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
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: Main book concept DOI: 10.5281/zenodo.17527179 Corpus Tree row: quantumtraction.org/doi-map/#record-20119663 Blog Map row: quantumtraction.org/blog-map/#corpus-record-20119663 Lexicon: quantumtraction.org/lexicon/ Related QTT DOI (isSupplementTo): 10.5281/zenodo.17527179 Related QTT DOI (cites): 10.5281/zenodo.20114403 Related QTT DOI (cites): 10.5281/zenodo.20118242 Related QTT DOI (references): 10.5281/zenodo.19979594 Related QTT DOI (references): 10.5281/zenodo.19960813 Related QTT DOI (references): 10.5281/zenodo.19975260 Related QTT DOI (references): 10.5281/zenodo.20042421 Related QTT DOI (references): 10.5281/zenodo.20042612 Included files: qtt_schrodinger_v1_3.tex qtt_schrodinger_v1_3.pdf
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: Main book concept DOI: 10.5281/zenodo.17527179 Corpus Tree row: quantumtraction.org/doi-map/#record-20119663 Blog Map row: quantumtraction.org/blog-map/#corpus-record-20119663 Lexicon: quantumtraction.org/lexicon/ Related QTT DOI (isSupplementTo): 10.5281/zenodo.17527179 Related QTT DOI (cites): 10.5281/zenodo.20114403 Related QTT DOI (cites): 10.5281/zenodo.20118242 Related QTT DOI (references): 10.5281/zenodo.19979594 Related QTT DOI (references): 10.5281/zenodo.19960813 Related QTT DOI (references): 10.5281/zenodo.19975260 Related QTT DOI (references): 10.5281/zenodo.20042421 Related QTT DOI (references): 10.5281/zenodo.20042612 Included files: qtt_schrodinger_v1_3.tex qtt_schrodinger_v1_3.pdf
Hamilton's Principle, Feynman's Path Integral, and the Action Quantum h = 2πℏ as Capacity-Rotor Theorems: A Parameter-Free Derivation from QTT Axioms A1–A7U Version: 1.2 Concept DOI: 10.5281/zenodo.20098143 Version DOI: 10.5281/zenodo.20098144 Author: Ali Attar Website: quantumtraction.org Corpus category: Action, Feynman, path integrals, and quantum foundations Central result. This paper derives, from the axioms of Quantum Traction Theory (QTT) including the new A7U closure, three results that are usually treated as independent postulates of textbook physics: Hamilton's stationary-action principle (δS = 0) as the macroscopic shadow of dial coherence; Feynman's path integral 𝒜 = ∫𝒟x exp(JS/ℏ) as the continuum limit of capacity-bounded per-tick rotor kernels; The action quantum h = 2πℏ as the dial-revolution closure theorem, with the Planck–Einstein ET = h, the de Broglie pλ = h, the Bohr–Sommerfeld ∮p·dq = nh, and the magnetic-flux quantization qΦ = nh as immediate corollaries. No fitted parameter is introduced at any step. The physical primitive is a real two-component dial at each world-cell address, and a history contributes because it rotates that dial by an angle fixed by its action ledger, dθ = dStot/ℏ. The recovered mathematical condition is stationary action, not necessarily a minimum — minima, maxima, and saddle paths can all be stationary in the standard semiclassical sense. Position relative to Feynman. Feynman's path-integral construction postulates the unit-circle history phase eiS/ℏ and shows that classical mechanics is its stationary-phase limit. QTT does not weaken that result; it supplies its substrate justification and extends it. In the QTT reading the history weight is the unique real one-parameter group that simultaneously preserves dial norm (orthogonality), composes additively over concatenated histories, and closes after one full 2π of accumulated action. That group is SO(2), realized on the real dial as the J-rotor RJ(θ) = cos θ·I + sin θ·J with J² = −I. The complex shorthand eiθ and the real rotor RJ(θ) carry the same stationary-phase mathematics under the packaging J ↦ i; what QTT changes is the primitive. The path-integral weight is therefore not assumed in QTT — its real-rotor representative is derived. The Feynman