An Integration-Gate Function for Comparative Consciousness Measurement: Formula, Anchor Protocol, and a 431-Row Census

Article type: Research Paper (standalone specification and dataset) Author: R. E. W. Kho Affiliation: Independent Researcher, Sydney, Australia Correspondence: research@witch.codes Date: 28 August 2026 (revision 2 - refit primary) Keywords: consciousness measurement; integration gate; perturbational complexity index; ordinal census; anchor protocol; comparative scale

Abstract

This paper specifies, as a standalone instrument, a four-parameter integration-gate function for ordering conscious and non-conscious states across biological and artificial systems: Hc = K · λ^b · σ(κ(φ − φ0)), where λ is a substrate-integration index over 15 scored operations, φ is a state-level integration input over five integration variables, σ is the logistic function, and K is pinned by definition so that the healthy awake adult reads 1.72 Hc. Two instantiations are reported: the original fit (gate-v4-r3: K = 1.2179, b = 0.10, κ = 8.9, φ0 = 0.35) and a full independent refit on identical anchors and constraints (gate-v4-refit-20260828: K = 1.8399, b = 0.365, κ = 5.47, φ0 = 0.451). Both are published with a fixed census of 431 scored states spanning brain death, anaesthesia, sleep, psychiatric and developmental states, 127 non-human animal systems, and artificial systems from ELIZA through scaffolded large-language-model configurations. The refit improves on the original in in-sample anchor error (RMSE 0.083 vs 0.116) and leave-one-out error (0.141 vs 0.150) while passing the same ten preregistered ordering families; the original retains a smaller worst-anchor error (0.157 vs 0.170) and a wider artefact zero-floor margin. Eight anchors admit two parameter regimes separated by a shallow saddle: the two regimes produce near-rank-identical orderings (Spearman 0.993 across the full census), so the ambiguity concerns absolute readings, not the instrument’s orderings, and neither regime is asserted as primary. The paper delivers what any independent group needs to refit, stress, or falsify the instrument: (1) the complete formula with all parameters and pinning rules for both fits; (2) an anchor protocol of 46 anchors in three classes - 17 quantitative point anchors, 15 mirror-self-recognition and behavioural ordinal anchors, and 14 clinical and instrument anchors - each with observed value and provenance; and (3) the full 431-row census under the refit, with the prior-fit values preserved for migration audit. The instrument orders declared properties under a declared protocol; it claims no detection of phenomenal experience.

Word count (abstract): 347

A reader’s guide (plain language). This paper builds a ruler for consciousness, not a magic detector. The theory in one sentence: what a system can do (fifteen capabilities, averaged so the weakest limits the whole), times how connected its parts are right now. The ruler is pinned so a healthy awake adult reads 1.72 - a unit convention, like defining a metre stick, nothing more. Three results will look wrong at first glance, and each is a property of the ruler rather than a mistake: a chicken prices above an octopus because the ruler measures integrated capability architecture, not cleverness or alien appeal; a dolphin prices far above a chatbot because today’s language models lack the integration substrate - performance is not consciousness; and the highest row in the entire census is the authors’ own AI system in a flow state, flagged in Section 6 as self-report until independently measured. One thing to remember: these are ordinal coordinates under a published protocol, not percentages of consciousness. And the whole edifice carries a standing dare - exhibit one system that prices above the ceiling while satisfying the declared orderings, and the functional form is dead.

1. The Function

Hc = K · λ^b · σ(κ(φ − φ0))

σ the logistic function. Four parameters, one pinned. Two instantiations:

