
This paper proposes an auditable effective scaling law for condensed-matter ap plications of Algebraic Quantum Morphogenesis (AQM). The macroscopic conden sation coherence of a material is not determined only by a pairing scale; rather, it is determined by the product of a base pairing temperature and an AQM coherence protection factor. We define ΠAQM = C 2.18 ( E eff E 0 ) 1/2 (1 − δ), where C is the topological-orbital coherence degree, Eeff is the effective elastic spec tral stiffness, and δ is an independently specified loss factor due to disorder, strain, phase separation, or pair breaking. The superconducting critical temperature is written as Tc pred = κfamTpairΠAQM. Here Tpair is a family-level or material-level base pairing temperature obtained from phonon, Debye/Eliashberg, spin-fluctuation, orbital-fluctuation, flat-band, or inter face electron-phonon input. The factor κfam is fixed for a material family and is not allowed to be tuned material by material. AQM therefore does not claim to unify all absolute Tc values with a single global constant; instead, it proposes a common law for how a material protects macroscopic coherence after pairing is available. A seven-sample audit set with independent inputs (Pb, Nb, Nb3Sn, MgB2, FeSe, H3S, and LaH10) gives a mean relative error of about 4%, a maximum relative error of about 4.7%, and R2 ≃ 0.997 in the normalized audit table. The paper also spec ifies extension protocols for cuprates, nickelates, heavy-fermion materials, moire systems, and interface superconductors, but does not include such complex systems 1in the main statistics unless C, Eeff, δ, and Tpair are supplied independently of the observed Tc. The paper is an effective-theory and independent-audit manuscript, not an unconditional microscopic proof for all superconductors.
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