A Covariant Symplectic Structure for Velocity-Space Curvature and the Spacetime Metric on Phase Space T*M: An Open Framework for the Open Problem of P

The Arrow of Time and the Growing Causal Sphere: Reading Penrose’s Weyl Curvature Hypothesis as the Growth of the Light Sphere’s Entropy — The Close o

The Yamagishi Patch within Emergent Gravity: Reading G=4π as the Elastic Constant of Spacetime — The Umbrella over the Thermodynamic Arc (Papers 62, 6

The “1/4” in Black-Hole Entropy: Anchoring It via the 4π Solid Angle, the Euler Characteristic, and Equipartition — and Placing the Causal Sphere on J

Reframing the Cosmological Constant: Λ as an Integration Constant, Not a Vacuum Energy — Unimodular Gravity and the +C Duality of Paper 62.

Born’s Exponent and Gleason’s Theorem: Placing the Geometric Reading Beneath the Stronger Derivation — and the Qubit, Where Gleason Is Silent.

The Home of the Constants: 4π and 32π² as Index-Theorem Normalizations — Placing the Yamagishi Patch in the Atiyah–Singer Family, Without Merging Its

The Dimension Census: Why 3+1 Dimensions, as an Over-Determination by Independent Roots.

The Qubit as a Hopf Fibration: Is Born’s “2” the Same Root as the Hopf Map’s “2”? — A Disciplined Census of the Twos.

The Euler-Characteristic Origin of the 4π Patch: Reading m = 4π as 2π·χ(S²) via Poincaré–Hopf.