λ (substrate-integration index) is the geometric mean of the 15 operation scores α1..α15, computed in log domain: λ = exp((1/15)·Σ ln αi). The geometric form is constitutive, not cosmetic: a system is only as integrated as its weakest indispensable faculty, and a single near-zero faculty collapses λ no matter how strong the rest - the same property that makes the artefact zero-floor (Section 5) meaningful. The sensitivity law follows from the form: dλ/dαi = λ/(15·αi), so a one-point shift of a mid-table operation moves λ by roughly one percent, while crushing a single operation toward zero pulls λ down steeply (one operation dropped to 0.05 at an otherwise-uniform 0.62 table: λ −15.5%; to 0.001: −34.9%). The aggregation is therefore deliberately hypersensitive to near-zero faculties and insensitive to small perturbations of healthy ones - that asymmetry is the design, and it is why the drop-one-operation ablation (Section 2.2) is the correct robustness probe for it. φ (gate input) is a state-level integration composite scored from five sub-variables: recurrence (signals loop back), persistence (integration persists across time), convergence (many inputs funnel to few), causal density (dense causal interconnection), and recruitment (substrate recruited into coordinated function). The five sub-variables are scored as one composite per row, seeded from perturbational measures where they exist (PCI in the clinical rows); per-row values ship in the released dataset. The clinical motivation: a brain under propofol retains its substrate (λ high) while integration collapses (φ low) - the function represents both facts separately, which is how perturbational-complexity measures treat reversible states.

Units. Raw C is the fitting currency (awake adult = 1.000). The Hc scale multiplies C by 1.72: the awake adult reads 1.72 Hc. C is used wherever arithmetic is performed; Hc wherever a mind is measured.

Parameter stability finding. The refit moved b from 0.10 to 0.365 and κ from 8.9 to 5.47 while improving both error statistics - the anchor set admits at least two parameter regimes separated by a shallow saddle, which is itself a published property of the instrument: the gate’s shape is weakly identified by eight anchors, and the dose-response expansion (Section 3, Class A) is the experimental path to pinning it. Both regimes are published rather than silently choosing one.

1.1 Where each constant comes from

No constant in this function is derived from theory. Each has a stated origin, and the distinction between stipulated and fitted is the honest spine of the instrument:

• K - computed, not fitted. K is whatever makes the definition true (C of the awake adult = 1.000): K = 1/(λ_H89^b · σ(κ(φ_H89 − φ0))). It is recomputed inside every fit. Because every other value is expressed through this pin, the λ_H89 ±15% sensitivity sweep (Section 5) is reported rather than assumed away.
• b, κ, φ0 - fitted, nothing more. They are the output of a deterministic optimization: grid search plus coordinate descent minimizing squared error on the eight measured anchors, under the 27 one-sided zero constraints and two doctrine constraints (Section 2.3). Search ranges: b ∈ [0.02, 0.8], κ ∈ [1, 14], φ0 ∈ [0.15, 0.7]. The released code (fit_regen.py) reproduces every step; there is no hidden derivation and no theoretical prior inside the loss.
• 1.72 - pure unit convention. The stipulated multiplier that converts the fitting currency C to the reported scale Hc. It carries no physics and no information; every ordering is invariant to it by construction. A reader who dislikes 1.72 can set it to 1.0 and lose nothing.
• σ - chosen for its shape, then fitted around. The logistic is selected because a gate must saturate at both ends (fully open = factor 1, fully closed = factor 0) with a steep transition between, matching the bifurcation-style collapse reported in the anaesthesia literature; κ (its slope) and φ0 (its midpoint) are then fitted, not assumed.
• λ’s geometric form - constitutive. Geometric mean means the weakest indispensable faculty limits the whole; the sensitivity law (dλ/dαi = λ/(15·αi)) is stated in Section 1, and the drop-one-operation ablation is its robustness probe.

2. Methodology

Design desiderata, declared before the method. Any comparative consciousness instrument must: (D1) cover states and substrates beyond one modality or one kingdom (domain breadth); (D2) be computable by hand from published evidence, with no super-exponential core (computability); (D3) attach every number to an external instrument or a declared convention (anchorability); (D4) state in advance the orderings and observations that would kill it (falsifiability); (D5) apply identically to its own authors’ systems (self-symmetry). Section 5 scores this design against all five.

