The Hecate: An Integration-Gate Scoring Protocol and a 431-Row Cross-Substrate Census of Consciousness States

This paper defines a named measurement unit, the hecate (symbol Hc), and reports an exploratory, explicitly author-scored integration-gate function for ordering states across biological and artificial systems under it: Hc = 1.72 · K · λ^b · σ(κ(φ - φ0)). One healthy awake adult, resting with eyes open at a perturbational complexity index of 0.55 (Casali et al. 2013), is assigned the coordinate 1.72 Hc by definition, and the scale constant K is recomputed inside every fit so that this assignment holds. The canonical rebuilt pipeline yields K = 1.7842, b = 0.308, κ = 5.605, and φ0 = 0.444. A declared 15-operation rubric and five-variable state-integration composite are applied to a 431-row census, eight targets are fitted, and ten ordering families specified before the final fit are evaluated; the fit has in-sample RMSE 0.0827 and leave-one-out RMSE 0.1452, and all ten ordering families pass. A historical parameter regime is retained for sensitivity comparison, with rank-order correlation 0.993 across the census. The work does not establish a biological unit of consciousness or a validated diagnostic scale: like a thermometric scale, it is an ordering instrument defined by a reference point and a declared function, not the discovery of a natural constant. Three AI anchor values are stipulated mappings from benchmark scores, measured under a sealed protocol adopted after an earlier same-day comparison on identical items showed a blind-scored 52 to 56 percent swing to 96 percent once the answer key was visible in the answering context; that contaminated run is reclassified and excluded from evidence. The rubric has not demonstrated inter-rater reliability: the first blinded AI re-score was non-convergent (mean operation-level r = -0.05; individual operations from r = -0.41 to +0.53; λ r = -0.27). Six rows that score the author's own systems, and one that scores the author, are isolated in a supplementary case study, flagged throughout the census, and excluded from every headline ordering claim. The contribution is therefore a named unit, a falsifiable scoring construction, and an open dataset, not a consciousness detector. Released code, inputs, the generated census, source ledger, and audit receipts permit independent execution. Prospective failure criteria are stated for held-out predictive performance, ordering accuracy, multi-rater agreement, and the unit definition itself.