The whole corpus in one place — the ten-paper spine that builds the framework step by step, then the foundation texts and the extensions that carry it into the electroweak sector, the dark sector, lattice Yang–Mills, thermodynamics, and the horizon. Each entry says what the paper does in plain English, with a link to read it in full on Zenodo and, where one exists, the code behind it. Concept DOIs always resolve to the latest version.
Most results in the program are published twice. The main paper is the argument — it states the claim, walks the reasoning in plain prose, and gives proof sketches with pointers into the formal layer. It is meant to be read start to finish.
The Technical Supplement is the proof — the proof-dense, canonical layer where each theorem is stated and discharged in full. It is the source of truth; formal corrections flow from the supplement back to the paper, never the other way. Read the paper to see what is claimed and why; open the supplement when you want to check that it holds. On Zenodo the two are deposited separately, the supplement linked to its paper via isSupplementTo.
The spine of the program is ten short papers, each building on the one before. Here is the core of each in a few sentences — with a link to read it in full, and the code behind all of them on GitHub.
Start with a plain criterion: a physical difference is real only if the world can hold it in place against disturbance, and holding it costs something. Most differences can be defended one at a time. But some pairs cannot — defending both at once costs more than defending each alone, and the order you do it in changes what budget is left over.
That order-sensitivity is the crack quantum mechanics grows from. When the order of two operations changes the outcome, the accounting can no longer be ordinary commuting arithmetic; it has to be the non-commuting kind quantum theory uses. Paper 1 makes the link precise and shows where the familiar complex Hilbert space starts to appear.
Demands that are each affordable on their own can overspend when they meet at the same interface — the budget simply does not add up. Paper 2 calls this non-closure and shows it is the engine behind competition and structure throughout the framework.
Non-closure cannot be carried by simple additive symmetry; it forces the richer, non-abelian kind. Working through every compact simple Lie algebra leaves only SU(3) × SU(2) × U(1), and the cheapest version has three colours. A filtered scan of thousands of candidate matter contents leaves exactly one survivor: the Standard Model's 45 fermions. Counting the channels gives a fixed budget of 61 — which in turn sets the cosmic energy split, about 69% dark energy and the rest matter.
Paper 2 gave the space its rooms; Paper 3 gives it a direction. Once a distinction is recorded by spreading into its surroundings, no local action can pull it back. That irreversibility is the arrow of time — derived here, not assumed as a boundary condition.
Along the way entropy gets a concrete meaning: it is the capacity currently tied up in the correlations an interface is holding. The familiar laws of thermodynamics follow as corollaries, and the rule that physical evolution must be “completely positive” — usually taken as an axiom — becomes a theorem.
Why three families of matter, and not two or four? Paper 4 turns it into a budget question: each generation costs a fixed amount of capacity, and three fit under the ceiling while a fourth would overflow it.
The same accounting pins the weak mixing angle at 3/13 — within 0.2% of the measured value — as the stable point of a competition between two sectors, fixes the full Standard-Model matter content as the one anomaly-free option that survives out of thousands, and reframes dark matter not as a missing particle but as a geometric correlation the ledger requires.
Paper 1 showed why the accounting must be non-commuting; Paper 5 builds the rest of quantum mechanics on top of it. Hilbert space, the Born rule for probabilities, tensor products for combining systems, and the rules for how states evolve all come out as the cheapest consistent way to keep the books where joint distinctions cannot be separated.
Two payoffs stand out. The reason quantum theory uses complex numbers — rather than real or quaternionic ones — is derived, not chosen. And measurement stops being a mysterious “collapse”: it is simply a change in which bookkeeping scheme is in force.
Where do space, time, and gravity come from? Paper 6 treats geometry as bookkeeping: the distance between two things is the least cost of correlating them, and curvature is what appears where capacity varies from place to place. Run this in four dimensions and Einstein's equations emerge as the only consistent closure.
The picture also says where ordinary physics stops. Smooth equations of motion hold only in well-behaved regimes; at a horizon, at saturation, or the moment a record locks in, the equations give out — even though the underlying accounting still makes sense.