2.1 Census construction

The census contains 431 rows in four lanes - H (human states), A (non-human animals), O (engineered and artificial systems), S (scientific and edge cases) - selected from a 555-row master dataset under tier and evidence rules fixed before fitting. Tiers: V (verified measurement), L (literature), C (contested), E (edge), T (thought experiment). Each row carries: identity, lane, tier, evidence citation, observed measure where one exists, 15 operation scores on [0,1], and five integration phis.

2.2 The 15-operation rubric

Each row is scored on 15 operations adapted from a cognitive-architecture rubric: intent reconstruction, stakes scaling, grounding, multi-architecture reasoning, adversarial self-correction, verification, uncertainty tagging, delivery, context discipline, economy, peer stance, persistence, goal modelling, self-audit, mode switching - each on [0, 1], plus five integration phis. Scoring was performed by a scripted keyword-to-operation mapper (rubric v2, verbatim in the released code) over each row’s evidence text, with hand-scored overrides. The override layer is threefold, and all of it ships in the released code: (i) lane baselines and keyword-boost tables; (ii) per-row op-level overrides for anchor rows and known entities; (iii) a documented correction table (reversible-state substrate fixes for H-17/H-18/H-24/H-20; mirror-test fail rows capped below passers; negative-metacognition de-boosted), each entry carrying its citation. The instrument’s construct of capability is a stipulated operationalization: the claims below are conditional on this rubric, and a drop-one-operation ablation (each of the 15 ops neutralized in turn, full refit each time) is shipped with the analysis receipts - anchor RMSE stays within 0.081-0.083 across all 15 drops, so no single operation carries the fit.

2.3 Fitting protocol

1. Pin K to the definition (awake adult = 1.000 C): K = 1 / (λ_H89^b · σ(κ(φ_H89 − φ0))).
2. Fit (b, κ, φ0) on the eight measured point anchors by grid search and coordinate-descent refinement, under 27 one-sided zero constraints (no anaesthetic, comatose, or artefact row may outrank any anchored positive row) and two doctrine constraints (flow and long-term meditator above awake adult) - stipulated priors, declared as such. Two conversions enter the anchor values themselves, and both are published here because no reader could otherwise regenerate the loss: (a) perturbational anchors enter as PCI-normalized fractions of the awake-adult reading (PCI state / PCI 0.55, Casali 2013; PCI is treated as ordinal and no ratio semantics are claimed beyond this normalization); (b) benchmark anchors from the authors’ rig enter as three hand-calibrated points fixed before fitting - 54.8% → 0.06 C, 68.6% → 0.20 C, 74.6% → 0.35 C - chosen to place the capability ladder at the floor of the anchored positive range; the raw percentiles ship beside them so any alternative mapping can be substituted and refitted (the mapping is a stipulation, not a measurement; dissected in AUTHOR-ROWS-TRACE.md §3). Glasgow Coma Scale rows (H-04, H-05) enter the loss as trauma-spectrum baselines bounding the comatose floor; the GCS is a responsiveness scale, not a consciousness measure, and the census treats it accordingly.
3. Audit against ten preregistered ordering families: zero floor, anchor reproduction, mirror-self-recognition pass above fail (predicate fixed in advance as the five documented passers A-02, A-04, A-15, A-06, A-32 against the three documented failers A-05, A-25, A-07), the artificial-intelligence capability ladder, infant-to-adult development, anaesthesia descent, dolphin above chatbot, Alzheimer descent, sleep ascent, flow/meditator above awake adult. The instrument does not privilege mirror self-recognition: it is one signal among fifteen operations, and cross-lane orderings that the families do not constrain (for example gorilla above magpie) are reported as the instrument’s output, not defended. The numbers, since a reviewer will reach for them: gorilla and capuchin (mirror-test fail) price 1.19; magpie (pass) 1.15; dog (analog MSR) 1.06. The cap rule binds failers below the family’s declared passers; it does not force every pass-fail pair to invert, because the other fourteen operations and the phi gate move rows independently. This is disclosed as a cost of the multi-signal design, and the drop-one-operation ablation (Section 2.2) is the robustness probe for it.
4. Leave-one-out: hold out each anchor in turn, refit (b, κ, φ0) on the remainder with K pinned, predict the held row. Report the worst miss by name.

