Research from Aotearoa New Zealand
Exact questions.
Open evidence.
Research by S. Tobias Croydon-McRae, with publication records, source, computations and review evidence available alongside the reported results.
Current programme release · 20 September 2026
Boundary-Complete Relational Dynamics as a Four-Dimensional Quantum-Gravity Model
A Five-Rung Derivation to the Linearised Einstein Sector in a Coherent Near-Flat Riemannian Regime. The synthesis composes five independently tested interfaces from a finite-spin orientation-resolved four-simplex amplitude through a quadratic reduction whose leading two-derivative metric operator is the linearised Einstein-Hilbert operator.
The claim is deliberately scope-bound: Riemannian/Euclidean, coherent nondegenerate, admissible large-spin, near-flat fluctuation-ball, selected-local-branch, regular/centrally-subdivided Dittrich-Kogios and quadratic regime. It does not claim a complete Lorentzian theory, nonlinear continuum Einstein dynamics, arbitrary-triangulation independence, universal finiteness or a nonperturbative continuum fixed point.
Earlier public release · 9 September 2026
What can a quantum process afford to forget?
A system can look redundant at one instant while its later measurements still need the information you discarded. This paper makes that distinction explicit in a small quantum model, using exact arithmetic and an independently reconstructed implementation.
- 26
- candidate gradings tested
(19 distinct maps) - 0
- exact descents of
the original process - 17
- modified laws that remain
informationally complete
The commutant of an instantaneous algebra need not be the redundancy of the process it generates
Full research catalogue · 9 September 2026
Every lane, including the unfinished ones
Explore the accepted exploratory results, checked calculations, working drafts, parked and retired investigations, and withdrawn claims. Each lane carries its actual status and links to its source or evidence. Publication does not imply peer review or a quantum-gravity result.
Open the full research catalogue → · Wedge obstruction · Conservation bridge · Retractions
Companion working paper · 9 September 2026
Nearest-neighbour terms are not sufficient for locality
The original BCRD register couples to an extended region. The companion paper examines that hub through exact short-time coefficients and finite-chain controls, and reports a local process-complete alternative.
Read the register-hub locality paper → · Its source and evidence
Public evidence archive · 9 September 2026
The full physics research estate
Branches, worktrees, July material, unfinished drafts, superseded attempts and no-go results are preserved in a dated, hash-checked snapshot.
A result you can inspect
The independent calculation rebuilds the singlet model from the total spin-raising kernel, proves an exact change of basis for all 15 pair operators, both Hamiltonians and six projectors, then reproduces every scan row.
Where this sits
Boundary-Complete Relational Dynamics (BCRD) began with finite quantum-process questions about what boundary information must survive composition and reduction. The current programme record now includes a scope-bounded four-dimensional quantum-gravity model claim whose leading metric dynamics reproduce the linearised Einstein-Hilbert operator in the stated Riemannian near-flat regime.
The programme does not present that result as a complete Lorentzian, nonlinear, arbitrary-triangulation or nonperturbative final theory. Earlier finite-model results remain part of the public provenance rather than being rewritten retrospectively.
The public record distinguishes internal cross-checking and hostile review from external peer review; external expert scrutiny remains welcome.