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Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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The Griffiths Group of the Mirror Quintic: A CRMLint Squeeze (Paper 94, Constructive Reverse Mathematics Series)

Authors: Lee, Paul Chun-Kit;

The Griffiths Group of the Mirror Quintic: A CRMLint Squeeze (Paper 94, Constructive Reverse Mathematics Series)

Abstract

Description:This paper applies the CRMLint Squeeze protocol to the Griffiths group of a Calabi-Yau 3-fold, using the mirror quintic as the primary test case. Walcher (2007) computed the inhomogeneous Picard-Fuchs equation for the real Lagrangian RP^3 in the mirror quintic X_5: the domainwall tension T(z) satisfies L * T(z) = (15/8) * sqrt(z), where L is the 4th-order Picard-Fuchs operator in CDGP coordinates. The source term is algebraic, determined by the topology of the real cycle. The normal function expansion T = sqrt(z) * sum b_n z^n has leading coefficient b_0 = 30 (Walcher's disk count of holomorphic disks of minimal area) and b_n satisfying a rational recurrence. Four theorems: (A) The PF differential algebra is BISH (13 sub-results verified by ring/norm_num/rfl). (B) Walcher's inhomogeneous equation verified algebraically: source coefficient (15/8)^2 = 225/64, disk count b_0 = 30, recurrence at 5 indices. (C) The Normal Function Squeeze: detection via algebraic source term is BISH, Abel-Jacobi integration and Baire category infinite generation are irreducibly CLASS. (D) Voisin decomposition: 11 BISH + 3 CLASS, all CLASS unused in constructive path. Lean 4 formalization with Mathlib, approximately 500 lines, 0 sorry. Keywords: constructive reverse mathematics, Griffiths group, Calabi-Yau threefold, mirror quintic, Picard-Fuchs equation, normal function, Walcher, open mirror symmetry, Lean 4, formal verification License: Creative Commons Attribution 4.0 International (CC BY 4.0) Related identifiers:- Paper 93: DOI 10.5281/zenodo.18816989- Paper 80: DOI 10.5281/zenodo.18791985- Paper 87: DOI 10.5281/zenodo.18809903 DOI: 10.5281/zenodo.18820969 Upload type: publicationPublication type: preprint

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
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