A companion paper predicted a two-step quantum–classical threshold at 13.1–22.6 μg from a close-packed vacuum lattice, resting on a stated hypothesis (P3): the lattice sustains a coherent mass excitation only while it can resolve the excitation's Compton wavelength. Here we derive as much of that structure as the lattice's own error-correcting code permits, working exactly on the [[3L_s^3, 2L_s^3+2, 3]] CSS family. Results: (1) an exact dephasing law — the vacuum code's own syndrome extraction dephases center-of-mass superpositions of edge-supported excitations at a rate set by the weight variance of the stabilizer group on the excitation's support; (2) a revival dichotomy theorem — at clock phase π per cycle, coherence is exactly 1 or exactly 0, decided by a one-line kernel criterion; (3) exact locality and composite laws — the composite clock runs at total mass because rest energies add, and dephasing is exactly additive beyond contact range, with a subadditive co-monitoring correction at contact; (4) a tracking band, conditional on one isolated dynamical assumption: if passive verification gives way to active checking at phase aliasing, the crossover spans m_alias = h/(8Lc) = 10.3 μg to m_wrap = h/(4Lc) = 20.5 μg — a cadence-derived band that the geometric window 13.1–22.6 μg overlaps without coinciding, so two independently constructed mechanisms select the same narrow microgram regime; and (5) the calibration foundation — the vacuum's entanglement obeys an exact area law on flat cuts, and for ball regions the exactly derived staircase factor of 3/2 is numerically compensated by inter-facet correlations to 10–15% at the tested sizes, with exactness of the compensation conjectured. What is not derived is stated with equal care: the existence of the passive-to-active transition is postulated, not derived, and the precise geometric endpoints and their √3 ratio remain inputs. Every claim carries a status tag.
A companion paper predicted a two-step quantum–classical threshold at 13.1–22.6 μg from a close-packed vacuum lattice, resting on a stated hypothesis (P3): the lattice sustains a coherent mass excitation only while it can resolve the excitation's Compton wavelength. Here we derive as much of that structure as the lattice's own error-correcting code permits, working exactly on the [[3L_s^3, 2L_s^3+2, 3]] CSS family. Results: (1) an exact dephasing law — the vacuum code's own syndrome extraction dephases center-of-mass superpositions of edge-supported excitations at a rate set by the weight variance of the stabilizer group on the excitation's support; (2) a revival dichotomy theorem — at clock phase π per cycle, coherence is exactly 1 or exactly 0, decided by a one-line kernel criterion; (3) exact locality and composite laws — the composite clock runs at total mass because rest energies add, and dephasing is exactly additive beyond contact range, with a subadditive co-monitoring correction at contact; (4) a tracking band, conditional on one isolated dynamical assumption: if passive verification gives way to active checking at phase aliasing, the crossover spans m_alias = h/(8Lc) = 10.3 μg to m_wrap = h/(4Lc) = 20.5 μg — a cadence-derived band that the geometric window 13.1–22.6 μg overlaps without coinciding, so two independently constructed mechanisms select the same narrow microgram regime; and (5) the calibration foundation — the vacuum's entanglement obeys an exact area law on flat cuts, and for ball regions the exactly derived staircase factor of 3/2 is numerically compensated by inter-facet correlations to 10–15% at the tested sizes, with exactness of the compensation conjectured. What is not derived is stated with equal care: the existence of the passive-to-active transition is postulated, not derived, and the precise geometric endpoints and their √3 ratio remain inputs. Every claim carries a status tag.
We model the vacuum as a discrete face-centered-cubic (K=12) tensor network with Bell-pair bonds and use it to predict a two-step quantum-to-classical threshold for macroscopic center-of-mass superpositions. A reversible dispersive deformation of the center-of-mass mode sets in at msoft≈13.1μg, and coherence becomes geometrically unsustainable at mhard≈22.6μg. The two scales are separated by the exact, parameter-free ratio 3, fixed by the edge-to-circumradius ratio of the cuboctahedral triangular face. Gravitational-collapse models predict a single scale of the same order, so the distinctive, falsifiable content is the two-step structure and the exact 3 separation, testable by a mass scan across the window; the recent 16.2μg cat-state oscillator of Bild et al. falls between the thresholds, where coherence is not ruled out. The absolute window depends on the bond length L=4ln2ℓP≈1.665ℓP, fixed by one calibration against the Bekenstein–Hawking area law. This calibration and the Compton representability hypothesis—that a mass excitation remains coherent only while its reduced Compton wavelength is resolvable by the lattice—are stated model inputs rather than derivations, motivated by the Compton frequency internal clock of massive excitations, the mass cutoff generic to lattice-regularized field theories, and the total-mass dependence observed in composite-object interferometry. Open problems are stated explicitly.
A model of the vacuum as a face-centered-cubic lattice predicts a two-step quantum–classical threshold, at 13.1 and 22.6 µg, from the hypothesis that a center-of-mass excitation stays coherent only while its reduced Compton wavelength is resolvable by the lattice. Collapse models also limit macroscopic coherence, so the two must be told apart by more than a scale. We derive three discriminators from the model's postulates and compute the counterpart in Diósi–Penrose collapse and in continuous spontaneous localization (CSL). The thresholds depend on total mass alone, while both collapse models depend on density. Below 13.1 µg the model predicts no intrinsic decoherence, where collapse takes 1 s for Diósi–Penrose and about a microsecond for CSL at its experimental bound, for 10⁻¹⁵ kg over 1 µm. The model predicts no measurable heating; read as position localization, its own rate scale would exceed the LISA Pathfinder bound by 66 orders of magnitude, so coherence loss above the threshold must be dephasing in the energy basis. If its effective mode mass is the relevant mass, a 16.2 µg mechanical cat state then bounds the irreversible coupling at 38 orders below its natural scale. A worked levitated-particle example and a public script complete the analysis.
