Quantum phenomenology from a classical integer automaton: an emergent Schrödinger sector, a measurable collapse law, exact exchange statistics, CHSH violation without randomness, and a surviving isotropy no-go

A single bit-exactly reversible, integer-valued lattice automaton in which a broad range of quantum phenomenology arises as measurable, checksum-reproducible behaviour of one classical substrate. A second-order Frenkel–Kontorova / sine-Gordon integer automaton supports localized particles with additive mass towers (1 : 2 : 3 and 1 : 4 : 9), emergent Lorentz contraction (fitted c to 0.3 %), and a token-accounted local-time sector with a general-relativity-like time well (ω ∝ n to 0.06 %). Within it, a first-order Visscher–Feistel integer Schrödinger sector is realized in pure integer arithmetic with exact bit-reversibility. The integer/floor-reversible lifting of the Visscher scheme was already noted by Fredkin (1999) and Martin-Delgado (2004); the contribution here is its first computationally tested and validated realization — against exact dispersion, group velocity and envelope reduction — embedded in an interacting substrate. Main results: Emergence bridge. The narrow-band envelope of the classical automaton obeys the Schrödinger equation with an effective mass fixed by the curvature of the exact discrete dispersion (group velocity to ≤0.2 %, curvature to ≤2 %). The dimensionless spreading of two microscopically different substrates collapses onto the single universal law √(1+τ²). Deterministic quantum statistics. Bohmian tracers reproduce double-slit single-object interference (p < 10⁻⁴), with trajectories matching the weak-measurement reconstruction of Kocsis et al. (2011). Bell / CHSH. A value of S = 2.79 from position-valued outcomes with a no-signalling control (0.3 %), via explicitly nonlocal guidance in configuration space. Measurement. A measurable Gaussian collapse law (R² = 0.997); a quantum eraser with literal bit-reversible un-measurement of the entire measurement chain; Pauli exclusion as a bit-conserved invariant; and relaxation to the Born rule with a reversible arrow of time. Surviving the isotropy no-go, and a falsifiable prediction (new in v2). On the live integer engine, velocity anisotropy vanishes as k² in the infrared with first-principles coefficients in both 2D and 3D (agreement ≈ 1 %) — rotational isotropy emerges as an infrared fixed point, meeting the sharpest no-go every lattice candidate faces. From the same structure follows a concrete, quadratically Planck-suppressed dispersion prediction (δγ,2 ≈ 2×10−40 GeV−2, subluminal), lying only ~50× below the tightest ultra-high-energy cosmic-ray bound — the programme's first falsifiable departure from standard QM/GR. Individual phenomena have known precedents — double-slit Bohmian trajectories (Philippidis, Dewdney integer lifting Fredkin 1999, Martin-Delgado 2004) — and are framed accordingly. The contribution is their tested, validated realization on one exactly reproducible integer substrate, several genuinely new exact constructions (tested integer bit-reversible Schrödinger sector; literal bit-exact un-measurement; exchange statistics as a bit-conserved invariant; two-substrate universal collapse; measured lattice isotropy with a Planck-scale dispersion prediction), and a pre-registered, falsification-first methodology (criteria committed to version control before each run; fourteen self-retractions on record). This is an existence result, strengthened by a survived no-go and a falsifiable prediction — not a claim that our universe is this automaton (that step requires a prediction to pass experiment): a fully classical, deterministic, reversible integer computation can carry quantum phenomenology, quantitatively and reproducibly, and this substrate meets a no-go every discrete candidate must survive. Preprint v2 (self-contained; bibliographic audit completed against arXiv/DOI sources). Code, pre-registered gates, per-run reports and figures are included in this archive. Produced in an AI-assisted workflow (Anthropic Claude) under the author's direction; all pre-registration and interpretation is on record in the version history.