Research from Aotearoa New Zealand
Exact questions.
Open evidence.
Research notes by S. Tobias Croydon-McRae, with the source, computations and review record available alongside each result. This page is the full catalogue: every lane appears, including the ones that are parked, blocked, retired, or that produced claims later withdrawn.
Pre-publication draft · 9 September 2026
Nearest-neighbour terms are not sufficient for locality
A two-state register attached to a constrained spin chain looks local: every term of its Hamiltonian acts on neighbouring sites. That inference fails. One conditional term makes the register a hub with edges to a whole region, and the resulting short-time obstruction does not decay with distance or shrink with system size. The hub also turns out to be avoidable, which is what makes its cost worth reporting.
- 1/16
- third-order coefficient,
independent of separation - 0
- orders below third
that survive - 2
- controls that recover
a clean cone
An exact short-time obstruction from a conditional register coupling, with the global constraint exonerated
What this is not
None of the work below derives a metric, an entropy–area law or gravitational dynamics. The two accepted results are exploratory theorems about finite declared models; neither is canonical, and neither bears on the truth of quantum gravity. Where a lane is parked or blocked, it is listed as parked or blocked rather than quietly omitted.
How it was checked
Results marked Accepted passed a fresh review by an agent that did not author them, working from the declared model rather than the author's scripts, and are bound to an exact commit. Editing that commit voids the acceptance.
Cross-checking between AI implementations is not peer review. No external expert has reviewed any of this work.
What the labels mean
- Published Deposited with a DOI and frozen. Non-author agent review complete; external peer review open.
- Accepted Passed fresh non-author review; bound to an exact commit.
- Checked Reproduced by a second agent, but no fresh review.
- Draft Written up, not yet reviewed. Read as work in progress.
- Verification Someone else's result, checked here. Not our finding.
- Parked Inactive by decision, not abandoned.
- Blocked Stopped on a named obstacle.
- Retired Closed out, with a recorded null.
- Retracted Claimed, then withdrawn. Kept visible on purpose.
Published preprints
Deposited publicly with DOIs and frozen source. Each carries an internal hostile re-review by a non-author agent; none has been externally peer reviewed, and the record says so. Scope statements below are the papers' own.
Boundary-Complete Relational Dynamics as a Four-Dimensional Quantum-Gravity Model Published
A Five-Rung Derivation to the Linearised Einstein Sector in a Coherent Near-Flat Riemannian Regime. 20 September 2026. Five composed rungs, from an orientation-resolved finite-spin four-simplex amplitude to a quadratic reduction whose leading two-derivative metric operator is the linearised Einstein–Hilbert one, reproducing the Dittrich–Kogios p² coefficient to about one part in 10⁶.
Scope, as stated in the paper: Riemannian signature, coherent nondegenerate boundary data, admissible large spin, the near-flat fluctuation ball, a selected local branch, quadratic order. It does not claim Lorentzian completion, nonlinear or generic-background dynamics, a UV definition, universal finiteness, or a graviton propagator; those are listed as open problems.
Oriented Area-Regge Asymptotics of a Native Four-Simplex Vertex Published
19 September 2026. Leading large-spin asymptotics of a single orientation-resolved vertex with the full tetrahedral intertwiner geometry retained.
Scope: one vertex, leading order. No refinement or continuum limit, no bulk-spin-sum control, no Lorentzian or nonlinear dynamics, and no derivation of four-dimensional general relativity.
Accepted results
Two results have passed a fresh review by an agent that did not write them. Acceptance is bound to an exact commit: any scientific edit to that commit voids it. Acceptance here is not promotion into canonical state, and neither result bears on quantum gravity.
Positive wedge-toggle kinetics give a dense condensate Accepted
The unrestricted ground sector of the declared positive wedge-toggle Hamiltonian is connected, and asymptotically dense with one-edge density 5/6 — not the sparse, manifold-like geometry such a rule was built to produce. This kills a natural dense-phase architecture. It does not solve, or bear on, quantum gravity.
An exact finite weak conservation identity Accepted
A properly declared fixed-incidence discrete conservation ledger has an exact finite weak identity, with a correctly scoped conditional interface to continuum weak balance. Six continuum hypotheses are stated and left undischarged, which is the honest limit of the result.
Working papers
Written up and readable, but not through review. The locality paper below is pre-publication; its framing was deliberately weakened twice in response to an external reviewer.
