General Transfer-of-State Model (GTOSM): A Minimum Structural Reconstruction of Quantum Mechanics, Gravitation, and Cosmology

GTOSM is a discrete lattice framework with tick evolution that declares a closed primitive update law for identity persistence, constraint history, and forced constraint replacement. Space is an immutable lattice topology `𝓛` (spacing `ℓ∗`) ; global time is a tick index `n` (duration `τ∗`, with bookkeeping time `t = nτ∗` and propagation bound `c = ℓ∗/τ∗`). Fermionic identities are coherence domains: connected supports defined by exclusive occupancy `O (j; x, n) ∈ 0, 1`. Domain boundaries carry a bias mask `C (j; x, ê, n) ∈ 0, 1` that enforces corridor forbiddance on selected boundary corridors. Each tick, each domain selects one attempted boundary corridor `a (j;n) ` and draws a corridor-local non-optimal indicator `η (j; x, ê, n) `. In the optimal regime `η=0`, completion is stochastic with probability `P (h=1) =f (x, n) ·Wₑff (j; x, ê, n) ` where `Wₑff = Wₗattice· (1−C) ` and `f` is the externally throttled hit fraction. In non‑optimal events `η=1`, completion is forced, the active bias mask is replaced, and the associated constraint-change count produces an integer number of dimensional adjustments `ΔNₐdj`, releasing energy `ΔE = ΔNₐdj 𝒟`. Electron calibration fixes the unit bridge `mₑ c² = Nₑ 𝒟`. Mass-demand `MD` (arising from matter density, fermionic lattice-site consumption and exported bias deposition) modulates `f` and provides the gravitational dictionary; in weak‑field regimes the operational proper‑time map is `dτ = f dt`. Standard continuum formalisms (quantum, gauge‑effective, relativistic, thermodynamic, classical) appear only as dictionaries on declared coarse windows `Ωcg`, under explicit regime hypotheses and error control. The wavefunction `ψ` is not a primitive: it is the `η=0` (pre‑measurement) coarse ledger that represents admissibility-and-phase bookkeeping and supports unitary tick updates in Schrödinger-valid regimes. Measurement is a physical event class (a fermionic non‑optimal transfer) and is specified operationally by QMTF measurement declarations ` (Ω, R∗, T∗, Δx, Δt, εdisc) `. Three falsification-class predictions are stated in QMTF form: (I) sub‑threshold excitation after UV preparation via constraint‑discharge triggering; (II) absence of gravity‑mediated entanglement in gravity‑only entanglement‑witness protocols; (III) quantum‑eraser conditional fringes only when the required postselection record is physically available without cross‑run contamination (no retrocausal reading). Version note (v2) This version incorporates editorial clarifications and presentation corrections relative to the initial public release. These include: correction of Unicode symbol rendering across formats, explicit naming of operational elements in experimental descriptions (e. g. , signal, idler, detector interfaces, and shared interaction surfaces), and minor wording refinements to prevent misinterpretation of scope or intent. No primitives, structural rules, regime reconstructions, or declared predictions of GTOSM have been modified. Version note (v3) This version marks the consolidation of GTOSM into a fully formal, rule-declared mathematical framework. Narrative, motivational, and explanatory material has been removed or relocated to companion papers, and the manuscript is now presented strictly as a closed system of primitives, definitions, lemmas, and update rules. Key changes include: explicit lemma-level closure of lattice site retirement and generation, formal quantization of dimensional adjustment and bosonic excitation, and a fully operational specification of measurement and gravitational dictionaries. All symbols, units, and update rules have been synchronized for internal consistency. No new empirical claims or predictions are introduced. Previously stated predictions are unchanged and are now expressed uniformly in QMTF form. This version is intended as the canonical target for formal mathematical and internal-consistency audit.