iε prescription likewise becomes a substantive QTT statement: it is a real-dial tilt J·0+ selected by A1 causal time ordering and A6 capacity continuity. The action quantum as a closure theorem. Combining dθ = dS/ℏ (A4) with the dial periodicity θ ~ θ + 2π (A7) yields, with no further input, ΔSone revolution = ℏ·2π ≡ h. Planck's constant h is, in QTT, the action required to close one full dial circle, and ℏ is the action per radian. The Planck–Einstein, de Broglie, Bohr–Sommerfeld, and magnetic-flux-quantization rules then follow as direct readings of this closure on different time, space, phase-space-loop, and gauge-loop projections. QTT mechanism (axioms used). A1 supplies the Absolute Background Clock and the measured-time projection. A4 supplies the real dial and the quarter-turn generator J. A5 composes histories over world-cell addresses. A6 bounds energy, power, and action throughput per address (one ℏ per tick) and gives the history sum a physical capacity endpoint. A7 fixes the 2π modular closure of complete existence. A7U sharpens A7: the hidden complement of a visible subsystem is not arbitrary extra matter; it is the distributed visible share of the other co-members of the same complete bundle. The exact variational object is therefore the complete distributed Planck bundle, while the laboratory sees a reduced, locally accessible marginal. The explicit per-tick short-time kernel with Gaussian normalization and its complex-packaging form (§6.1). Theorem 1 — the continuum Feynman path integral as a QTT theorem (§6.3). Theorem 2 — the dial-revolution closure theorem h = 2πℏ (§7.1). Corollaries 1–4 — Planck–Einstein, de Broglie, Bohr–Sommerfeld, magnetic-flux quantization (§7.2). Theorem 4 — the Feynman propagator with the real-dial J·0+ prescription, replacing the standard iε contour-deformation argument with a substrate-derived causal tilt (§13). The WKB derivation of the Hamilton–Jacobi equation from the QTT Schrödinger shadow (§11.1). The Wilson-loop / gauge-holonomy reading with explicit Stokes-form and an Aharonov–Bohm derivation, plus a no-double-counting methodological warning (§12). The Wick-rotation status statement: Euclidean weights exp(−SE/ℏ) are computational tools, not the ontic QTT primitive (§14). The capacity-regularized covariant kernel 𝒦ℓ̃ = K(−ℓ̃² DJ⊤ DJ) as a substrate UV cutoff (§15). The dial-covariant Noether current jJμ for fields (§16). Three new falsifiers: action-quantum closure failure, wrong-tilt Feynman prescription, unitary path-integral measure violation. The axioms, the existing v1.2 derivations, and the A7U content are unchanged. No new fitted parameter is introduced; every new equation is forced by the same dθ = dS/ℏ plus 2π closure that already supports v1.2. Cross-paper coherence. The visible-share count Nb appearing as the inertial coefficient in this paper's reduced variational equation is the same substrate count that supplies (i) the worldline-acceleration response F = Nbm*·ẍ, (ii) the gravitational source-density coefficient in ∇·g = −4πGρ with G = ℓ̃²c³/ℏ, and (iii) the per-tick Reality-Work power Pexist = Mc²/t̃, as derived in the companion inertia paper (10.5281/zenodo.20059780). Hamilton's principle, Newton's second law, E = Mc², and the action quantum h are therefore four readings of one substrate count, not four independent postulates. Status legend used in the paper. ✓ consistent with established experimental or mathematical physics; ⋆ useful QTT consequence or rule of thumb; ⋆⋆ QTT-novel structure or result; ⋆⋆⋆ potential paradigm-shifter if confirmed. Falsifiers. The paper is exposed to experiment in nine concrete channels , spanning ordinary-mechanics tests, A7U graph residuals, action-quantum closure rules, Feynman propagator pole structure, and the unitary measure of the per-tick kernel. Main status labels: GREEN: