The 2dm Minimum Topological Structural Unit: From the Relational-Information Axiom to the Dark-Energy Capsule and the Cosmological Residual Potential

AbstractInformation is not an intrinsic property of an isolated object but a measure of the distinguishablerelations between objects. Starting from this general relational-information principle,we independently derive the 2dm Minimum Topological Structural Unit axiom: theminimum span required for two indivisible minimal units (each with ontological minimumdm) to first establish a distinguishable relation is 2dm. This derivation does not depend onwhat physical quantity dm represents—it may be a spatial scale, an energy, a momentum,or the dark-energy capsule unit discussed in this work. We use the Bekenstein–Hawkingblack-hole entropy formula and the holographic principle as an independent, cross-scaletheoretical corroboration, showing that the axiom is exactly consistent with the result thatstoring 1 bit of entropy requires at least 4 Planck areas. Applying this axiom separatelyto the dark-energy capsule unit and to massless particles (e.g., photons), we find that bothhave the same equivalent diameter 2ℓp—not by design, but as a natural coincidence arisingfrom the same axiom acting independently on two different objects. A further energy accountingshows that the capsule’s zero-point energy and the massless particle’s maximumenergy likewise coincide exactly at the Planck energy EP . Building on this capsule structure,we revisit the vacuum energy density paradox—the conflict of 10^120–10^123 orders ofmagnitude between the standard quantum-field-theoretic prediction and the cosmologicalobservation. Through a full topological renormalization of the capsule volume, two classicalpaths (the gravitational mass-energy limit and the quantum zero-point field) achieve an exact1:1 algebraic equality, simultaneously resolving the three classical physical oppositionsof “substance vs. vacuum,” “upper bound vs. lower bound,” and “gravity vs. repulsion,”and reinterpreting the observed dark-energy density as the small, non-equilibrium topologicalphase-transition residual (δ ≈ 10^−123ρp) left behind when the explicate-order spacetimedeviates from the ideal symmetry point during its holographic unfolding. We further proposethat this residual potential may originate from the continuous, discrete creation ofdark-energy capsule units at a fixed per-capsule energy on cosmological scales, and we givea falsifiable creation-rate equation tied to the Hubble parameter. This work is presented asa logically self-consistent, falsifiable, first-principles theoretical framework that has alreadybeen cross-validated through multiple independent paths.