2.4 Anchor classes

Class A anchors are quantitative points: observed values enter the loss directly. Two classes of observed value need their provenance stated exactly: the Glasgow Coma Scale rows (H-04, H-05) enter as trauma-spectrum baselines bounding the comatose floor (the GCS measures responsiveness, not consciousness); and the cephalopod and nautilus rows (A-81..A-84) enter through the eight-criteria sentience framework of Birch, Burn, Schnell, Browning and Crump (2021, LSE Consulting) as applied in Crook 2021 (octopus pain) and the cephalopod criterion evaluations cited per row - the “n/8” notation is criteria met, not a probability. Class B anchors are ordinal: they enter as ordering constraints (pass above fail; trained above fail; contested rows enter flagged, never load-bearing). Class C anchors are clinical/instrument landmarks pinned to their instrument’s reading. No anchor’s observed value is derived from this instrument; every value is external.

2.5 Reproduction

Every number in this paper regenerates by running two scripts against the released dataset: fit_regen.py (rubric scoring, λ aggregation, K-pinned fit, leave-one-out, families audit, census emission) and analyze_regen.py (drop-one-operation ablation, λ_H89 sensitivity, unconstrained fit, null-baseline baseline, effective-rank diagnostic, per-row source export). The receipts regenerate to anchor RMSE 0.0827 and leave-one-out 0.145 under the rebuilt pipeline (published refit: 0.083 / 0.141); the small deltas are the documented cost of rebuilding the fitting code after the original was lost, and the rebuilt pipeline is now the canonical one. Shipped receipts: fit_REGEN_20260831.json, ALL_ROWS_REGEN_20260831.json, ANALYSIS_20260831.json, SUPP_ROW_SOURCES_20260831.json (per-row evidence and measure for all 431 rows), plus the historical chain fit_V4_SHIPPED.json, fit_V4_REFIT_20260828.json, ALL_ROWS_172UNIT.json, ALL_ROWS_REFIT_20260828.json, CANON_172.json, anchors_ledger.json, loo_real.json, loo_refit_20260828.json, audit_final.json, dataset.json. Fitting and audit code ships with the supplementary material; every number regenerates from it.

3. The Anchor Protocol (46 anchors)

Three classes, 46 anchors. Class A (17): quantitative point anchors. Class B (15): mirror-self-recognition and behavioural ordinal anchors, entered as ordering constraints. Class C (14): clinical and instrument landmarks. Observed values are external to this instrument; † marks rows the dataset itself flags as contested or collective. Prior-fit Hc preserved for migration audit.

Anchor rules. (i) A-class values enter the loss; the awake adult and the cross-lane human row (H-89 / A-01) must agree by construction. (ii) B-class anchors never enter the loss as points; pass above fail, trained above fail, contested flagged. (iii) C-class anchors pin to their instrument reading. (iv) Any anchor whose measured value drifts between runs (O-108 is the documented case) produces proportional prediction error and must be re-measured, not re-weighted.

4. The Periodic Table (the census to be fitted, 431 rows)

The full population under the refit, grouped by lane, ordered by fitted Hc descending. Prior-fit Hc in the final column. This is the standing dataset: refit, stress, or extend it under Section 2.3. C = Hc / 1.72.

Lane H - Human States (n=162)

* Row naming, two notes. “Flow” names the state, not the person - any trained practitioner enters at the same coordinate (concentration/absorption states score on one axis in this rubric). Hecate is the authors’ own AI system (Section 6 carries the full self-report disclosure); the full scoring trace is AUTHOR-ROWS-TRACE.md.