Σ-OPEN-ZENODO-RECORD-PUBLISHED GREEN: Σ-CONCEPT-DOI-STABLE-CITATION GREEN: Σ-VERSION-DOI-RECONSTRUCTION-AVAILABLE SCOPE: Σ-CLAIM-STATUS-DEFINED-IN-PAPER 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: Main book concept DOI: 10.5281/zenodo.17527179 Corpus Tree row: quantumtraction.org/doi-map/#record-20098144 Blog Map row: quantumtraction.org/blog-map/#corpus-record-20098144 Derivation Atlas: quantumtraction.org/derivation-atlas/ Lexicon: quantumtraction.org/lexicon/ Related QTT DOI (isSupplementTo): 10.5281/zenodo.17527179 Related QTT DOI (cites): 10.5281/zenodo.20059779 Related QTT DOI (cites): 10.5281/zenodo.20042843 Related QTT DOI (cites): 10.5281/zenodo.20057430 Related QTT DOI (cites): 10.5281/zenodo.20045306 Related QTT DOI (cites): 10.5281/zenodo.20051961 Related QTT DOI (cites): 10.5281/zenodo.20042421 Related QTT DOI (isCompiledBy): 10.5281/zenodo.20657182 Included files: qtt_least_action_a7u_v2_01.pdf qtt_least_action_a7u_v2_01.tex
Reading the Schrödinger Hamiltonian as a laboratory shadow of a real source generator Version: 3.04 Concept DOI: 10.5281/zenodo.20484906 Author: Ali Attar Website: quantumtraction.org Main book anchor: Quantum Traction Theory: Main Book v10.01 Textbook quantum mechanics begins with a Hamiltonian operator acting in laboratory time. This framework asks what that operator is a readout of when the source layer is a finite ledger of completed address events, a real phase rotor, and a capacity ceiling. The source evolution equation is real- J: JΣℏ∂T∣ρΣ⟩=HΣsrc∣ρΣ⟩. After a declared access window represents the real J-dial by the laboratory imaginary unit and selects the lab clock, the familiar equation appears: iℏ∂tlabψ=HWlabψ. The Hamiltonian constructor order is therefore completed address events⟶real J-source module⟶HΣsrc⟶Access Law⟶HWlab. The no-retune condition is ∂{observed spectrum, fitted laboratory constants}∂HΣsrc=0. The paper is a framework for writing QTT sector Hamiltonians: name the completed event set, define the source generator, state the A6/A7 capacity and closure gates, project through access, and then compare with observation.
The Artian Hamiltonian Framework for QTT Version: 10.01 Concept DOI: 10.5281/zenodo.20484906 Version DOI: 10.5281/zenodo.20484907 Author: Ali Attar Website: quantumtraction.org Corpus category: Action, Feynman, path integrals, and quantum foundations This paper develops the Hamiltonian of Quantum Traction Theory (QTT) on Artian Geometry as a finite-capacity source generator of completed address events. The laboratory Hamiltonian is not taken as the primitive object: it is the access image of a deeper substrate ledger. Where a textbook Hamiltonian generates time evolution for a system already placed in a laboratory frame, the QTT Hamiltonian must first specify which completed address events are being funded, which clock is being used, which same-universe bundle has closed, and which access channel is permitted to read the result. From the axioms A1–A7 the framework is built in strict constructor order: the completed address event with its noncircular Artian ruler; the real J-dial source Hilbert module; the source Hamiltonian core; the full Artian ledger generator including birth (B_A3), endurance/destruction (D_A2), and bundle-closure (C_A7) maps; the Access Law mapping the source generator to its laboratory image through a clock Jacobian; the Unified Equilibrium Law (UEL) tying energy, action, four-volume support, and gravitational readout to a single Artian capacity endpoint E* = ℏ/t̃_A = ℏc/ℓ_A; the A6 finite-capacity ceilings; and the A7 same-universe bundle closure Q_bundle = 2π. Every standard sector — free particles, photons, fermions, scalar/Higgs, QCD, thermal reservoirs, measurement, and gravity — is placed in the same grammar, in each case separating the source rail from the laboratory readout. Companion rails