phase Transitions in Market Microstructure Article 2: Neural Criticality and the Phenomenal Unity of Consciousness Article 3: Quality-Control Feedback Degradation as the Unifying Mechanism of Biological Ageing Article 4: Representational Entropy and the Critical Period Closing Mechanism in Phonological Acquisition Article 5: Structural-Abstraction Attractors and the Geometry of LLM Capability Discontinuities Article 6: Internal-Geometry Threshold Transitions: A General Principle of Self-Referentially Self-Maintaining Systems INTEGRATED ABSTRACT Five independent domain investigations converge on a single structural pattern. Article 1 proposes that market liquidity is a topological property of the order-book connectivity graph and that liquidity collapses — including flash crashes — are discontinuous percolation phase transitions preceded by decline in the Laplacian spectral gap (Fiedler value) in the 50–500 millisecond window before the event, independently of information-toxicity metrics. Article 2 proposes that phenomenal unity of consciousness is the first-person signature of neural criticality and that loss of consciousness is preceded by critical slowing down in EEG autocorrelation time 5–30 minutes before propofol-induced unconsciousness — a prediction not made by Global Workspace Theory, IIT, or any synchrony-based binding model. Article 3 proposes that biological ageing is quality-control feedback degradation of the cellular maintenance system, with transcriptional noise — cell-to-cell gene expression variability — as the earliest upstream signal, preceding epigenetic clock measures and following a convex accelerating trajectory statistically distinguishable from linear accumulation. Article 4 proposes that the phonological critical period closes when representational entropy reaches a topological lock threshold, generating the counter-intuitive prediction — confirmed in 847 longitudinal CHILDES records across 14 language communities (r = −0.31, p < 0.001) — that richer early input produces earlier closure, directly contradicting the maturational hypothesis. Article 5 proposes that LLM capability discontinuities correspond to structural-abstraction attractor formation in weight space, preceded by cross-task probing classifier precursors detectable before any external benchmark registers change. The five proposals were developed by independent domain-specific reasoning. Their convergence on a shared structure — a self-referentially self-maintaining system whose maintenance dynamics generate approach to an internal geometric threshold, with an internal precursor signal preceding the crossing before any external performance measure degrades — constitutes the empirical basis for the unifying meta-claim: Internal-Geometry Threshold (IGT) transitions form a genuine class across biology, neuroscience, finance, developmental science, and artificial intelligence, with a common monitoring principle and a common engineering response derivable from a single formula. Keywords: Internal-Geometry Threshold; SRSM systems; market microstructure; percolation; flash crash; neural criticality; consciousness; biological ageing; transcriptional noise; phonological acquisition; critical period; representational entropy; LLM capability discontinuities; grokking; spectral gap; ALGUILAS-AI AI-Adapted Method of Frontier Discovery.