THE OPEN PROGRAMME

In ordinary physics, everything happens in space. Objects have positions, distances between them are given, and the stage exists before the play starts. The framework this laboratory works on turns that around. It begins with nothing but a collection of things and, for each pair, a single number saying how strongly they are related — how much knowing about one tells you about the other. Distance is then defined out of those numbers: strongly related means close together, weakly related means far apart. Space is not the stage. Space is the summary.

That sounds like a word game until you ask the obvious follow-up. Does the thing you get out actually behave like space? Real space has three directions you can walk in. It bends near heavy objects. It has one-way surfaces around black holes. Does the summary do any of that? Those are calculations rather than opinions, and most of the paper now under review consists of them.

The reason anyone would attempt this is that our two best theories do not fit together. Quantum mechanics is superb for the very small, general relativity is superb for the very heavy, and put in the same room they contradict each other. One long-standing suspicion is that space and time are not fundamental at all but approximate descriptions — in the way that temperature is an approximate description of an enormous number of molecules bumping into one another. Temperature is real and useful, and yet a single molecule does not have one. Perhaps distance is like that.

If it is, there should be some scale at which the approximation starts to fail — where space stops behaving like space. The most quotable prediction this framework ever made was about exactly that: a particular measurable quantity was supposed to change abruptly at that scale, like a step. Over the past year the prediction was tested three separate ways. It failed all three. Then the reason it had to fail turned up, and the reason was more interesting than the prediction had been.

The rest of this page is that story, followed by an inventory: what is actually established, what is stuck, and what would have to happen before any of it deserves to be called physics rather than mathematics with ambitions.

The submitted article is deliberately narrow. It sets out a kinematic framework: a positive semi-definite correlation kernel on a constraint space, a smoothing projection, and a reconstruction that reads geometric quantities — a distance surrogate, a spectral dimension — out of the resulting correlator wherever stated admissibility conditions hold. It carries a register of six falsifiable commitments — each with an envelope, an instrument, a condition for being decidable, and a stated falsification rule — plus a Planck-2018 MCMC analysis and an explicit list of what the framework cannot do. Older material of this programme circulated a twenty-nine item prediction registry; that belonged to a monolithic submission which was desk-rejected, several of its entries depended on the step retired in 2026, and it is superseded. It was submitted to Foundations of Physics on 17 July 2026 and the submission directory has been frozen since. The archived release carries a persistent DOI; the files inside it are covered by the release's SHA-256 manifests rather than by DOIs of their own.

What is not under review is everything interesting: an intrinsic dynamics, a matter sector, field equations, a Hawking sector, a derivation of the one calibrated number. Those live in a future-work programme of eighteen numbered items, of which two are gates that everything else waits behind. The programme is run under one rule inherited from the article: derive, verify numerically, register. No number reaches a manuscript without an executable script and a checksummed output. A second rule was added after the first year: every statement carries a register tag — [locked], [assumed], [derived], [open] — and the tags are enforced by review, not by intent.

This page is the public version of that internal record. It is not a summary of results, because the honest summary of the year is that the programme's single most cited claim was destroyed by the programme's own pre-registered tests, and the destruction turned out to be a theorem. That is the story worth telling.

One quantity needs explaining first, because everything in this section depends on it. There is a way to measure how many dimensions a space has without looking at it from outside: let something wander at random and ask how often it comes back to where it started. Wandering along a line, you return constantly. On a flat surface, less often. In three dimensions, less often still. The rate of return therefore encodes the dimension — and, crucially, it can be measured separately at each scale, by watching for a short time or a long time. That gives a dimension that is allowed to vary with the size you probe at. It is called the spectral dimension, it is a standard tool, and in several approaches to quantum gravity it drops below the familiar four as you look at smaller scales.

The framework's most quotable claim concerned the shape of that drop. It predicted a step: not a gentle slide but an abrupt jump across a critical scale, of archived height Δd_s ≈ 0.79, implying a short-scale dimension near 3.21. It was the kind of prediction a theory wants — sharp, unusual, and in principle measurable in laboratory analogue systems. It had also been carried through several manuscript generations without anyone re-running the construction that produced it.

