FRC Paper 22 - The Three-Body Problem Proof using a Full Relativistic Finite Reality Capture-Relay

FRC Paper 22 - The Three-Body Problem Proof using a Full Relativistic Finite Reality Capture-Relay

Uncompressing the Full General Relativity Equations of FRC Paper 01

By Joe Bloggs

“The advice of the pass is the map.”

FRC Paper 22 takes the unchanged General Relativity equations retained in FRC Paper 01 and applies the same reality-first language repair to the three-body problem.

It introduces no new force, stability law, escape law or FRC correction term. Instead, it uncompresses the metric, connection, curvature, Einstein equations, conservation identities and 3+1 Cauchy evolution as one finite capture-release-recapture relay.

Rev01B established the weak-field proof. Rev02C carries that same structure through the full relativistic equation set. A spatial metric, extrinsic curvature and matter state satisfying the Hamiltonian and momentum constraints form one locally definite capture. The Einstein evolution equations release that captured relation into the next spatial state. The next admissible state is the recapture. The established Cauchy result supplies one maximal globally hyperbolic development up to diffeomorphism: coordinate stories may differ, while the spacetime relationship does not.

Two complementary strong-field anchors are supplied.

Three-centre Brill-Lindquist data provide a vacuum strong-field initial capture.

The exact three-centre Majumdar-Papapetrou Einstein-Maxwell solution provides a full spacetime in which one scalar U determines the lapse, spatial metric, electromagnetic potential, connection and curvature. This supplies the paper’s single-substrate result: potential is the scalar capture and field is the directional advice derived from that same dynamic structural-memory volume.

Appendices C, D and E provide the global classical generative formula, the coordinate-projection rule, the finite classical incompleteness receipt and the proof-internal FRC continuation operator Q_FRC.

The global law is captured once. Realised outcomes are generated through finite handover rather than existing as a detached pre-written coordinate catalogue.

The offline replay is provided with the supporting information.

The Brill-Lindquist Hamiltonian residual converges at observed order 1.984976 or better. The maximum relative Einstein-Maxwell residual is 3.023 × 10^-7. The maximum Maxwell divergence is 7.691 × 10^-7 and the minimum sampled U is 2.175139. The exact metric returns to the FRC Paper 01 weak-field g00 relation at approximately second order under source scaling.

The Supporting Information Rev01C package supplies an offline dynamic 3D capture-relay viewer, source receipts, integrity checks, explanatory pages and a complete SHA256 manifest.

The viewer explicitly separates:

• the pale observer-reference grid, which is graph paper only and carries no physical substrate meaning;
• the darker scalar capture surface defined within Paper 22 Rev02C;
• the arrows, which represent directional advice derived from the gradient or directional derivative of that same scalar capture;
• the body and centre markers, which represent local finite captures and
• the trails, which record completed handovers.

The viewer is an observer-readable replay of the proof receipts. It is not additional evidence and it does not invent missing evolution.

Within the exact Rev02C claim, the internal derivation is complete. Independent external replay and mathematical and physical peer review are the remaining validation boundary.

FRAMEWORK POSITION

Phase V - Reality Audit, Correspondence and Empirical Accountability.

Paper 22 follows Paper 21b and acts as a programme-level test of the FRC bridge between reality and symbolic expression. It uses FRC Paper 01 as its primary General Relativity basis and returns the unchanged equations as a finite capture-relay account.

RELATIONSHIP TO FRC PAPER 01

FRC Paper 01 retained the tested mathematics of General Relativity while reframing metric, curvature, gravity and gravitational time dilation as deviation, persistence, gradient and local rate.

Paper 22 continues that exact operation.

It does not replace Paper 01. It uncompresses the finite local and global handover structure already carried by the Paper 01 equations and applies that structure to the relativistic three-body problem.