Planck-Regime Research from Mathematical Structure Alone: The EAS Scalar-Field Method

This paper is archived as a speculative research work. Foundational work at the Planck regime faces a starting-structure problem: mathematical structures indispensable to successful physical theories need not thereby be built into a framework intended to investigate their mathematical antecedents. We examine Entanglement–Algebraic Spacetime (EAS), specifically its Scalar-Field (SF) formulation, as a mathematics-only research protocol. Within EAS, scalar points, scalar values, associations, recurrence, and second-order ordering have only mathematical meaning; no EAS symbol is assigned an internal physical referent. The method separates stated EAS-native mathematical conditions, target-independent derived consequences, and downstream physical-theory interfaces or empirical tests. Five cases probe this ordering. Closed recurrence composition yields the first nondegenerate intrinsic orientation and supports the electron spin- 12 interface; completed-support handed structure supports an independent charge-facing classification; constrained remap topology generates charged-lepton-facing ratios before empirical mass comparison; under a stated gravity-sector settlement admissibility and an independent loading normalization, conditioned-exterior recurrence yields the scale-agnostic relation D(L)=Q_B/L, which after explicit calibration admits an exact Schwarzschild exterior representation; and, under stated exterior-reconstruction and selector assumptions, rank-3 recurrence-density anisotropy supplies an additional equal-K route to recurrence-phase incoherence and gravity-like accommodation. Physical semantics enter only downstream of each EAS construction. The claim is methodological: mathematical structure alone can support structural derivation, independent classification, quantitative generation, pre-geometric representation, and consequence generation before conventional physical mathematics enters as interface or test. The paper does not claim a complete fundamental theory, identity between EAS mathematics and physical objects, or uniqueness of the resulting physical representations.