The Independence of Artian Quantum Capacity: A Necessity and Countermodel Theorem for QTT Axiom A6

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, \[ \nu(U)=\frac{1}{2\pi}\oint_U d\theta\in\mathbb Z, \] 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 \[ \boxed{ \mathcal M_N:\quad \nu(e_1)=\cdots=\nu(e_N)=1, \qquad a(e_j)=a, \quad s(e_j)=n, \quad t(e_j)=n+1. } \] 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: \[ \boxed{ \mathfrak B_0\cup\mathfrak T_{\rm std}\not\models {\rm A6}_{\!*}. } \] 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: \[ \boxed{ \nu=\frac{1}{2\pi}\oint d\theta, \qquad S_{\rm can}=2\pi\hbar\nu, \qquad \mathcal C_A=\hbar\sum_j|\nu_j|. } \] 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 \[ \boxed{ \text{QTT finite local capacity} \Longrightarrow \text{A6 or a logically equivalent source law is required.} } \] The result preserves A1 and retains A6 as a separate axiom. Its status is structural rather than empirical: \[ \boxed{ \texttt{A6 NECESSITY AND RELATIVE INDEPENDENCE: CLOSED} } \] 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