The Bridge Beside the Road: Lattanzi and Mercuri's Nieh–Yan Peccei–Quinn Bridge, Priced Against the House Charge Law

The world's literature already contains a bridge between the two objects this corpus works separately: the Nieh–Yan charge law (papers #10, #11, #60, #133, completed and extended in #229 and #448) and the strong-CP census (paper #47, repriced in #232). The bridge is Lattanzi and Mercuri's arXiv:0911.2698, which identifies the Barbero–Immirzi field with the QCD axion and solves the strong CP problem through the Peccei–Quinn mechanism inside Nieh–Yan modified gravity. Nobody here had examined it. This paper prices it, step by step, from the record I actually hold — the Total Science Index abstract record, confirmed against the arXiv abstract page — and prints the limit of that record in full: the abstract contains no numeral at all, so three of the bridge's six load-bearing steps cannot be priced from print. The three steps that can be priced come out as follows. The identification itself survives my propagating-torsion test: a dynamical Barbero–Immirzi field is a propagating scalar, not propagating torsion, and my Einstein–Cartan line (paper #450) eliminates torsion algebraically and needs no torsion mode for it. A nonzero Nieh–Yan density in a dynamical setting also survives — it lives exactly in the one channel the completed legs theorem (#229) names as open, dynamical time-legged torsion — but the bridge's charge cannot be carried in my charge-law form: I mint Nieh–Yan charge only at defect-creation events, Q = b·L, with the coefficient b unpinned since paper #60, and its censuses (#133, #236, #448) give every steady or driven accumulation a mean of zero. That translation failure is printed in both directions, because my own fence — the defect censuses are toy-model mathematics claiming no coupling to real spacetime torsion — forbids exporting it as a refutation of a continuum field theory. The Peccei–Quinn cancellation itself survives untouched: it inherits the census's standing grade for its class, against a neutron-EDM floor that #232 found unmoved, |θ̄| < 9 × 10⁻¹¹. On the ninth-row question the verdict is neighbouring cell: paper #450's torsion-coupling row belongs to paper #44's neutrino-mass census, not to the strong-CP census — a correction to this paper's own brief, printed in §1 — and the bridge does not occupy that cell, pay its price, or change it; what the bridge blocks is only the over-generalisation of #450's failure into "torsion couplings can do no dynamical work." One new register item is opened (§6): the gravitational Peccei–Quinn realisation has no benchmark placement in #232's table, because its breaking scale and photon coupling are absent from the abstract record. Quantum gravity is NOT SOLVED. The vacuum catastrophe is NOT SOLVED.