connect the framework to the wider QTT corpus: unitarity as real-dial geometry, time reversal and Kramers degeneracy from dial conjugation, gauge covariance from local dial re-zeroing, the two-clock half-angle cos(π/8), the Faraday effect as a clock/access test, the endurance-to-Newton route fixing G_A = ℓ_A²c³/ℏ, worked sector dossiers, explicit laboratory-recovery derivations (Schrödinger, Dirac, Maxwell, Boltzmann, path integral), and a sector-by-sector status ledger. Every load-bearing relation is parameter-free, reducing to fundamental constants and fixed integers or angles forced by the axioms; no fitted scalar enters the source layer. A no-smuggling discipline forbids inserting an observed value into the Hamiltonian and naming it afterward. The discipline is deliberately plain: source first, access second, audit last — and a residual is treated not as a nuisance term but as a request for a missing source rail, access map, or axiom-level correction. In the last version we added: systematic page-level anchoring to the QTT monograph (v10.01) for every construction, a visual reading map of the constructor order, and refined epistemic labelling, making each claim auditable against its source. Main status labels: GREEN: Σ-OPEN-ZENODO-RECORD-PUBLISHED GREEN: Σ-CONCEPT-DOI-STABLE-CITATION GREEN: Σ-VERSION-DOI-RECONSTRUCTION-AVAILABLE SCOPE: Σ-CLAIM-STATUS-DEFINED-IN-PAPER 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: Main book concept DOI: 10.5281/zenodo.17527179 Corpus Tree row: quantumtraction.org/doi-map/#record-20484907 Blog Map row: quantumtraction.org/blog-map/#corpus-record-20484907 Derivation Atlas: quantumtraction.org/derivation-atlas/ Lexicon: quantumtraction.org/lexicon/ Related QTT DOI (isVersionOf): 10.5281/zenodo.17527179 Included files: qtt_artian_hamiltonian_framework_v3_01.pdf
Why topology and textbook quantum mechanics do not fix a local quantum-capacity ceiling Version: 1.0 Concept DOI: 10.5281/zenodo.21701184 Author: Ali Attar Website: quantumtraction.org Main book: Quantum Traction Theory: Main Book v10.01 A closed dial path determines an integer winding, ν(U)=2π1∮Udθ∈Z, but it does not determine how many independent degree-one completions may occupy one local clock slot. For every positive integer N, the same pre-capacity axioms admit MN:ν(e1)=⋯=ν(eN)=1,a(ej)=a,s(ej)=n,t(ej)=n+1. The paper constructs both a one-event model and a two-event model of the same weak premises. It therefore proves the relative independence of the A6 one-slot rule and, because that rule is a conjunct of the declared A6 family, the non-derivability of A6 itself: B0∪Tstd⊨A6∗. Here the weak base retains A1 unchanged, together with the real-J dial, pre-capacity A5 support, and exact lifted A7 closure. No A6-dependent downstream theorem is used upstream. The action ledger is separated into three objects: ν=2π1∮dθ,Scan=2πℏν,CA=ℏj∑∣νj∣. Topology fixes the degree. Canonical mechanics assigns the full phase-turn action. A6 supplies the positive capacity spend and the one-funded-transaction rule. The physical ℏ-capacity token is not obtained by renaming the topological winding. Independent countermodels also show that ordinary unitary mechanics permits arbitrary Hamiltonian rescaling, infinitely many zero-energy labels, fixed-integral spikes of arbitrarily large height, and nonlocal one-step permutation updates unless extra source hypotheses are imposed. The resulting necessity theorem is QTT finite local capacity⟹A6 or a logically equivalent source law is required. The result preserves A1 and retains A6 as a separate axiom. Its status is structural rather than empirical: A6 NECESSITY AND RELATIVE INDEPENDENCE: CLOSED The physical truth of A6 remains separately falsifiable. Reproducibility: the release includes the 24-page paper and a reconstruction package containing the LaTeX source, finite-countermodel verifier, detailed machine certificate, scientific audit, render audit, and SHA-256 manifest. The verifier reports 80/80 checks passed. Related anchors: QTT Main Book v10.01 Completed-Event Hamiltonian magnitude no-go theorem Source-Completion and Winding Framework A6 Hadamard Center-Sheet theorem QTT Lexicon: A6 Quantum Capacity QTT Derivation Atlas