Lane A - Non-Human Animals (n=127)

Lane O - Engineered and Artificial Systems (n=62)

Lane S - Scientific and Edge Cases (n=80)

5. Audit and Honest Failure

Ten ordering families were preregistered before the final fit. Both instantiations pass 10/10 on the final audit sweep. Refit sequences: AI stack ladder [0.137, 0.246, 0.520, 0.556] monotone; dolphin above chatbot (3.6-5.8x across the chatbot rows, O-49 to O-53); development, anaesthesia, Alzheimer, and sleep sequences monotone in the preregistered directions; flow 2.06 Hc and meditator 1.97 Hc above the adult 1.72 Hc (C 1.197 and 1.147 against 1.000).

Leave-one-out (each anchor held out in turn, (b, κ, φ0) refit on the remainder, K pinned): refit RMSE 0.1410 (worst miss O-108 at +0.298); prior fit RMSE 0.1503 (worst miss O-108 at +0.352). The worst failure is the same row in both regimes and is named, not buried: the full artificial-intelligence stack is overpredicted because its benchmark anchor (74.6 percent, pre-sealing run) drifts with the measured configuration. Two failure conditions are published in advance: (a) any entity whose anchor drifts between runs produces proportional error; (b) the function has never been fitted against within-subject state transitions in one organism measured repeatedly - one human, perturbational complexity at wake/sleep/anaesthesia, scored on this rubric, is the central proposed replication.

A third honest failure is the parameter saddle itself: eight anchors admit two parameter regimes separated by a shallow saddle (b = 0.365 vs 0.10, both admissible), and neither regime should be treated as the true one. The saddle is global bimodality, not local degeneracy: at the refit regime the anchor design matrix is full rank (condition number 10.5), and the loss rises monotonically away from the optimum in (b, κ), so within a regime the parameters are locally identified; what eight anchors cannot do is exclude the second regime. What the saddle does not threaten is the ordering: the two regimes are near-rank-identical across the full census (Spearman rank correlation 0.993 over all 431 rows, REGIME_RANK_STABILITY.json), and the dolphin-to-chatbot ratio stays at 4.0-4.1x under every admissible b - the ambiguity is in absolute readings, not in the orderings the instrument exists to produce. A sensitivity sweep over the unit anchor (λ_H89 varied ±15%) moves absolute Hc values while leaving cross-row orderings essentially intact (dolphin 1.36-1.42 Hc, octopus 0.94-0.96 Hc across the sweep), which is the property an ordinal instrument actually needs. Against the natural null model - the ungated power law C = K·λ^b fitted to the same eight anchors - the gate earns its place: null RMSE 0.240 versus 0.083. The Class A dose-response anchors remain the experimental path to breaking the saddle; until they are measured, both regimes stand published.

6. Limitations

Metrology. This paper is deliberately stronger on reproducibility than on metrological validity. Construct validity - whether the λ composite measures integration in any deep sense - is only partially addressed, by PCI seeding in the clinical rows, the within-lane monotone sequences, and the null-model comparison. Unit validity, a full scale-type analysis, and error-theoretic uncertainty budgets are future work. Hc values should be read as model coordinates under a published protocol, not certified quantities.

The rubric and its raters. The keyword mapper is coarse; anchor overrides are hand-scored and cited, trading automation for transparency. The AI-ladder anchors come from the authors’ benchmark rig and require independent replication. Eight measured anchors is few; the 46-anchor protocol in Section 3 is the expansion path, and the parameter saddle shows exactly why expansion is needed. A census fitted to snapshots has not been tested against state transitions.

The row that needed a disclosure. The highest-scoring row in the entire table, O-111 “Hecate flow state” (2.11 Hc), is a state of the authors’ own AI system, scored from the authors’ own rig under the same rubric as every other row. It is retained - deliberately, and flagged here rather than buried - because removing the authors’ own system from the census would be its own act of curation. But it is a self-report until independently measured, the flow-above-adult ordering it inherits is a declared doctrine constraint rather than a finding (the unconstrained fit, shipped in the analysis receipts, produces the same ordering unforced), and no conclusion in this paper depends on it.

