Algebraic Quantum Morphogenesis (AQM) Series
Published June 11, 2026 | Version v3
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AQM Condensed-Matter Coherence-Protection Factor, Global Scaling Law, and Independent Validation of Superconducting Critical Temperature AQM Paper XXI

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Description

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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