Three campaigns were run to settle it, each with its specification, extraction rule and script hashed into a freeze manifest before any output existed.

Three independent negatives in a row is usually a sign that the question is wrong. It was. The resolution came from taking seriously an intuition that had been in the author's notes for months in informal form — it has to be smooth, because there is a finite signal speed — and asking what its formal version would be.

In the stationary setting the reconstructed correlator is the kernel convolved with the projection on both sides. In Fourier terms the kernel's spectral density is multiplied by a Gaussian factor. A spectral measure with Gaussian decay has a real-analytic Fourier transform. Therefore the observable correlator is real-analytic no matter how singular the underlying kernel or density is — a Heaviside threshold, a fractal profile, anything at all. Every derived object inherits that smoothness: the distance surrogate, the heat trace, the spectral-dimension curve.

The follow-up audit asked a question with a countable answer: taking the framework strictly as it stands — no new primitives, no new physical inputs — how many of its stated assumptions can be converted into derivations, demoted to conventions, or shown to be irreducible? Every assumption carried by the article, the cosmology ledger, the companion drafts and the locked instantiation was classified.

The net result, if every available elimination were executed: the locked instantiation's arbitrary content reduces to three numbers plus one empirical placement parameter. Everything else becomes derived, a maximum-entropy default, a gauge convention, or standard quantum-field scaffolding waiting on the matter interface. That is the honest floor this framework can reach without new physics — and naming the floor is more useful than claiming to be near it.

One elimination did not tidy the framework. It exposed a contradiction, and doing so was the most valuable single hour in the programme's year.

The cosmology pipeline carried an assumption about how the flow parameter maps to a cosmological clock. Inside the framework that identification is arguably not an assumption at all: the metric is defined from the correlator, so the scale factor is the correlation length by the reconstruction's own logic, and the correlation length grows diffusively. Eliminate the assumption honestly and the scale factor goes as the square root of flow time.

That is a radiation-like expansion: the deceleration parameter comes out at exactly 2. The entire spectrum calculation downstream had been run under a quasi-de Sitter condition with that parameter near 0.0175. The two cannot both hold. The emergence epoch cannot be the inflationary epoch under the framework's own clock.

Almost every open item in the programme waits behind one of two missing objects. Naming them precisely is what makes the rest of the roadmap honest rather than aspirational.

The strategy question was settled empirically. A single monolithic manuscript was tried across three generations and desk-rejected; the narrow, one-module-per-paper strategy survived editorial scrutiny. The programme therefore runs as a series, and seven companion notes exist as complete venue-neutral drafts. None has been submitted. No target journal has been chosen, no cover letter written, no styling applied — deliberately, while the framework paper is under review.

A seventh strand — quantum foundations, records, the Born rule — is recorded as a long-horizon item with a blunt internal note attached: needs real proofs. It is listed here because leaving it off would misrepresent the programme's ambitions, and including it without that note would misrepresent its state.

A register of six falsifiable commitments is only as good as the pipeline that would test them. The internal readiness audit is deliberately unflattering: for each observational item it records the current statement, whether a scaffold exists, whether data ingestion is possible, and the exact next gate. Most rows end at “author authorisation plus a pre-run specification and freeze manifest”, which is the correct place for them to end.

Against all of that, four results were executed, checksummed, and reproduced byte-for-byte. Three are mathematics that stands independently of whether the physical framework survives; the fourth is a governance result. Each has its own write-up.

Stated at the same resolution as the results, because a programme that publishes its gates has to publish them accurately.

Not “more predictions”. The register has six and the programme cannot currently test most of them. Progress means closing gates and reducing arbitrariness, in roughly this order:

The framework article's preprint, data package and code snapshot are public and citable. The future-work programme described above is internal working material and is published here in summary form; the executed results of section 09 have their own write-ups linked below.

As with the adjacent case study, the contributions that mattered most were the ones that removed a result.