The Independence of Artian Quantum Capacity: A Necessity and Countermodel Theorem for QTT Axiom A6
- 1Quantum Traction Theory Project
Abstract
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)=1/2π∮U dθ∈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 boxed 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: boxed B0∪Tstdnot⊨ 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: boxed ν=1/2π∮ dθ, Scan=2πℏν, 𝒞A=ℏ∑j|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 boxed QTT finite local capacity Longrightarrow 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: boxed 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
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BibTeX
@misc{ali2026independence,
title = {{The Independence of Artian Quantum Capacity: A Necessity and Countermodel Theorem for QTT Axiom A6}},
author = {Attar Ali},
howpublished = {Zenodo (CERN European Organization for Nuclear Research)},
year = {2026},
month = jul,
doi = {10.5281/zenodo.21701184},
url = {https://doi.org/10.5281/zenodo.21701184},
note = {CC BY},
}
RIS
TY - UNPB
TI - The Independence of Artian Quantum Capacity: A Necessity and Countermodel Theorem for QTT Axiom A6
AU - Attar Ali
PY - 2026
DA - 2026/07/30
PB - Zenodo (CERN European Organization for Nuclear Research)
DO - 10.5281/zenodo.21701184
UR - https://doi.org/10.5281/zenodo.21701184
AB - 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)=1/2π∮_U dθ∈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 boxed ℳ_N: ν(e_1)=⋯=ν(e_N)=1, a(e_j)=a, s(e_j)=n, t(e_j)=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: boxed B_0∪T_stdnot⊨ 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: boxed ν=1/2π∮ dθ, S_can=2πℏν, 𝒞_A=ℏ∑_j|ν_j|. 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 boxed QTT finite local capacity Longrightarrow 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: boxed 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
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