A sharp upper bound on jointly coherent mass, rather than a collapse lifetime Can a jointly coherent mass keep growing without a physical ceiling? This paper states the global A6 hard-wall postulate in Artian geometry and gives it an explicit mathematical form. \[\boxed{\begin{aligned}\rho_\Gamma\in\mathcal S_{\rm coh}^{A}(\Gamma)&\ \Longrightarrow\ B_\Gamma\le1,\\B_\Gamma>1&\ \Longrightarrow\ \mathcal S_{\rm coh}^{A}(\Gamma)=\varnothing.\end{aligned}}\] Here \(B_\Gamma=M_\Gamma/m_A\) is the participating source-mass count of one coherent domain, with \(m_A=\hbar/(c\ell_A)\). An over-capacity coherent state is excluded from the physical state set, even transiently. There is no collapse lifetime or localization-rate coefficient. Distinct independently funded domains can still form ordinary macroscopic matter. The finite-dimensional realization replaces particle-count entanglement depth with a source-mass-weighted admissibility class: \[\mathfrak A_{\mathbf b}=\operatorname{conv}\!\bigcup_{\pi:\ \sum_{i\in C}b_i\le1\ \forall C\in\pi}\left\{\bigotimes_{C\in\pi}\rho_C\right\}.\] The paper proves convexity, closedness, partial-trace and local-operation stability, a coherent aggregation bound, and a prohibition on an over-budget entangling preparation. A directly checkable witness consequence is \[\boxed{\sum_i b_i>1\quad\Longrightarrow\quad\langle\mathrm{GHZ}_N|\rho|\mathrm{GHZ}_N\rangle\le\frac12\quad(\rho\in\mathfrak A_{\mathbf b}).}\] The GHZ overlap inequality is standard quantum-information mathematics. The QTT contribution is the physical mass-weighted restriction on which source states are admissible. A certified above-wall witness would falsify the proposed global postulate. The paper specifies the source-to-instrument certificate needed for that judgment, rather than counting an entire host object by convention. The relation to the existing local A6 law is explicit: common-address projection plus complete branchwise funding would imply the global wall. The complete-funding lemma is a separate derivation target; the global wall is adopted here as a postulate, not relabelled as an already-proved consequence of local capacity alone. Version 1.0 includes a self-contained onboarding route, source ontology, axiom and constructor cards, proofs, diagrams, a finite-state verifier, prior-work comparisons, and a blind-test protocol. Structural consequences are proved conditional on the postulate; experimental selection remains open. Stable paper DOI · Main Book v10.01 · A6 lexicon · Artian's Universe
A sharp upper bound on jointly coherent mass, rather than a collapse lifetime Can a jointly coherent mass keep growing without a physical ceiling? This paper states the global A6 hard-wall postulate in Artian geometry and gives it an explicit mathematical form. [\boxed{\begin{aligned}\rho_\Gamma\in\mathcal S_{\rm coh}^{A}(\Gamma)&\ \Longrightarrow\ B_\Gamma\le1,\B_\Gamma>1&\ \Longrightarrow\ \mathcal S_{\rm coh}^{A}(\Gamma)=\varnothing.\end{aligned}}] Here (B_\Gamma=M_\Gamma/m_A) is the participating source-mass count of one coherent domain, with (m_A=\hbar/(c\ell_A)). An over-capacity coherent state is excluded from the physical state set, even transiently. There is no collapse lifetime or localization-rate coefficient. Distinct independently funded domains can still form ordinary macroscopic matter. The finite-dimensional realization replaces particle-count entanglement depth with a source-mass-weighted admissibility class: [\mathfrak A_{\mathbf b}=\operatorname{conv}!\bigcup_{\pi:\ \sum_{i\in C}b_i\le1\ \forall C\in\pi}\left{\bigotimes_{C\in\pi}\rho_C\right}.] The paper proves convexity, closedness, partial-trace and local-operation stability, a coherent aggregation bound, and a prohibition on an over-budget entangling preparation. A directly checkable witness consequence is [\boxed{\sum_i b_i>1\quad\Longrightarrow\quad\langle\mathrm{GHZ}_N|\rho|\mathrm{GHZ}N\rangle\le\frac12\quad(\rho\in\mathfrak A{\mathbf b}).}] The GHZ overlap inequality is standard quantum-information mathematics. The QTT contribution is the physical mass-weighted restriction on which source states are admissible. A certified above-wall witness would falsify the proposed global postulate. The paper specifies the source-to-instrument certificate needed for that judgment, rather than counting an entire host object by convention. The relation to the existing local A6 law is explicit: common-address projection plus complete branchwise funding would imply the global wall. The complete-funding lemma is a separate derivation target; the global wall is adopted here as a postulate, not relabelled as an already-proved consequence of local capacity alone. Version 1.0 includes a self-contained onboarding route, source ontology, axiom and constructor cards, proofs, diagrams, a finite-state verifier, prior-work comparisons, and a blind-test protocol. Structural consequences are proved conditional on the postulate; experimental selection remains open. Stable paper DOI · Main Book v10.01 · A6 lexicon · Artian's Universe
One local wall, three exact consequences Version: 1.0 Concept DOI: 10.5281/zenodo.21702144 Author: Ali Attar Website: quantumtraction.org Main book: Quantum Traction Theory: Main Book v10.01 Here capacity wall means a source-level per-address bound on generator width, reduced action, mutually distinguishable records, and their shared funding. It is distinct from the quantum-channel capacity Q(N) of quantum Shannon theory. The dynamical face turns a local spectral-width ceiling into a tight quantum-speed theorem: ΘFS(ψ0,ψT)≤2ℏ1∫0TdiamspecHw(t)dt≤2tAT and therefore T≥2tAarccosF,T⊥≥πtA. The orthogonalization constant is saturated by a two-level system. The informational face begins with one faithful reference state. If every mutually orthogonal physical record obeys D(∣ψj⟩⟨ψj∣∥ω)≤C⋆, then M≤eC⋆. For a finite region this produces a finite-dimensional physical observable algebra, a finite Gibbs trace, bounded exact moments, and norm-convergent Dyson evolution: 1≤ZR(β)=Tre−βHR≤DR≤d⋆NR. The