The Harmonic Early-Warning Theorem: Tipping-Point Monitoring as a Thermodynamic Detection Problem

Working paper, not peer reviewed. The Lean sources have not been re-checked by our current certification pipeline.

The Harmonic Early-Warning model (HEWT) treats tipping-point monitoring as a detection problem near a critical threshold. Within the model, Lean 4 checks that: (i) the monitored variance equals the noise constant times the susceptibility, which holds by the model's definitions; (ii) the variance grows without bound as the system nears the threshold; (iii) the signal-to-noise ratio of the detection statistic falls near the threshold and peaks at an interior distance ε_opt = ε₀·3^(−1/m); (iv) passive sensing beats active sensing below a closed-form crossover; and (v) the sensor-alignment efficiency cos²Θ lies in [0, 1].

Assumed, not derived: a minimum dissipation of 2 k_B ln 2 per bit of early warning, a Landauer plus thermodynamic-uncertainty premise entered as a model input. Lean checks only that adding non-negative slack keeps a cost above it. The link to spurious alarms in the ecological early-warning literature is a hypothesis from the model, to be tested against monitoring data; this record cites no study of that literature yet.

Formal status: Conditional (model algebra), with two Definition-expansion lemmas. Interpretive status: Empirical-hypothesis.

Authorship and AI use. Justin D. Hart is the accountable author. Lean proofs were generated with the Aristotle prover (Harmonic, project 205845a5). Tools are credited as contributors, not authors.