This is the Technical Supplement — the proof-dense companion and the canonical formal record for the paper's claims. The main paper argues; the supplement proves. Every load-bearing claim traces to a named check function in the APF verification engine, and the supplement is the document a referee should audit first. The supplement is self-contained for Paper 14: every definition, proof, and grade the paper rests on appears in this one document — the substrate primitives and the marginal admissibility floor, proved; the locality and cost-uniqueness lemmas; the Δ calculus with both fences' witnesses written out; the Boolean-defender bridge with its five certified physical hypotheses and the 3-4-5 worked witness computed on the page; the gate pipeline with a gate-by-axiom comparison to the operational-reconstruction literature (Hardy; Chiribella–D'Ariano–Perinotti; Masanes–Müller; Barnum–Wilce; Spekkens; Abramsky–Brandenburger); the native correlation family constructed explicitly, rung by rung; the resolution triad set against standard thermodynamics (Landauer, erasure, environment-assisted recovery); a consolidated readings register listing every claim below [P] with its falsifier and status; a glossary mapping the framework's vocabulary onto standard quantum-information terms; and a worked end-to-end instance — device to interrogation normal form to exact feasibility certificate to priced ledger, with every tolerance explicit. A reproducibility appendix pins every claim to the APF theorem bank at a named GitHub commit and the archived Engine release (DOI 10.5281/zenodo.18529115); the certificates reproduce deterministically in exact rational arithmetic. About the series. Admissibility Physics is a structural realist reconstruction program built on a single commitment: any bounded region of the world can hold only finitely many distinctions. A principle of least enforcement cost then selects, among all the ways those distinctions might be arranged, the configurations a finite world can sustain. From this the content of physics is reconstructed rather than postulated: the Standard Model's gauge group and matter content, the Hilbert-space and Born-rule architecture of quantum mechanics, the geometry and field equations of general relativity, the four laws of thermodynamics, and the large-scale budget of cosmology emerge as different readings of one finite-capacity ledger. The unification is quantitative as well as conceptual: the framework's dimensionless constants appear not as free parameters but as counts read off that ledger — among them the dark-energy fraction ΩΛ = 42/61 and the weak mixing angle sin2θW = 3/13 — fixed, in the strongest cases, to within current measurement. The core derivation runs Papers 0–11; the extension papers carry the individual sectors. Each paper's main text and Technical Supplement is deposited separately; every quantitative claim traces to a named, executable check in the public theorem bank (over 3,800 bank-registered theorems, 48 quantitative predictions); and each result is carried at an explicit, graded level of confidence — from analytically forced to structurally grounded — with the measurements that would refute it named. Admissibility Physics is offered as a candidate, not a finished theory. If the program holds, the laws of physics could not have been otherwise: they are what a finite world permits. Website: admissibilityphysics.com. Engine and theorem bank: https://github.com/Ethan-Brooke/APF-Engine. Full