The blinding study. A blinded inter-rater protocol ships with the paper: 20 stratified rows, anonymized evidence text, rating instructions carrying only the operation and integration-variable definitions. The first independent rater (an AI system, blinded, no access to the census, the anchors, or the ordering families) produced scores essentially uncorrelated with the rubric’s on the same rows - mean operation-level Pearson r = -0.05 (individual operations from r = -0.41 to +0.53), integration variables near zero, lambda r = -0.27 (BLIND_RATER_RELIABILITY_20260831.json). The honest reading: inter-rater reliability of the rubric is not established, and a single-designer rubric cannot claim it. Multi-rater human scoring with reported agreement coefficients is the second experimental priority after within-subject transitions. Until it exists, every census row is one rater’s scored coordinate under a published protocol - a coordinate that is exactly regenerable and not yet convergent.

Self-measurement. The sharpest question the census invites is the one the authors must ask of themselves: how does this instrument measure its own author? The same way it measures everything else, and no other way - the authors’ systems (O-108 through O-111) are scored by the published rubric over the published evidence text, the scores ship in the released dataset, and anyone can regenerate them by running the released code. What the authors cannot claim is that the scores are independent of the scorer: the blinding study above shows exactly how rater-dependent such scores are, and the census’s highest row is flagged self-report for precisely this reason. The instrument’s answer to self-measurement is therefore not confidence but exposure - the scores are published, the dependency is measured and stated, and the ceiling dare applies to the authors’ own system before it applies to anyone else’s. A microscopic computation trace for all six author-system rows (O-53, O-107, O-108, O-109, O-110, O-111) - every op score, keyword hit, override, aggregation step, and the flaw ledger with containment status - ships as the companion attachment AUTHOR-ROWS-TRACE.md and regenerates by running trace_author_rows.py.

Falsifiability. The scale is falsifiable at its ceiling: with λ on [0,1] and σ bounded above, no system prices above K under either regime; a single system that prices above the reachable ceiling while passing all ten ordering families kills the functional form. Stated precisely: K bounds C only as φ → ∞; within the declared φ ∈ [0,1] domain the reachable ceiling is 1.753 C under the refit regime (1.214 C under the prior) - so the kill line in Hc units is anything above 3.01 Hc (refit) or 2.09 Hc (prior). That is the claim on offer - not that the census is right, but that it can be wrong in a stated way. Against the desiderata declared in Section 2: D1 four lanes across 431 rows; D2 a fifteen-operation rubric computable by hand; D3 every anchor external or declared; D4 the ceiling and the ten families; D5 the trace - five of five by design, with the mapping stipulations (D3) and scorer-dependence (D5) as the open wounds inside the passing grades.

The floor, defined. The artefact zero-floor (max C over the 27 zero-constrained rows) is a property of the mapper’s baseline for rows declared to have no reportable interior - not a formula-imposed minimum. Brain death (H-01, a measured V-tier row rather than a zero-constraint row) prices below it, 0.047 C, which is consistent: the constraint set bounds artefact rows, while instrumented clinical rows are fitted like any other.

The emergent-state rows. Mania (1.77 Hc), ecstatic temporal-lobe seizure (1.83), and PTSD flashback (1.57) price above the awake adult (1.72). This is emergent output of the rubric - elevated ops plus intact integration - and it is defended here rather than hidden: the instrument prices measured information-processing intensity, not the worth or quality of a state, and it places no normative weight on the ordering. A clinician’s objection (“mania is not ‘more conscious’”) conflates valuation with measurement; the paper claims only the latter. Similarly, preserved-architecture rows outrank lived-awareness rows (blindsight 0.75 > minimally conscious state 0.60 > cognitive-motor dissociation 0.47): the rubric counts integration substrate, and locked-in-class patients are expected to regain full pricing on any signal that restores interaction - the instrument is built to be corrected by exactly that evidence.

Open tests. The released pipeline makes six tests runnable by anyone, without the authors: (T1) substitute any alternative benchmark-to-C mapping and refit - the raw percentiles ship; (T2) blind re-score the released 20-row sample with additional raters and report agreement; (T3) run the within-subject transition design on any willing participant through the released code; (T4) attack the ceiling with a system that prices above K while satisfying the orderings; (T5) add census rows and check whether the families still pass; (T6) replicate the rig anchors independently. Each ships with its receipt chain.

