Fundamental Dyadic Closure and Mirror-Doublet Exclusion in Quantum Traction Theory

Core claim. In Quantum Traction Theory (QTT), the numerical sum π+π=2π is not sufficient for dyadicity. Dyadicity is fixed by address-support cardinality: dyadic ≡ |I| = 2, I = w1, w2 ⊂ W, w1 ≠ w2 where W is the framework manuscript's Reality Dimension and I is the bundle's sub-address index set. The intra-address alternative π+ (w) + π− (w) = 2πw has |I| = 1. It is monadic saturation under the A5 visible/hidden re-labelling, or it is forbidden double-counting against A7. It is never a fundamental dyad. The intra-address mirror dyad does not exist as a dyadic structure; the question of forbidding it is a question about a non-object. Two-layer theorem. The QTT chirality paper (doi: 10. 5281/zenodo. 20051962) ruled out a parity-doubled fundamental dyad by the cross-address budget+localisation argument (4π > 2π at one address). It did not address the intra-address loophole: why cannot the dyadic share decomposition π+π be re-purposed at one address as a chirality decomposition L+R? The present paper closes that loophole in two independent layers, either of which suffices. Layer 1 — Categorical. Address-support cardinality forbids the mirror partition: |I| = 1 is monadic, not dyadic. The proposed object is a category error. Layer 2 — Structural. Granting the chirality-paper shorthand intra-address reading, three independent obstructions each forbid the mirror partition: (i) Wigner-Weyl Capacity. A1 local Lorentz recovery and the Wigner classification lift the J-complex space V2 ≅ CJ2 to exactly one irreducible chiral SL (2, C) module, V2 ∈ (½, 0), (0, ½). The Dirac extension V4 = (½, 0) ⊕ (0, ½) has dimJ = 4, i. e. n = 4, forbidden by A6. ii. (ii) γ5-Non-Endomorphism. The chirality involution γ5 is not an endomorphism of V2. It acquires non-trivial action only after embedding into the forbidden V4; on V2 alone it reduces to a scalar ±1 and cannot relabel sub-addresses, hence γ5 ∉ UJ (2). Imposing a chirality grading Γchir collapses the centralizer CUJ (2) (Γchir) ≅ UJ (1) L × UJ (1) R, removing the off-diagonal SU (2) generators T1, T2 and leaving only T3. (iii) Layer-collapse. The unique bipartite tensor split of V2 derivable from A4–A7 is the A5 visible/hidden split. Re-purposing it as the chirality split deletes A5, an axiom independent of A6. Consequence. The chirality paper's Single-Chirality Theorem now stands on five independent legs (cross-address budget, cross-address localisation, the categorical Layer 1, plus three intra-address obstructions in Layer 2), where the chirality paper used two. The Orientation–Chirality Lemma is reduced from the most isolated falsifiability point to a basis-and-convention statement; the Visibility-Gauge Theorem becomes the Sub-Address/A5 Lock applied to the dyadic gauge connection. Six concrete falsifiers are listed, each tied to a specific QTT axiom. The construction adds no continuous parameters, no new fields, and no new axioms. Posture. Mirror dyads do not exist in QTT. This is what the axiom system must produce; it is not a phenomenological accommodation of the empirical V−A structure. Conditional inputs / Framework dependence. QTT axioms A1 (substrate orientation), A4 (real dial, J2 = −1), A5 (visible/hidden factorization), A6 (capacity convexity + birth-minimality n ∈ 1, 2, 3), A7 (bundled existence Qbundlew = 2π) from the QTT framework manuscript (doi: 10. 5281/zenodo. 17527179) ; the equal-share J-unitary relabelling lemma from the QTT charge-ledger paper (doi: 10. 5281/zenodo. 20045141) ; the Wigner classification of relativistic one-particle states (Wigner 1939; Weinberg 1995). What is not claimed. This paper does not derive the numerical electroweak couplings gW, gY, v; the Higgs sector or sin2θW; the number of generations; or the cosmological mechanism by which the universe selected one absolute spatial orientation everywhere (the "why left, not right" question, which remains a labelling convention fixed by Wu 1957). The construction is conditional on the QTT axiom system and inherits its falsifiers. Falsifier. Any one of: (i) discovery of an elementary low-energy weak multiplet whose minimal birth requires J-dimension ≥ 4 (i. e. n ≥ 4 as fundamental, not composite) ; (ii) demonstration that the equal-share relabelling group at n=2 is strictly larger than UJ (2) and includes γ5; (iii) derivation of the A5 visible/hidden factorization from A6 alone; (iv) discovery of a fundamental low-energy V+A weak current at any √s ≤ 10 TeV; (v) confirmed observation of an elementary L+R Dirac multiplet whose two chiralities live at exactly the same QTT sub-address with non-zero SU (2) charge on both branches; (vi) demonstration that the framework manuscript's I ⊂ W reading is not the correct definition of "dyadic. " Companion to. Closure paper for the QTT chirality paper (doi: 10. 5281/zenodo. 20051962). Companion to the QTT framework manuscript (doi: 10. 5281/zenodo. 17527179) and the QTT Standard Model charge-ledger paper (doi: 10. 5281/zenodo. 20045141).