Theory of Information Memory (TMI): Physical Memory, Gravitation and the Conditional Energy-Memory Coupling

Theory of Information Memory (TMI) — Preprint 1.2, RC6.6 (v15) Author and originator: Alexander Sheridan Figus MacLeod, independent researcher. Research question and objective. TMI asks whether a gravitating physical sector could carry accessible records of its history and whether such records might be linked to energy response and temporal order. Its founding conjecture is that cosmological dark matter might itself be a primordial quantum fluid (PQF/FQP), rather than a substance contained within such a fluid. This identification remains unverified. The programme retains general relativity in 3+1 dimensions and seeks an independently testable prediction beyond conventional dark-sector and memory-bearing models. Founding hypotheses. The historical proposal T = (L, W) distinguishes operational duration L from a putative informational 'width' W, not an extra spacetime coordinate. The exploratory expression E = mc²W asks whether a separately defined sector property can affect a probe's energy. With measured invariant rest mass, however, E = mc² requires W = 1. No universal energy–memory law is claimed. Different predictive, causal-record, readout and effective-energy definitions of W remain distinct and have not been unified. Mathematical work and internal checks. RC6.6 preserves a GR-compatible illustrative two-scalar construction. Eliminating an internal classical mode gives an exact causal Volterra history kernel in the reduced equation. A separately stipulated scalar-dependent probe mass, m_eff(χ) = m₀ exp(βχ/q*), yields the conditional PM01-P1 energy–history identity in the passive-probe limit; finite probe backreaction requires an additional retarded source term and a corrected conserved energy budget. The β = 0 and g = 0 controls show that history dependence and energy modulation do not imply one another. Derivations, solver comparisons, convergence checks and reproducibility scripts test these models internally. They do not establish dark matter, a persistent readable record, emergent time or a new universal law. TMI–YM–01: mass gap and spectral memory. A proposed dark Yang–Mills sector with a positive physical gap Δ_D motivates the conditional Euclidean correlator C_O(τ) = ∫ exp(−Eτ/ħ) dμ_O(E). Under stated positivity and spectral assumptions, a gap bounds its Euclidean decay, but does not determine a unique real-time response or an intrinsic memory lifetime. Two explicit spectra sharing the same threshold produce different causal sine responses. An operator threshold need not equal the global gap; possible gapless Goldstone/phonon channels require a separately specified phase. This research does not solve the Clay Yang–Mills existence and mass-gap problem. TMI–YM–02: an explicit gauge interaction. The preprint defines a finite-regulator SU(N) lattice gauge sector, a gauge-invariant smeared plaquette observable O_f and a weak detector interaction H_int = −λqO_f. Linear response gives an operator-resolved retarded history kernel K_YM(t) = −λ²χ_+(t), with its Lehmann spectral representation. If the coupled operator has a positive excitation threshold Δ_f, weak-probe absorption at zero temperature has a conditional onset at ω = Δ_f/ħ. Spectral examples and SU(2) gauge-invariance checks are reproducible toy calculations; the actual non-Abelian continuum spectral weights have not been computed. This gap-dependent onset is not distinctive of TMI: a conventional gauge model with the same Hamiltonian, state, coupling and detector predicts the same response. What remains to be demonstrated. TMI requires (i) a consistent, stable and covariant dark-sector microphysics with cosmological constraints; (ii) a controlled write–retain–read experiment; (iii) an independent measurable definition of W and any derived energy coupling; (iv) a complete gauge-spectrum and detector calculation beyond the regulator; and (v) a preregistered differential prediction that survives comparison with conventional gauge, scalar and non-Markovian models. Null and inconclusive outcomes are part of the proposed testing programme. A common origin of memory and temporal order remains an open conjecture; current models already assume time. Human research and AI disclosure. Alexander Sheridan Figus MacLeod originated and developed the founding questions, made key conceptual corrections, directed the research, reports study of primary literature and review of the manuscript and equations, and retains responsibility and release approval. He designed Protocol S.O.P.H.I.A. (Systematic Operational Protocol for Hypothesis Investigation and Assessment) to make human–AI research traceable, critically testable and accountable. Sophia denotes the ChatGPT-based research assistant, not an independently trained or autonomous scientific author. ChatGPT/GPT-6 (OpenAI) substantially assisted in literature comparison, modelling, mathematical exposition, code, numerical checks, adversarial review and drafting; this assistance is disclosed rather than presented as independent validation. Status and materials. AI-assisted exploratory, non-peer-reviewed preprint; no original TMI experiment, cosmological fit, confirmed dark-matter mechanism or uniquely TMI-specific prediction is claimed. The deposit includes the full RC6.6 v15 preprint, this updated description and a reproducibility archive (scripts, model data, figures, source files and integrity records). Publication records a research version, not scientific endorsement. Original text and documentation are marked CC BY-NC 4.0 and original project software PolyForm Noncommercial 1.0.0, subject to the rights actually held and applicable third-party licences.