The loophole-free Bell experiments recognized by the 2022 Nobel Prize established that entangled correlations are real, irreducible, and available across kilometers. In the Selection–Stitch Model the vacuum is a face-centered-cubic lattice grown by crystallization, carrying a stabilizer code, with spatial adjacency emergent from the network. Within the model, the natural vacuum is hypothesized to be an FCC interaction network built from entanglement bonds, whose microscopic verification dynamics produces the observed propagation speed c. A single entanglement provides no causal shortcut, only entanglement correlations — but can an FCC structure of such bonds, assembled into the model's full machinery, become one? We formulate this question without identifying entanglement with interaction. Three graphs are separated: an embedding graph, a correlation graph, and a Hamiltonian interaction graph. We prove that pre-shared Bell pairs, local operations, and unconditioned stabilizer correction cannot transmit a controllable signal; hence an entangled edge is not by itself a spacetime edge. We distinguish the necessary conditions for a signalling claim — an autonomous response with closed causal accounting — from the additional persistence, robustness, and composability conditions required to interpret a collection of dynamical edges as synthetic geometry. A minimal switchable-edge Hamiltonian makes the new assumption explicit and yields an exact influence time, while a Lieb–Robinson analysis shows that a macroscopic shortcut follows only after the interaction edge has been physically established. An FCC network is shown to provide a homogeneous coordination-12 graph and an isotropic leading-order continuum operator, but it does not evade the no-signalling obstruction. The result is conditional and experimentally sharp: ordinary entanglement predicts a null result, whereas a genuine SSM adjacency transition predicts a distance-independent dynamical response. No faster-than-light mechanism is claimed within standard quantum theory.
For decades, theoretical physics has struggled to discretize spacetime without inadvertently breaking Lorentz invariance [1,2]. Building upon the Selection-Stitch Model (SSM) [3], we model the vacuum as an emergent Face-Centered Cubic (FCC, K = 12) tensor network. In this unified framework, we demonstrate that the foun- dational scales of both relativity and quantum mechanics emerge naturally from the strict geometric limits of this saturated lattice. First, we show that the macroscopic speed of light (c) is simply a geometric renormalization of the underlying lattice hopping speed (c = 4vlattice). Second, rather than treating the Planck scale as an arbitrary mathematical cutoff, we derive the fundamental lattice spacing a≈0.77lP as the exact limit where the vacuum’s elastic energy density strikes the absolute a/√3 kinematic exclusion limit (the metric wall) [4]. Third, by treating the vacuum as a Chiral Cosserat continuum, we explicitly derive the complex unit i and the Schr¨odinger equation from lattice gyroscopics. Finally, by intersecting this wave mechanics with the metric wall, we predict a strictly falsifiable, two-step decoher- ence limit for macroscopic superposition: a soft onset of Schr¨odinger breakdown at msoft ≈28µg, and an absolute structural hard cutoff at mhard = √3msoft ≈49µg.
Self-Initiated Phase Re-Coherence (SIPR) asks whether an open quantum system can autonomously recover a phase-compatible state after perturbation through fixed system-environment dynamics, without measurement-conditioned feedback. The original SIPR v2.1.1 proposal used a two-bath pure-dephasing model and claimed a nearly universal recoherence threshold and a metastable plateau. Here the published coherence law is audited exactly. For dimensionless time u = Γt, frequency ratio r = ω_R/Γ, and structured-bath strength R = λ_R²/[γ_N Γ(1+r²)], transient growth of the coherence magnitude occurs if and only if r exp[-3π/(2r)] > 1 and R > [r exp(-3π/(2r)) - 1]⁻¹. The unique frequency threshold is r★ = 3.6441736716456…, while the asymptotic logarithmic decay rate remains -γ_N(1+R); therefore the original universal threshold and nonzero long-time plateau do not follow from the published equation. Two structural no-go results then delimit the microscopic programme. First, a Gaussian pure-dephasing channel can exhibit information backflow and partial revival but cannot selectively contract an arbitrary relative-phase error toward a prescribed phase. Second, a passive excitation-conserving single-pseudomode architecture that makes a Bell singlet dark also leaves the ground state stationary, preventing a unique global Bell attractor. These results redirect SIPR from passive revival toward a nonequilibrium, autonomous repair cycle inspired by biological kinetic proofreading. In the proposed network, phase mismatch populates a bright Bell sector, stationary hot resources lift bright and ground sectors into an auxiliary manifold, and a cold phase-selective decay deposits population into a target dark Bell state. The target terminates the cycle because all ideal repair operators annihilate it. The paper specifies the effective Lindblad network, local-detailed-balance constraints, uniqueness conditions, phase-activated repair current, thermodynamic ledger, pseudomode memory intervention, temporal-window analysis, comparator battery, and optional geometric and dynamical-criticality qualification layers. Loschmidt-amplitude or DQPT-like events are treated only as preregistered diagnostics, never as proof of SIPR by themselves. No simulation result is claimed. The contribution is an exact correction, two explicit no-go statements, and a falsifiable programme for deciding whether environment-powered quantum phase proofreading is merely known reservoir engineering or a distinct SIPR regime.