Fissure Geometry, Topological Projection, and the Emergence of Fundamental Physical Constants: A Unified Perspective Based on the Dual-Helix Generating Function

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The original version is archived at Figshare:https://doi.org/10.6084/m9.figshare.34783557

The Standard Model of modern physics treats fundamental physical constants (such as thePlanck constant h and the fine-structure constant α) as free parameters measured experimentallybut lacking a theoretical origin . At the same time, the“magic angle” of twisted bilayer graphenein condensed-matter physics has long lacked a purely geometric analytical solution . Based onthe mother framework of the“Dual-Helix Generating Function,” this paper proposes a unifiedpurely geometric-topological emergence mechanism . It is shown that when a higher-dimensionaltopological manifold is projected onto a lower-dimensional observational basis, the phase jumpat a geometric singularity (branch point) generates a specific“fissure constant.” By introducingthe fissure angle

δθ_Xu = arccos(e/π) − 30^◦ ≈ 0.08817^◦

and the fissure cosine

δy_Xu = cos30^◦ − e/π ≈ 7.69425 × 10 ⁻⁴ ,

this paper gives zero-free-parameter analytical constructions of fundamental constants . Theerror in the dimensionless principal part of the Planck constant is only 0. 083%, and the experimental error of the fine-structure constant α_calc = 0 .0072956 is about 0. 024% . In addition, thesame fissure angle, through twelvefold topological accumulation, predicts the graphene magicangle

θ_magic = 12δθ_Xu ≈ 1.0580^◦

(error < 1%) . This paper strictly follows epistemological stratification and clearly delineates theboundary between“relational mapping” (numerical correspondence from geometric quantitiesto physical quantities) and“field-theoretic mapping” (causal derivation of the Lagrangian) . Thisframework not only reveals the geometric isomorphism underlying physical quantities at differentenergy scales but also opens a falsifiable topological-geometric path for the problem of the originof constants .