series and latest deposits: Zenodo community admissibility_physics. The Engine — Admissibility Physics: An Executable Constraint Framework and Constants Map — DOI 10.5281/zenodo.18529115. Paper 0 — What Physics Permits: A Constraint-First Framework for Physics — DOI 10.5281/zenodo.18439523 Paper 1 — The Enforceability of Distinction — DOI 10.5281/zenodo.18439200 Paper 2 — Finite Admissibility and the Failure of Global Description — DOI 10.5281/zenodo.18439274 Paper 3 — Entropy, Time, and Accumulated Cost — DOI 10.5281/zenodo.18439363 Paper 4 — Admissibility Constraints and Structural Saturation — DOI 10.5281/zenodo.18439397 Paper 5 — Quantum Structure from Finite Enforceability — DOI 10.5281/zenodo.18439433 Paper 6 — Dynamics and Geometry as Optimal Admissible Reallocation — DOI 10.5281/zenodo.18439445 Paper 7 — A Minimal Quantum of Action from Finite Admissibility — DOI 10.5281/zenodo.18439513 Paper 8 — The Admissibility-Capacity Ledger — DOI 10.5281/zenodo.19721384 Paper 9 — The Geometric Substrate as Cost Structure of Comparison Continuations — DOI 10.5281/zenodo.20041675 Paper 10 — The Calculus of Finite Continuability — DOI 10.5281/zenodo.20041680 Paper 11 — Forced Universality from Capacity-Bounded Admissibility — DOI 10.5281/zenodo.20684198 Paper 12 — The Gauge Sector of Admissibility Physics — DOI 10.5281/zenodo.21212521 Paper 13 — The Minimal Admissibility Core — DOI 10.5281/zenodo.18361446 Paper 14 — The Quantum Story — DOI 10.5281/zenodo.21212188 Paper 16 — Markov Breakdown and the Hard Problems — DOI 10.5281/zenodo.20684207 Paper 18 — The Electroweak Sector as a Capacity Equilibrium — DOI 10.5281/zenodo.20684209 Paper 19 — Large-Angle CMB Suppression as a Finite-Continuability Constraint — DOI 10.5281/zenodo.21199218 Paper 20 — The Enforcement Crystal — DOI 10.5281/zenodo.18531732 Paper 23 — Magnetically Dark Winding-Class Quantum Processors — DOI 10.5281/zenodo.21199220 Paper 24 — The Recruitment-Radius Extension — Foundations — DOI 10.5281/zenodo.20684211 Paper 25 — The Recruitment-Radius Extension: Applications — DOI 10.5281/zenodo.21199222 Paper 28 — Absolute Mass Scales from Electroweak Capacity Saturation — DOI 10.5281/zenodo.20684215 Paper 29 — Plaquette Representation Dominance and Confinement — DOI 10.5281/zenodo.20684218 Paper 30 — A Tube Mechanism for the Lattice Mass Gap — DOI 10.5281/zenodo.20684220 Paper 31 — Osterwalder–Schrader Structure of Lattice Yang–Mills — DOI 10.5281/zenodo.20684222 Paper 32 — Quark Anchors as APF Trace Masses — DOI 10.5281/zenodo.21199226 Paper 33 — Trace-to-Scheme Export Architecture — DOI 10.5281/zenodo.20684224 Paper 35 — The Dark Sector as a Two-Role Capacity Decomposition — DOI 10.5281/zenodo.20684228 Paper 36 — The Missing Floor — DOI 10.5281/zenodo.21199228 Paper 37 — Collapse as Realignment — DOI 10.5281/zenodo.21199231 Paper 38 — Unification as Ledger — DOI 10.5281/zenodo.21199233 Paper 39 — Coherent Phase Regimes in the APF Interface Engine — DOI 10.5281/zenodo.21199235 Paper 40 — The Thermodynamics of Finite Distinction (Between Symmetry and the Void) — DOI 10.5281/zenodo.20684235 Paper 41 — The Horizon as a Continuation Ledger — DOI 10.5281/zenodo.20684241 Paper 42 — The Weak Mixing Angle Is Not Free — DOI 10.5281/zenodo.20684245 Paper 43 — The Neutrino Sector — DOI 10.5281/zenodo.21194191 Paper 44 — What a Finite Theory Owes the Continuum — DOI 10.5281/zenodo.21195874 Paper 45 — What the Vacuum Can Keep — DOI 10.5281/zenodo.21194195 Paper 46 — The Strong CP Angle Is Not Free — DOI 10.5281/zenodo.21194197 Paper 47 — The Confinement Antecedent Is Not Forced — DOI 10.5281/zenodo.21194199 Paper 48 — The Light-Bending Weight Is Not Free — DOI 10.5281/zenodo.21199627 Technical Supplements cross-link to their main paper via isSupplementTo and to the engine via isDocumentedBy. Concept DOIs above resolve to the latest version.