shared-capacity face blocks multiplication of one local budget by species relabelling. For a finite region and for depth-L local boundary generation, SvN(ρA)≤NAlogd⋆,SvN(ρA)≤2Lb(A)logd⋆. The QTT surface ledger is kept in its exact saturation form: NHQTT=ηH4ℓA2A,0≤ηH≤1. The familiar quarter-area equality is the stationary capacity-saturated row ηH=1. The separate modular-to-von-Neumann normalization bridge remains explicitly open. The three converse countermodels combine into the paper's master necessity statement: nonzero local orthogonalization time+finite exact source regions+finite species-independent record capacity⟹an A6-equivalent local capacity wall. The result does not assert that QTT is the only possible syntax for that wall. It identifies the mathematical work that any equivalent local principle must perform. The upstream independence question is closed separately: A1, A4, primitive A7 closure, and textbook quantum mechanics do not derive A6 in the declared weak class. This paper is the downstream complement: it establishes why A6, or a mathematically equivalent local law, is necessary for the three universal consequence families. Reproducibility: the release includes the 25-page PDF and a reconstruction package containing the LaTeX source, proof-status ledger, four scientific audits, verification script, 10-check machine certificate, render audit, and SHA-256 manifest. All 10 computational checks pass. Related anchors: A6 independence and countermodel theorem QTT Main Book v10.01 QTT Lexicon: A6 Quantum Capacity Artian's Universe and source/readout ontology QTT Derivation Atlas QTT DOI Map / Corpus Tree
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
When does finite phase-space entropy stop guaranteeing proximity to coherent light? This article determines sharp thresholds for two broad optical source classes when the number of modes may grow. It separates the roles of entropy, mode number and photon energy in approximating an optical state by a single pure coherent state. For an m-mode state ρ, write Qρ(α)=⟨α∣ρ∣α⟩, with dμm=π−md2mα, and define M(ρ)=2m∫Qρ(α)2dμm(α),s=−lnM(ρ),D(ρ)=infα∥ρ−∣α⟩⟨α∣∥1. Here s is the second-order Wehrl entropy excess and D is the full trace-norm distance, whose maximum is 2. The collision quantity M is also the output purity after half loss and can be accessed using interference of two independent, identically prepared copies. Exact source-class thresholds. The two classes are states diagonal in a common passive-mode number basis, and arbitrary states supported on the vacuum together with configurations whose photons occupy only one mode at a time in a common passive basis. The latter class retains arbitrary complex coherences, including vacuum coherences. For either class X, with FX(s)=supρ∈X,−lnM(ρ)=sD(ρ)2 and the supremum over all finite mode numbers, FX(s)=4⟺s≥ln4. The plateau is approached through growing-mode sequences, not attained by a finite-mode state. At its onset, vanishing coherent overlap and M→1/4 force the one-photon probability to approach one, without an energy-bound assumption. This probability rigidity does not assert convergence of the mean energy. Sharp boundary geometry and energy. For the full number-diagonal class D, the approach from below has the exact corner lims↑ln4ln4−s4−FD(s)=e4. A small vacuum component changes the optimal coherent peak and produces the sharp slope. Separate all-state energy bounds show that vanishing coherent overlap requires at least one photon asymptotically, or two photons for pure states. Explicit sources attain these limiting energy costs, and exact-entropy constructions include their additional photon costs. The proofs retain arbitrary photon tails and constants uniform in the mode number. The earliest-threshold and corner results apply to the source classes stated above. The integrated article contains the complete proofs and two figure groups.
A no-signaling theory may, in principle, be more nonlocal than quantum mechanics: the Popescu--Rohrlich box reaches the algebraic Clauser--Horne--Shimony--Holt value 4, whereas nature stops at the Tsirelson value 22. Absolute Frame Theory (AFT) produces nonlocal correlations---two systems entangled in M share a single point of the substratum A (Axiom II)---and forbids superluminal signaling (the channel is Bremermann-bounded). We ask where those correlations fall, and we establish, by two independent routes, that they cannot exceed the Tsirelson bound: AFT admits no super-quantum correlations. The operator route proves, inside the reconstructed Hilbert theory, the Tsirelson operator identity, with the local commutativity [Ai,Bj]=0 itself derived from AFT structure---the tensor factorization that local tomography supplies and the field microcausality of the constrained embedding---rather than assumed. The information route reduces the bound to a physical principle: AFT's shared resource is read out through a completely positive, trace-preserving channel of finite classical capacity (a theorem of the channel, founded on action quantization and the trace over the inaccessible fiber), this channel obeys the data-processing inequality, and the combination places AFT in the class that satisfies Information Causality, which singles out 22 among the no-signaling theories. We state plainly what this does and does not achieve. It does not close the question of why the bound is 22 rather than some other value: both routes, chased to their foundations, terminate at the same posited fact---the M--A signature transition (the Wick rotation) that installs the complex-Hilbert structure---and finite capacity alone, stripped of that structure, does not exclude a Popescu--Rohrlich box. The two routes are thus the operator-algebraic and information-theoretic faces of one ceiling, and they reduce the selection of 22 to a single substratum fact, with the residue an instance of the deepest open question of the programme rather than a problem specific to nonlocal correlations.
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