Artian Rotor-to-Wavefunction Projection Theorem: A Conditional QTT Recovery of the Schrödinger Equation, the A6 Bounded-Generator Gate, and the Macroscopic-Ceiling No-Go

@misc{ali2026artian,
  title = {{Artian Rotor-to-Wavefunction Projection Theorem: A Conditional QTT Recovery of the Schrödinger Equation, the A6 Bounded-Generator Gate, and the Macroscopic-Ceiling No-Go}},
  author = {Attar Ali},
  howpublished = {Zenodo (CERN European Organization for Nuclear Research)},
  year = {2026},
  month = may,
  doi = {10.5281/zenodo.20119662},
  url = {https://doi.org/10.5281/zenodo.20119662},
  note = {CC BY},
}

TY  - UNPB
TI  - Artian Rotor-to-Wavefunction Projection Theorem: A Conditional QTT Recovery of the Schrödinger Equation, the A6 Bounded-Generator Gate, and the Macroscopic-Ceiling No-Go
AU  - Attar Ali
PY  - 2026
DA  - 2026/05/11
PB  - Zenodo (CERN European Organization for Nuclear Research)
DO  - 10.5281/zenodo.20119662
UR  - https://doi.org/10.5281/zenodo.20119662
AB  - From Rotor to Wavefunction: How Schrödinger's Cat Is Gone Version: 1.3 Concept DOI: 10.5281/zenodo.20119662 Version DOI: 10.5281/zenodo.20119663 Author: Ali Attar Website: quantumtraction.org Corpus category: Action, Feynman, path integrals, and quantum foundations The Schrödinger equation has been the workhorse of quantum mechanics for ninety-nine years. Its empirical reach is enormous; its status is that of a postulate. Every textbook formulation introduces iℏ ∂_τ Ψ = HΨ as a starting equation, with no derivation from a deeper layer, no upper bound on the mass of coherent solutions, and regularization schemes (cutoffs, dimensional regularization, counter-terms) added by hand whenever the formalism overcounts modes. This paper derives the Schrödinger equation as a theorem within Quantum Traction Theory (QTT), with three structurally distinctive features that standard quantum mechanics lacks. First, the textbook wavefunction Ψ(x, τ) is not primitive but a projection from a discrete address-indexed real-dial ledger ρ((x,n) | T) ∈ ℝ²_J at substrate time T. Second, the per-address action throughput is bounded by axiom A6, and the modular bundle closes at 2π by axiom A7, providing a physical capacity ceiling that replaces ad hoc UV regularization. A worked vacuum-energy-density example shows where the A6 bound caps the standard divergent integral, yielding the finite substrate-level density ρ* = ℏc/(4π ℓ̃⁴). Third, and most consequentially, the same capacity bounds impose a hard macroscopic-superposition prohibition: no single coherent quantum system of total mass exceeding the Planck mass m_P = √(ℏc/G) ≈ 2.176 × 10⁻⁸ kg ≈ 21.76 μg can sustain a superposition of macroscopically distinct outcomes. The Schrödinger-cat thought experiment is empirically forbidden in QTT, not merely difficult to prepare: a domestic cat is roughly 2 × 10⁷ times heavier than the QTT ceiling. The cat is gone, by axiom, as a structural consequence of A6 and A7. The derivation proceeds in three steps. First, local rotor transport at each address (x, n) takes the canonical first-order form Jℏ ∂_T ρ = Hρ, where J is the real quarter-turn generator with J² = −I. The first-order time derivative is forced by the one-parameter-group structure of the substrate update on single-time states (Stone's theorem); the A6 capacity bound separately bounds the generator's operator norm. Second, the address-projection map Ψ(x, τ) = N_Ψ^(-1/2) Σ_n ρ((x, n) | T(τ)) commutes with H for address-blind Hamiltonians. Third, the two-clock relation dτ = N dT converts the substrate equation into laboratory form iℏ ∂_τ Ψ = HΨ, with i identified as the complex packaging of J. The master QTT-Schrödinger equation displays four capacity constraints alongside the dynamical equation: (i) the A6 action-throughput bound, (ii) the A6 energy ceiling, (iii) the A7 modular bundle closure, and (iv) the macroscopic mass ceiling at m_P. Standard QM carries none of these. The same axiom base delivers the Klein–Gordon and Dirac equations by the same projection method, with the reconciliation of first-order non-relativistic and second-order relativistic forms explained via the doubled phase space. The substrate is shared with the Born-rule derivation (companion paper, doi:10.5281/zenodo.20118242 and the measurement-problem dissolution (companion paper, doi:10.5281/zenodo.20114403 Together, the three papers address the three foundational postulates of standard quantum mechanics from one substrate ontology with one axiom base. Conditional on QTT axioms A1, A4, A5, A6, A7, the Schrödinger equation ceases to be a founding postulate of quantum mechanics; it becomes a derived projection law of a capacity-bounded substrate with a sharp, parameter-free, falsifiable upper mass limit on coherent quantum states. No fitted parameter, no tunable cutoff, no environment cut, and no two-clock cos(π/8) input appears in the proof. Falsifier: a single demonstrated quantum superposition involving a coherent system of mass greater than m_P ≈ 21.76 μg, in decoherence-free conditions, would falsify the framework. This is the strongest empirical statement the QTT Schrödinger equation makes and is the cleanest place to falsify it. The QTT prediction is a sharp ceiling at m_P, distinguishing it from GRW and CSL (gradual suppression with fitted parameters) and from Diósi–Penrose gravitational collapse (threshold near 10⁻¹⁷ kg). Current matter-wave-interferometry experiments (fullerenes, oligo-porphyrins, proposed nanospheres up to ~10⁻¹⁷ kg) lie many orders of magnitude below the QTT ceiling and are consistent with the framework; the frontier (MAQRO, OTIMA) will approach the ceiling over the coming decade. The paper corresponds to and elaborates §20.40–§20.41 of the framework manuscript (doi:10.5281/zenodo.17527179, where equations (D1)–(D5) state the substrate transport rule and assert the laboratory Schrödinger projection. The present paper makes that material standalone and referee-ready by supplying the full Stone-type group argument for the first-order substrate generator, the real-dial-to-complex isomorphism explicitly, the substrate Hamiltonian uniquely from A4 minimal coupling plus J-norm conservation, the address-projection commutation as a separate theorem, and the A6/A7 capacity ceiling as a built-in UV regulator with a worked vacuum-energy-density example. Status: conditional theorem inside a QTT-axiomatic framework, not a claim that the axioms are established physics yet. The paper claims that, conditional on A1, A4, A5, A6, A7, the Schrödinger equation is forced as a projection theorem with sharp empirical bounds, rather than postulated. Main status labels: GREEN: Σ_ Audit and claim scope: Concept DOI is the stable citation target for this research family. Version DOI and Zenodo record ID identify this exact public release for reconstruction. This description is a record-level guide; the paper itself controls theorem status, assumptions, and falsifiers. Related QTT anchors:…
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