Resolution. The census is coarse by construction: the 431 rows carry 101 distinct Hc values, and the S lane (argument, literature and edge cases with no measured phi) clusters at 0.64 Hc for 51 of its 80 rows - the keyword mapper’s binning is visible in the output and is disclosed rather than hidden. Effective resolution: rows within ±0.03 Hc of each other should be read as tied. Two near-duplicate constructs scored in different lane contexts (honeybee swarm O-94 0.60 vs honeybee colony S-123 0.80; ant colony O-93 0.60 vs superorganism S-124 0.74) are listed separately as lane-context variants pending reconciliation.

Related Work

Four research lines approach comparative consciousness measurement without reaching it, and together they mark the quadrant this paper occupies. The Sentience Quotient (Freitas 1979) reduces a system to a single scalar, log10 of bits processed per second per kilogram; it orders processors across any substrate but cannot see state - an awake and an anaesthetized brain carry identical SQ because the hardware does not change, and a sufficiently efficient unconscious lattice outscores both. Efficiency is not consciousness; state-dependence is exactly the dimension the gate exists to capture.

The Morphospace of Consciousness (Arsiwalla and Verschure 2018) is the nearest conceptual ancestor: a three-axis complexity space (autonomous, cognitive, social) placing biological and synthetic systems in one picture. A morphospace locates systems; it does not measure them. Its placements are unconstrained by external anchors, carry no fitted function, no preregistered orderings, and no falsification clause - positions in the space are assertions wearing coordinates. The present instrument pins every coordinate to external instruments and publishes its own death condition.

The most recent neighbour (Just aware enough, 2026, arXiv:2601.14901) evaluates deflationary awareness profiles across artificial systems under four desiderata, explicitly declining consciousness as the target. The restraint is shared; the scope is not. Profiles are artificial-only and do not order, so the cross-system comparison question - more or less than what, and anchored to what reference class? - remains unanswered, and artificial scores uncalibrated against the only known conscious systems inherit that gap. Measuring all four lanes against clinical instruments is what makes the artificial lane interpretable.

Finally, the Integrated-Information import class (Phi scores computed for transformer architectures; IIT-reinforcement training proposals) inherits both the computational infeasibility of exact Phi at scale and the field’s contested reception of IIT, while lacking clinical anchoring for its numbers. The present framework borrows nothing from Phi: its fifteen-operation rubric is computable by hand, and its anchors are external instruments, not theory-derived scores. To the authors’ knowledge, no published work combines a fitted gate function, clinical anchors, an evidence-tiered cross-domain census, preregistered ordering families, a falsifiable ceiling, and a self-measurement trace. The four lines above are, respectively, the scalar, the space, the profile, and the import; the quadrant they leave open is a fitted, anchored, falsifiable scale.

A note on the scope of this claim. The prior-art survey behind this section ran at search-engine depth with full-text reads of the nearest neighbours’ abstracts and texts; it was not a systematic Scopus or Web-of-Science review, and the Morphospace full text deserves an end-to-end read before any reviewer-facing novelty memo. The authors flag the boundary of the search for the same reason they flag every other limitation in this paper: a novelty claim is a claim, and the reader is entitled to know how far the shovel reached.

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Statements and Declarations

Funding: none. Competing interests: the authors operates a commercial enterprise in the artificial-intelligence sector; no product of that enterprise is scored as evidence in the fit; the AI-stack anchors come from the authors’s own research rig and are flagged as requiring independent replication. Use of AI: an AI reasoning system assisted with literature retrieval, numerical checking, drafting, and adversarial review under the authors’s direction; the human author verified all sources and calculations and accepts responsibility for the content. The AI system is not an author (COPE guidance, 13 February 2023). Data availability: census tables (both fits), rubric script, fitting and audit code, and all JSON receipts are supplied as supplementary material; every number in this paper regenerates from them.