Finite Source-Graph Uniqueness and Normalized Energy-Shape Theorems for Chiral Spin Filtering

A finite-graph test of mirror-antisymmetric spin filtering Chiral spin filtering presents two distinct questions: how many independent chirality-odd source generators are legal for a declared molecular/interface graph, and whether different mirror samples read the same energy shape after sample amplitude is removed. This paper separates those questions and gives an executable theorem for each. The finite source-graph theorem is \[ \boxed{ \dim W_{ab} = \#\left\{[\Gamma]\in\mathcal C/\mathcal K: \chi_{ab}\big|_{\operatorname{Stab}(\Gamma)}\equiv1 \right\}. } \] It counts the legal chirality-odd generator lines in a certified finite graph grammar. The certificate declares the graph class, equivalence relation, reversal action, discarded variables, discrete choices, and refinement rule. A one-line result is therefore auditable and falsifiable rather than inferred from a preferred molecular drawing. When the count is one and the independently declared access maps share one energy kernel on that line, \[ \mathcal A_{c,E}\big|_{W_{ab}} =\lambda_c\mathcal A_E\big|_{W_{ab}}, \qquad \lambda_c>0, \] the normalized mirror responses obey \[ \boxed{ \widehat p_{+}(E)=-\widehat p_{-}(E), \qquad \widehat p_{\chi}(E) = \frac{p_{\chi}(E)}{ \left[\int_{\mathcal W}w(E)p_{\chi}^{2}(E)\,dE\right]^{1/2}}. } \] This is a zero-amplitude-fit shape statement. Constant detector gain, contact area, and independently measured enantiomeric dilution cancel. The paper also proves the converse warning: one source line by itself does not imply one laboratory profile when the access kernels differ. Empirical scale of the observed chirality-odd sector Published bifacial-ladder polarizations of \(+90\pm5\%\) and \(-88\pm5\%\) are separated by \(25.17\) quadrature-combined quoted-uncertainty units under the explicitly provisional independent-Gaussian interpretation; the departure from exact antisymmetry is only \(0.283\) such units. Independent heptahelicene data give a \(14.38\)-unit opposite-sign separation. These are high-separation empirical supports for a chirality-odd sector and for the joint A4--A7 finite-source dependency used by the theorem. They are not relabelled as full-likelihood discovery significances because the published joint covariance packets are unavailable, and they do not isolate each axiom independently. Vector-resolved 3-MCHO/Cu(643) data place \(80.9\%\) of the digitized squared odd contrast along the independently constructed terrace direction. A fixed-surface no-go theorem proves that one surface enantiomer cannot separate molecule-odd response from the molecule--surface mixed sector. The paper therefore specifies the decisive four-cell experiment using both molecular and surface enantiomers, finite-purity correction, common-frame axial transport, blinding, randomization, replication, and full covariance. The theorem forms were developed after inspecting the ladder and Cu patterns. Those discovery rows remain permanently declared under the Newton Protocol. They are retroprediction constructors, while the four-cell experiment and graph-refinement tests are the prospective falsifiers. Public anchors Paper concept DOI Quantum Traction Theory: Main Book v10.01, especially pp. 48, 80--82, 263--266, and 912--916 QTT Lexicon Source/readout ontology QTT Corpus Tree The reconstruction ZIP contains the LaTeX source, empirical audit figure, formal and empirical machine receipts, executable theorem and mutation tests, three adversarial audit reports, the feedback decision ledger, and the exact SHA-256 manifest. The PDF is the primary reader-facing file.