This paper tells the quantum-mechanical account of Admissibility Physics in one place, from the first declared fact to the last committed record. From a single finite-capacity axiom (A1) plus one declared occupancy fact, the story runs through the Δ calculus that prices jointness (Δ = ε(J − R), derived, with two fences: Δ is not an information functional, and Δ > 0 is not a quantum criterion); the separable / irreducibly-joint fork, decided by an exact Boole-polytope feasibility test; the Boolean-defender bridge that forces noncommutativity where the global Boolean section fails; the gate pipeline that earns complex Hilbert space and the finite Born trace rule as endpoint theorems rather than postulates; the correlation ladder from product states to Tsirelson, with a native family ceiling 2√2·102/103 carried at honest reading grade with a live falsifier; resolution as a class transition, with the free/spend/permanent triad proved as a composition of banked theorems and measurement, decoherence, the Page curve, and the Diósi–Penrose scale as four worked instances of one mechanism; and the arrow of time as the one-way ratchet of the admissibility floor — confinement, the second law, and the quantum as one axis read at graded strengths. Every load-bearing step is anchored to a named, machine-verified check function in the APF theorem bank; the grade of each step is stated where the step is made; and everything the story does not claim is stated in one place. The Technical Supplement (deposited alongside and linked from this record) is self-contained for this paper: every definition, proof, and grade the story rests on, in one document, with a worked end-to-end instance and a reproducibility appendix pinning the theorem bank to a public repository and an archived release. About the series. Admissibility Physics is a structural realist reconstruction program built on a single commitment: any bounded region of the world can hold only finitely many distinctions. A principle of least enforcement cost then selects, among all the ways those distinctions might be arranged, the configurations a finite world can sustain. From this the content of physics is reconstructed rather than postulated: the Standard Model's gauge group and matter content, the Hilbert-space and Born-rule architecture of quantum mechanics, the geometry and field equations of general relativity, the four laws of thermodynamics, and the large-scale budget of cosmology emerge as different readings of one finite-capacity ledger. The unification is quantitative as well as conceptual: the framework's dimensionless constants appear not as free parameters but as counts read off that ledger — among them the dark-energy fraction ΩΛ = 42/61 and the weak mixing angle sin2θW = 3/13 — fixed, in the strongest cases, to within current measurement. The core derivation runs Papers 0–11; the extension papers carry the individual sectors. Each paper's main text and Technical Supplement is deposited separately; every quantitative claim traces to a named, executable check in the public theorem bank (over 3,800 bank-registered theorems, 48 quantitative predictions); and each result is carried at an explicit, graded level of confidence — from analytically forced to structurally grounded — with the measurements that would refute it named. Admissibility Physics is offered as a candidate, not a finished theory. If the program holds, the laws of physics could not have been otherwise: they are what a finite world permits. Website: admissibilityphysics.com. Engine and theorem bank: https://github.com/Ethan-Brooke/APF-Engine. Full series and latest deposits: Zenodo community admissibility_physics. The Engine — Admissibility Physics: An Executable