Scholarly record
Research summary
Paper X v2.0 establishes a coherent source-normalized Einstein–real-scalar history through independent characteristic developments and advances that history across its first positive-radius marginal seed boundary. Exact mass reanchoring and two-arrival nonlinear overlap uniqueness produce a C² physical-past Einstein–scalar spacetime; the complete finite-region two-sided gravitational action, including interface, Gibbons–Hawking–York, exterior-wall and corner terms, descends consistently with admitted first variations. The local sign-flexible crossing is identified with the physical-past solution throughout their common earned domains. A conserved positive discriminant extends the physical retarded clock through the pre-turning interval; source-owned local pre-turning exteriors are glued and joined through a proven open equality collar to yield a time-oriented, nondegenerate C² Einstein–scalar history strictly extending the selected post-edge domain. On this joined geometry a conserved real scalar-wave current yields a normalized, nondegenerate alternating pairing on an explicitly represented two-dimensional real on-shell wave subspace, with lateral-wall flux retained. This is a constructive classical continuation on the stated domains, not a maximal history, complete quantum-state transport, a global Fock representation, or a completed free-edge variational theory.
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Scientific context
This paper belongs to the Relational Quantum Gravity research program.