Nearest-neighbour terms are not sufficient for locality Draft
An exact short-time obstruction from a conditional register coupling, with the global constraint exonerated. Stated as "not sufficient for locality" rather than "not local": a fixed Taylor coefficient does not support an asymptotic no-cone claim, because higher orders may depend on system size. Nine claims made during this work were retracted.
The commutant of an instantaneous algebra need not be the redundancy of the process it generates Draft
An instantaneous algebra is not a predictively sufficient process description. In an exact finite model, 26 candidate gradings give no exact descents and 17 modified laws are informationally complete. Section 6 separates three senses of "reduction" that had been running together — exact descent, informational completeness of a modified law, and reconstruction from sufficient boundary data — which is what released the manuscript for circulation.
Independently checked, not accepted
Reproduced by an agent other than the author, but without a fresh review. These are the strongest results that are not yet banked, and they should be read as promising rather than settled.
A predictive cut invisible to the compressed algebra Checked
Eleven of eleven preregistered checks reproduced an integer coefficient exactly. The load-bearing observation is a counterexample inside the singlet sector: an intervention invisible to the compressed algebra still changes a later permitted readout. A compression that looks lossless instantaneously is not lossless for the continuing process.
Span of the declared process class Checked
The declared process class spans 100 directions, and 25 on the reduced description. Register-only measurement is informationally complete when coupled and collapses to 2 when uncoupled. Verified 17 of 17 against an external collaborator's independent computation.
Reduce-then-glue against compose-then-reduce Checked
Both sides were frozen before being compared — a blind split — and agreed exactly. Neutral charge-dephasing loses 32 directions, with an operational witness: two states with identical neutral data separate at a finite time. The obstruction is real and measurable, not an artefact of bookkeeping.
Verification of other people's results
Work done here to check a published result. The finding belongs to whoever published it first; this section exists so that a verification is never mistaken for a discovery.
A counterexample to the Jacobian conjecture, verified Verification
The counterexample to the Jacobian conjecture in dimension three was presented publicly by Levent Alpöge on 19 July 2026 and is credited to Claude Fable 5. It was reproduced and checked here six independent ways, including two by hand, two days after the public announcement. It is a genuine counterexample and it is not ours.
Withdrawn claims
Claims that were made here and then withdrawn. They are published because a research record that shows only the surviving claims is not a research record.
Thirteen withdrawn claims, with reasons Retracted
Four claims about quotient admissibility were withdrawn on 8 September 2026 — all four from one cause, an attempt to read a decomposition off the generators, where it is not visible. Nine more were withdrawn during the locality work. Each is listed with what killed it, and with the weaker statement that survived.
Parked, blocked and retired
Lanes that are not currently moving. Each is listed with the reason it stopped, because "no result" and "stopped for a stated reason" are different facts.
Quantum gravity sandbox — collapse, conservation and UV no-go Parked
Collapse/conservation experiments, CSL energy balance, relativistic particle energy martingales and a relativistic scalar UV no-go, each with a preregistration and a Python verifier. Parked since late July 2026. The decision on the last open gate was revise, and one analytic route was inconclusive because every exact bound was trivial.
Riemann sandbox — prime phase controls Parked
Three preregistered experiments from March 2026: a prime holonomy spectral sandbox, a twisted prime first experiment, and a phase rigidity sweep. Preregistrations and controls exist; the lane has not been revisited.
Predictive-model equivalence Blocked
Stopped on a named obstacle: the computational method required for one step is not available, so the step is recorded as blocked rather than attempted badly.
Sovereign Lattice Hypothesis Retired
Retired, not paused. Its physical content is a measured null on the corrected E8 lattice with a validated instrument. A null that is recorded and closed is a result; the lane is not being reopened, and no bridge from it to current work is supported.
Frozen preregistrations Parked
Twenty-four preregistrations are written, frozen and unexecuted. They are kept frozen so that if any is run later, the hypothesis and success criteria cannot have been adjusted after seeing the data.
On how this work is checked. Several results here were cross-checked by more than one AI system working independently, sometimes with implementations frozen before comparison. That catches real errors — it caught several, and thirteen claims were withdrawn as a result. It is not peer review, and it is not a substitute for it. No external expert has reviewed any of this work, and the accepted results are exploratory: they are bound to a commit and a declared model, not promoted into any canonical state.