Tobias Croydon-McRae

Current programme

Boundary-Complete Relational Dynamics

BCRD studies relational quantum dynamics, recoupling, spin-foam quantum geometry and controlled gravitational limits. The public repository is the curated scientific record for frozen publication manuscripts, reviewed results, reproducibility artifacts and provenance.

Open the public BCRD repository →

Published records

Figshare preprints and companion records

All 17 public deposits, newest first, taken from the Figshare record rather than from memory (verified 20 September 2026).

1. 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 — 2026-09-19.
2. After the Graviton: Refinement, Finiteness and Lorentzian Infrastructure for the W2 Spin-Foam Model — 2026-09-19.
3. A Spin-Foam Quantum-Gravity Model Whose Semiclassical Limit Contains the Graviton: Linearised Einstein Gravity from the Glued W2 State Sum on the Dittrich-Kogios Lattice — 2026-09-19.
4. Boundary-Complete Relational Dynamics to a Linearised Graviton: A Synthesis of the BCRD Programme, Its Dependency Structure, and Its Present Boundary — 2026-09-19.
5. W2 Gluing on the Dittrich-Kogios Lattice: Protection of the Einstein-Hilbert Graviton Block and the First Higher-Derivative Correction — 2026-09-19.
6. Oriented Area-Regge Asymptotics of a Native Four-Simplex Vertex: A Single Geometric Saddle on Nondegenerate Coherent Data — 2026-09-19.
7. Finite-Data Non-Identification of Effective Quantum Coarse Dynamics — 2026-09-19.
8. A Gluing Conjecture for Linearised Riemannian Gravity from a Finite Relational Spin Model: statement, computed evidence, and what would falsify it — 2026-09-18.
9. An Oriented Finite-Spin Vertex with Retained Tetrahedral Geometry: construction, canonical measure, and the gluing obstruction — 2026-09-18.
10. From Boundary Complete Relational Dynamics to a Riemannian Barrett–Crane State Sum: a conditional categorical reconstruction and a resolved-volume test — 2026-09-18.
11. Exact indistinguishability classes for a structured spin-chain probe — 2026-09-16.
12. An exact discrete weak balance identity and its conditional continuum interface — 2026-09-15.
13. No physical pentagon: an interface-relative obstruction to Racah–Regge dynamics in a finite relational record model — 2026-09-15.
14. Positive wedge-toggle kinetics produce a dense 5/6 relational condensate: an obstruction to sparse emergent geometry — 2026-09-15.
15. From Phase Sensitivity to Algebraic Identifiability in Finite Recoupling Dynamics — 2026-09-15.
16. Exact Reconstructive Autonomous Closure in Finite Singlet Quantum Systems — 2026-09-14.
17. BCRD: Auditable Finite Quantum Dynamics, Coarse Records, and the Present Boundary of a Quantum-Geometry Programme — 2026-09-13.

Current gravitational scope

What the latest paper claims

The 20 September 2026 synthesis supports a model-level four-dimensional quantum-gravity claim within an explicitly Riemannian/Euclidean, coherent nondegenerate, admissible large-spin, near-flat, selected-local-branch 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.

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Public identity

Source and author links

GitHub profile · BCRD public repository · Te Kete Ako research home

Formal publication name: S. Tobias Croydon-McRae. Location: Aotearoa New Zealand.