Constraint Framework and Constants Map — DOI 10.5281/zenodo.18529115. Paper 0 — What Physics Permits: A Constraint-First Framework for Physics — DOI 10.5281/zenodo.18439523 Paper 1 — The Enforceability of Distinction — DOI 10.5281/zenodo.18439200 Paper 2 — Finite Admissibility and the Failure of Global Description — DOI 10.5281/zenodo.18439274 Paper 3 — Entropy, Time, and Accumulated Cost — DOI 10.5281/zenodo.18439363 Paper 4 — Admissibility Constraints and Structural Saturation — DOI 10.5281/zenodo.18439397 Paper 5 — Quantum Structure from Finite Enforceability — DOI 10.5281/zenodo.18439433 Paper 6 — Dynamics and Geometry as Optimal Admissible Reallocation — DOI 10.5281/zenodo.18439445 Paper 7 — A Minimal Quantum of Action from Finite Admissibility — DOI 10.5281/zenodo.18439513 Paper 8 — The Admissibility-Capacity Ledger — DOI 10.5281/zenodo.19721384 Paper 9 — The Geometric Substrate as Cost Structure of Comparison Continuations — DOI 10.5281/zenodo.20041675 Paper 10 — The Calculus of Finite Continuability — DOI 10.5281/zenodo.20041680 Paper 11 — Forced Universality from Capacity-Bounded Admissibility — DOI 10.5281/zenodo.20684198 Paper 12 — The Gauge Sector of Admissibility Physics — DOI 10.5281/zenodo.21212521 Paper 13 — The Minimal Admissibility Core — DOI 10.5281/zenodo.18361446 Paper 14 — The Quantum Story — DOI 10.5281/zenodo.21212188 Paper 16 — Markov Breakdown and the Hard Problems — DOI 10.5281/zenodo.20684207 Paper 18 — The Electroweak Sector as a Capacity Equilibrium — DOI 10.5281/zenodo.20684209 Paper 19 — Large-Angle CMB Suppression as a Finite-Continuability Constraint — DOI 10.5281/zenodo.21199218 Paper 20 — The Enforcement Crystal — DOI 10.5281/zenodo.18531732 Paper 23 — Magnetically Dark Winding-Class Quantum Processors — DOI 10.5281/zenodo.21199220 Paper 24 — The Recruitment-Radius Extension — Foundations — DOI 10.5281/zenodo.20684211 Paper 25 — The Recruitment-Radius Extension: Applications — DOI 10.5281/zenodo.21199222 Paper 28 — Absolute Mass Scales from Electroweak Capacity Saturation — DOI 10.5281/zenodo.20684215 Paper 29 — Plaquette Representation Dominance and Confinement — DOI 10.5281/zenodo.20684218 Paper 30 — A Tube Mechanism for the Lattice Mass Gap — DOI 10.5281/zenodo.20684220 Paper 31 — Osterwalder–Schrader Structure of Lattice Yang–Mills — DOI 10.5281/zenodo.20684222 Paper 32 — Quark Anchors as APF Trace Masses — DOI 10.5281/zenodo.21199226 Paper 33 — Trace-to-Scheme Export Architecture — DOI 10.5281/zenodo.20684224 Paper 35 — The Dark Sector as a Two-Role Capacity Decomposition — DOI 10.5281/zenodo.20684228 Paper 36 — The Missing Floor — DOI 10.5281/zenodo.21199228 Paper 37 — Collapse as Realignment — DOI 10.5281/zenodo.21199231 Paper 38 — Unification as Ledger — DOI 10.5281/zenodo.21199233 Paper 39 — Coherent Phase Regimes in the APF Interface Engine — DOI 10.5281/zenodo.21199235 Paper 40 — The Thermodynamics of Finite Distinction (Between Symmetry and the Void) — DOI 10.5281/zenodo.20684235 Paper 41 — The Horizon as a Continuation Ledger — DOI 10.5281/zenodo.20684241 Paper 42 — The Weak Mixing Angle Is Not Free — DOI 10.5281/zenodo.20684245 Paper 43 — The Neutrino Sector — DOI 10.5281/zenodo.21194191 Paper 44 — What a Finite Theory Owes the Continuum — DOI 10.5281/zenodo.21195874 Paper 45 — What the Vacuum Can Keep — DOI 10.5281/zenodo.21194195 Paper 46 — The Strong CP Angle Is Not Free — DOI 10.5281/zenodo.21194197 Paper 47 — The Confinement Antecedent Is Not Forced — DOI 10.5281/zenodo.21194199 Paper 48 — The Light-Bending Weight Is Not Free — DOI 10.5281/zenodo.21199627 Technical Supplements cross-link to their main paper via isSupplementTo and to the engine via isDocumentedBy. Concept DOIs above resolve to the latest version.