Research Program
Registration Theory
A research program investigating how persistent physical structure, geometry, and effective observables can arise from primitive acts of physical registration.
The central question
The program asks what structure must precede familiar space, time, objects, and measurement, if these are reconstructed from physical registration rather than assumed at the outset.
From primitive registration to effective physics
A conceptual sequence, not a completed mathematical derivation: each arrow marks a direction the program is working to establish rigorously, not a step already proved in general.
- 01Trinity
- 02Registration
- 03Differentiation
- 04Persistent Consequence
- 05Relational Structure
- 06Effective Geometry
- 07Observable Physics
What has been established?
Full research ledger →Every claim on this site carries an explicit status. These examples illustrate the system; the complete ledger is on the status page.
ACRF-4 admits an exact 1 ⊕ 3 decomposition
R⁴ decomposes exactly as U ⊕ H4, with U = span{1} of dimension 1 and H4 = { r : 1ᵀr = 0 } of dimension 3, and R⁴ / U ≅ H4 ≅ R³.
Scope: A structural linear-algebra fact about the canonical finite ACRF-4 registration model. It does not by itself identify the four ACRF-4 coordinates with physical quantities.
- Does not constitute a derivation of physical spacetime from ACRF-4.
- Host calibration is downstream and does not supply a preferred basis automatically.
Last reviewed 2026-08-27
Reconstruction of physical spacetime from registration dynamics
ACRF-4 now has exact node-block nonautonomy and strict retained-edge densification, but its complete positive K-support graph does not derive sparse primitive-neighbor locality. Deriving physical spacetime still requires a forward-generated boundary-growth and inter-host transfer structure whose complete dynamics remain unresolved.
Last reviewed 2026-08-28
Direct physical identification of ACRF-4 structural sectors
Earlier formulations assigned direct physical meaning to the ACRF-4 structural decomposition. That identification has been withdrawn. ACRF-4 now provides downstream registration structure; physical time, space, and energetic distinctions require additional host-dependent reconstruction.
Last reviewed 2026-08-27
Current research frontier
Active problems, including reconstructing physical spacetime and metric structure from ACRF-4-type models, are tracked on the current frontier page as open problems rather than settled results.
Publications
Papers and Zenodo records are catalogued on the publications page as the corpus import proceeds.
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