The Unpaired Face: Pair-Unity's Price on the Weak Sector's Missing Partner, the Koide Identity Attempted as a Fixed Point, and rho = 1 Delimited Against Custodial Symmetry

Three cells of the Transplant Census in the weak column are worked under tolls and kill conditions pre-registered before any comparison was run. THE UNPAIRED FACE (S1 x WEAK): pair-unity, exported from Paper 29 (DOI 10.5281/zenodo.23768419), states its price on the weak sector's missing right-handed partner BEFORE the sterile-neutrino literature is consulted - the partner carries electric charge exactly 0 and is a colour singlet (gauge charges are shared between a pair's faces); its weak-isospin entry has exactly two legal values, a sterile singlet (1,1,0) or a mirror doublet owing a full SU(2)_R sector; neutrino mass forces closure of exactly one of two kinds, the face inside the mass matrix or a lepton-number leak of exactly Delta L = 2 graded by neutrinoless double beta decay (KamLAND-Zen 2024: T > 3.8 x 10^26 yr); a light partner must mix. Total absence is forbidden by the price, so the Census kill (accommodates everything) does not fire. Surveyed against the price, the literature matches on every line: the Dirac branch (Yukawa price y_nu approx 2.9 x 10^-13, computed in the paper, technically natural), type-I seesaw and the nuMSM on the Majorana branch (seesaw scale approx 6 x 10^14 GeV at order-one coupling), the eV-sterile branch price-legal but data-disfavoured (global 3+1 tension, MicroBooNE), the left-right doublet branch price-legal with its sector pushed to ~5 TeV and beyond; no surviving branch violates the price and no priced-out branch (charged or coloured face, fourth light doublet neutrino - independently excluded by N_nu = 2.9840 +/- 0.0082) survives. Grade: CONSTRAINS (the partner's allowed entries and the closure dichotomy); the dichotomy's skeleton RENAMES the standard Dirac/Majorana alternative; the pairing law underneath remains POINTER, its operator still owed even at home. THE KOIDE IDENTITY (S6 x WEAK): Q = 0.6666605 vs 2/3 from PDG 2024 pole masses (computed in the paper; deviation -6.2 x 10^-6, within the tau-mass-driven uncertainty 6.8 x 10^-6; geometric content the 45.00-degree bisector cone; the 1983 relation's implied m_tau = 1776.97 MeV inside today's 1776.86 +/- 0.12 MeV). Run as a generation-map fixed point (paper N9), both natural inheritance constructions fail: democratic inheritance fixes Q = 1/3 (sitting falsified), deviation-preserving inheritance fixes every cone (no selection - the kill's structural form). The one selector that would work, self-duality of the fixed cone under exchange of the democratic and perpendicular components, exists in the house only as the pairing's face-exchange symmetry, with no operator to carry it. Grade: the Koide value 2/3 is NOT DERIVED; the identity's form is POINTER with the upgrade path named; the same form on neutrino splittings returns 0.7496, so no second relation is claimed. RHO = 1 (S3 x WEAK): the paper delimits, at full size, what custodial SU(2) (Sikivie-Susskind-Voloshin-Zakharov 1980) already explains - rho = 1 at tree level for doublet sectors, the deviation pattern through the Peskin-Takeuchi T door (top loop Delta rho approx 0.0093, computed in the paper), and Georgi-Machacek representation discrimination - and grades the seam-identity transplant of Axiom H against it: Axiom H is a saturation identity carrying a constant across a horizon, rho is a symmetry identity carrying no constant and saturating nothing, across an electroweak transition that is a smooth crossover. Grade: rho = 1 from house machinery NOT DERIVED and the Census toll declared not paid (the kill's second horn fired verbatim); the seam reading is POINTER, thinned by two species mismatches. The Cabibbo first-row unitarity deficit (~3 sigma, PDG review Aug 2025) and its MeV-sterile literature appear as pointer-grade context only. The vacuum catastrophe is not spent anywhere in the paper and stands NOT SOLVED in the main program.