Relational Geometry and Spacetime Limits

Provisional Closure of Spacetime Dynamics and Gravity

Executive Summary (Plain English)

COR Theory evaluates whether Lorentzian spacetime geometry and gravity can be reconstructed from recoverability structures. In FA-LRG-01 and FA-AUTH-01 (BNP-TIII22R), the spacetime dynamics sequence is provisionally closed as unresolved and reopenable: no unique physical connection, curvature tensor, or Einstein dynamics is derived.

Evidence Class: Constitutional / Protocol·Scope: Layer 3: Local relational geometry, higher geometry, and gravity handoff

Last Audited: 2026-09-18

Claim Boundary & Exclusions Audit

Scope: Layer 3: Local relational geometry, higher geometry, and gravity handoff

What Is Claimed (Within Scope)

•Levi-Civita uniqueness is strictly conditional on a supplied smooth metric, metric compatibility, and zero torsion.
•Metric geodesics, affine paths, and free fall are not interchangeable without additional theorems.
•Bianchi identities are conditional compatibility relations, not unique selectors of Einstein field equations.
•The Emergent Operational Boundary (EOB) hardware family is closed negative; hardware remains no-go.

What Is NOT Claimed (Prohibited Inferences)

•Does NOT establish an intrinsic metric, Lorentzian signature, continuum spacetime, or gravity.
•Does NOT claim that general relativity has emerged from quantum records.

Technical Exposition & Formulation

Research Blueprint v13 (FA-LRG-01) audits the bridge from recovery geometry to Lorentzian spacetime. While candidate metric formulas exist (based on Fisher duration, recoverability metrics, and Lieb-Robinson diagnostics), they remain uncertified as unique, lossless encodings of nature. Spacetime dynamics is therefore classified as an open question with registered reopening triggers.