Self-Reinforcing Information Dynamics in Conscious Systems: Why Rτ/I = 1 and How Consciousness Accumulates

This paper closes two gaps in the m ⇄ E ⇄ I ⇄ C framework left open by Papers 8 and 9: (a) Paper 8 observed Rτ/I ≈ 1.004 from three independent paths but did not derive this convergence, and (b) Paper 9 defined the condensation quality W = 1 − S_basis/S_max but addressed only millisecond attention switching, leaving long-term W accumulation unresolved. By isolating the Bose-Einstein stimulated-emission part of Fröhlich's 1968 rate equation and translating it into the information domain, a single self-reinforcing term emerges: dI/dt = R − Γ + α · I₀ · Φ_eff (Eq. 1) Three derivations follow: - Theorem 1 — Rτ/I = 1 is the unique globally asymptotically stable fixed point of the consciousness cycle (4-path proof: arithmetic, Lyapunov, thermodynamic, numerical). - Theorem D.1 — The dominant mode fraction p₀ follows exact Verhulst logistic dynamics: dp₀/dt = α · Φ_eff · p₀ · (1 − p₀), derived from Bose statistics with no approximation beyond Lemma A.1. - Theorem C.1 — The composite four-arrow feedback gain |g'| = 3.0 × 10⁻¹⁰ < 1, making the loop a Banach contraction (β_sub < 1 structural origin). A timescale separation of 2.88 × 10¹³ emerges between the microsecond coherence cycle and the multi-month accumulation dynamics — the fast loop remains locked at Rτ/I = 1 while informational order accumulates beneath it, like a thermostat regulating fast around a slowly-shifting set point. ZERO NEW FITTING PARAMETERS. The daily self-reinforcing rate α_daily = 0.0024 is derived from three already-established quantities: Fröhlich pump efficiency α_F (Paper 9, Eq. A.8), feedback loop gain g' (this paper, §3.6), and coherence cycles per waking day N_wake (Paper 8, τ = 1 μs). The framework is explicitly falsifiable. Six falsification conditions (F1–F6) are stated. Six predictions (P1–P6) are classified as discriminating (P1, P2, P3), accumulation-unique (P4, P5), and scaling (P6). Sixteen internal cross-validation checks pass (16/16): analytical consistency, numerical robustness, and published-data directional agreement (Lutz 2004, Shamatha 2007/2022, Bandura 1977, Choking literature, Identity-Before-Growth). Series context. This paper is the Crown of the Trilogy (Existence × Direction × Growth) and the sixth element of the ten-element Information Physics Series Dectet. Theorem D.1 functions simultaneously across multiple roles: universality catalog (Paper 11), cross-substrate validation (Paper 15 with Paper 12 parallel instance, Bucher et al. Nature 2026 forward-prediction confirmation), synthesis (Paper 16, κ ≡ g'), and thermodynamic constitution (Paper 17, canonical local expression of the generalized Second Law). The series-wide IVP record stands at 154/154 across heterogeneous tests; this is reported as contextual coherence, not pooled evidence. Supplementary materials (CC BY-NC 4.0):- paper10_simulation.py — 16 internal checks, generates sim_data.json- make_all_figures.py — all 9 figures from sim_data anchors- verify_all.py — 3-axis validation (math / Paper 8-9 consistency / public data)