Artian A1 Projection-Exponent and Neutral-Branch Asymmetry Audit: Exact Cancellation, a Finite Minimal-Branch Certificate, and the Unclosed QTT Neutrino Source-Rank and Neutral-Completion Claims

Artian A1 Projection-Exponent and Neutral-Branch Asymmetry Audit Version: 1.1 Concept DOI: 10.5281/zenodo.21721466 Author: Ali Attar Website: quantumtraction.org This paper audits a load-bearing premise in the QTT neutrino family-rank program. It preserves the exact conditional identity \[ {Δ m₃₁^2}{Δ m₂₁^2} = ρ^2, ρ = 2πcos\!(π/8), \] while asking a narrower source question: what finite physical event makes \(ρ\) survive as a relative factor between the two nonzero neutral branches? The audit proves the common-factor firewall. If both branches carry the same completed A7 bundle, the same A1 projection count, and the same finite source coefficient, those factors cancel: \[ a_3/a_2 = C(χ_3)/C(χ_2) (2π)n_3-n_2 cos\!(π/8)q_3-q_2. \] Thus the conditional ratio is exact once the source vector is supplied, but it is not automatically a derivation of that source vector. Version 1.1 adds a finite equal-share dyad/triad witness. Two equal dyadic shares and three equal triadic shares each close one bundle: \[ (12,12,13,13,13) {pmatrix} 1&0\\ 1&0\\ 0&1\\ 0&1\\ 0&1 {pmatrix} = (1,1). \] With one common source-to-laboratory access crossing on each visible branch, \[ (n_2,q_2) = (n_3,q_3) = (1,1), Δ(n,q) = (0,0). \] This is an audit witness, not a claim to have constructed the full QTT neutral source complex. It shows that the present minimal dyad/triad and common-access content does not by itself derive \(m_2:m_3=1:ρ\). The release includes an 81-word exponent registry over \[ (n_2,n_3,q_2,q_3)∈\{0,1,2\}^4. \] Under the frozen minimal gate, only \[ (n_2,n_3,q_2,q_3) = (1,1,1,1) \] survives. None of the four ambient words with \[ (n_3-n_2,q_3-q_2) = (1,1) \] survives that gate. This finite result is not a universal no-go theorem: a richer source construction can supersede it only by printing a typed source event, a finite source alphabet, an equivalence quotient, and a reproducible rejected-word registry. The paper separately audits the candidate neutral scale bridge \[ m_Δ E_ = (2π)^5v_Q^2. \] The familiar mnemonic \(2_L+2_H+1anchor=5\) is retained as a candidate, not a theorem. No finite completion-word alphabet or event-incidence map yet certifies the count five against the neighboring counts four and six. Main status labels: GREEN: conditional neutrino mass-ratio algebra GREEN: common-factor cancellation firewall GREEN: finite equal-share minimal-audit witness AMBER: unique source branch pair with Delta(n,q,chi) = (1,1,0) AMBER: five-fold neutral-completion count CANDIDATE: empirical confirmation of A1 through this neutrino sector The no-smuggling receipt differentiates all 81 formal word ratios with respect to fourteen forbidden observational coordinates, including neutrino mass gaps, mixing coordinates, cosmological mass rows, \(G\), and the \(G\)-defined Planck length. The resulting formal dependency matrix is \[ Jacforb∈ R81×14=0. \] It verifies only that the finite audit was not selected using those observational coordinates; it does not replace a future physical source alphabet. Related QTT anchors: QTT Main Book v10.01: 10.5281/zenodo.17527179 Artian LIA Neutrino Mass Reference Framework: 10.5281/zenodo.20571452 QTT neutrino mass-squared ratio framework: 10.5281/zenodo.19960813 Artian/QTT PMNS Neutrino Mixing Reference Framework: 10.5281/zenodo.20735493 Capacity Selection of Left-Handed Weak Interactions: 10.5281/zenodo.20051961 Fundamental Dyadic Closure and Mirror-Doublet Exclusion: 10.5281/zenodo.20053461 Included files: PDF paper, Version 1.1 LaTeX source and QTT visual style file Primary and independent standard-library verification scripts 81-word branch registry Four/five/six completion-count audit No-smuggling dependency receipt SHA-256 manifest and reconstruction package