The manuscript advances a phase-theoretic formulation of consciousness by characterizing it as the ordered phase attained by a bounded physical system when its internal and external comparison ledger reaches a local minimum of comparison cost while sustaining stable self-reference, a phase-separated counterfactual channel, and coherent theta binding. The three central thresholds are operationalized without adjustable consciousness constants: the cost threshold equals the unit comparison threshold, the counterfactual threshold is fixed at the fifth self-reference rung, and the phase-locking threshold is the self-consistent ordered fraction of a ratio-coded boundary. Explicit numerical values are supplied as C_rec greater than or equal to 1, Z_cf equal to phi to the fifth power lying in the open interval from 11 to 12, PLV_crit equal to phi inverse approximately 0.618, and a saturation scale Theta_crit equal to phi to the 45th power marking the upper capacity regime. The proposal emphasizes that these thresholds are not metaphors but operational criteria, such that capacities are absent below them and phase transitions become available above them provided the boundary also occupies a local cost minimum. In Section 1 the claim sharpens the hard problem of consciousness by relocating the explanatory gap to the inhabitance posit within the comparison structure rather than positing an additional private extra atop physical states. Equation 4 introduces the relation C_rec of B equals kappa times A_grav of B, with a predicted prefactor kappa equal to 2.
The manuscript notes that a ledger-level derivation from reciprocal symmetry is anticipated but not executed in the present work, thereby rendering the associated mesoscopic prediction conditional upon completion of that bridge. The text tabulates the distinctions among algebraic structure, physical bridge assumptions, and empirical predictions to clarify the status of each component. The revised manuscript addresses the prior revision request by supplying in Section 4 a worked example on a rank-4 coupling graph. Synthetic phase offsets are assigned, bond-weighting values w_b are computed explicitly, the continuous Z is obtained as 2.5, and the ceiling is compared against phi to the fifth. One additional sentence notes that the offsets are chosen for illustration rather than drawn from measured data. This concrete half-page example demonstrates the bond-weighting procedure, cycle-basis definition, and ceiling discretization in action on an artificial graph. Five falsifiers are enumerated with concrete pre-registered rejection bands and matched controls. The theory fails if ordinary conscious access is observed in the absence of all three thresholds, if a system crosses all thresholds under controlled conditions yet exhibits no awareness signature, or if a single scalar field lacking a phase-separated memory channel passes history, counterfactual, and reflexivity tests. Additional falsifiers target the mesoscopic collapse prediction and the self-model scaling relation. Predictions are derived for theta phase locking, anesthesia transitions, counterfactual architecture, mesoscopic collapse, and self-model scaling, each tied to the operational thresholds.
The PLV_crit identification is explicitly labeled as a hypothesis supported by a mixture-model justification rather than a derived theorem. Assumptions include the absence of adjustable constants, the use of the golden ratio for self-similar scaling, and the requirement that the boundary achieve a local cost minimum for phase availability. The manuscript compares its approach to prior literature by providing explicit experimental protocols for EEG and MEG recordings, artificial dual-channel systems, and mesoscopic devices, thereby distinguishing the phase-transition account from frameworks that treat consciousness as an emergent add-on without specified thresholds or falsification routes. The separation of the algebraic core from the empirical hypotheses is presented in a tabulated format to facilitate independent assessment. The proof strategy relies on identifying the phase transition conditions from the cost geometry and topological charge without invoking external consciousness parameters. Regularity hypotheses include the stability of the self-reference loop and the coherence of theta binding across the binding cycle. Notation employs phi for the golden ratio throughout, with explicit interval notations for Z_cf. Comparison to prior work is implicit in the relocation of the explanatory gap and the provision of falsifiable protocols, which go beyond qualitative descriptions by supplying numerical thresholds and rejection criteria.