Physics is usually summarised by a Lagrangian — a single expression you write down and then take on faith. Paper 7 derives it instead. It first shows that any step leaving an irreversible record must cost at least a fixed minimum; identify that minimum with action and it is Planck's constant.
Then comes the central identity: the framework's partition function turns out to be the same object as Connes' spectral action from non-commutative geometry. Expanding it term by term hands back the cosmological constant, Einstein–Hilbert gravity, the gauge field terms, and the Higgs potential as separate coefficients. The Standard-Model Lagrangian is not postulated — it is read off.
Paper 8 is where the single ledger ties the very small to the very large. The same budget of 61 channels that fixes the Standard Model also partitions the cosmos: ordinary matter, dark matter, and dark energy come out as 3, 16, and 42 parts of 61 — roughly 5%, 26%, and 69%.
From the same accounting it reads off a value for the dark-energy density, a Hubble constant near 70 (sitting between the two clashing measurements), and a formula for the temperature of the cosmic microwave background that matches to a third of a percent. One integer, two interfaces — the particle world and the universe at large.
Paper 9 asks, carefully, what it would take to get general relativity's weak-field predictions out of the cost-of-comparison picture. It lays out a sequence of gates a derivation has to pass and shows that the “clock” part already recovers the gravitational redshift around a mass.
It is also candid about the gap: recovering the redshift alone does not yet fix the “ruler” part, and it names the exact remaining theorem that would close it. This is the framework showing its work — a real result paired with an explicit open target.
Paper 10 is the grammar underneath everything else. Its single primitive is a continuation: in a given context, one distinction is allowed to continue as another within a capacity budget. Everything is then phrased in that language — a field is an equilibrium pattern of where the substrate carries a continuation, gauge symmetry is relabelling that preserves it, entropy is its irreversible blurring, and dynamics is the selection among allowed continuations.
It does not prove the downstream theorems by itself. It supplies the common vocabulary and the discipline by which every later branch has to be checked.
The overview and the self-contained core; the runnable engine; and the extension papers where the framework meets the electroweak and dark sectors, lattice Yang–Mills, thermodynamics, and the horizon.
The narrative layer of the whole program. What the framework takes physics to be built on, what each commitment does, and what the technical papers derive from it — written for a reader who wants the picture before the proofs. The gentlest way in.
The shortest self-contained statement of the foundation — the framework reduced to its load-bearing core, for a reader who wants the spine without the scaffolding.
Why do utterly different systems fall into the same handful of behaviours? Paper 11 argues universality is forced: once admissibility is capacity-bounded, the available large-scale patterns collapse to a small set, almost independent of microscopic detail.
What happens when the memoryless assumption fails — when an interface's past can no longer be summarised by its present. Paper 16 locates that breakdown precisely and traces how the genuinely hard problems live exactly where the Markov property gives out.
The capacity-equilibrium treatment of the electroweak sector — the gauge-channel competition whose stable fixed point the weak angle sits at, and the forward strong-coupling prediction α_s(M_Z) = 0.1179 it implies.
A study of the proof structure as an object in its own right — the dependency graph of every derived result, its load-bearing joints, and how strongly the whole edifice holds when any single piece is removed.
Not a manuscript but a program. Thousands of registered checks tie the one assumption to every derived constant, each tagged by how strongly it is established — and you can run the full verification suite yourself in under a minute.
Foundations for the recruitment radius: how far an interface can reach to enlist capacity in holding a distinction in place, and what that range fixes for the structure built on top of it.
Where absolute mass scales come from. Paper 28 reads the electroweak scale off the point at which capacity saturates — fixing the size of masses, not only their ratios — up to the single dimensional anchor the framework takes from gravity.
Part of the rigorous lattice Yang–Mills program: why the dominant contribution organises around a particular representation, and how quark confinement follows from it.
A mechanism for the Yang–Mills mass gap on the lattice — the flux-tube picture that gives the gap its scale, a piece of one of the Clay Millennium problems approached from the capacity ledger.
The reflection-positivity and Osterwalder–Schrader structure that lets a lattice theory be continued to a sensible relativistic quantum field theory — the analytic backbone under the confinement and mass-gap results.
The bridge from the framework's internal, trace-level quantities to the physical, scheme-dependent masses experimentalists actually report — built so that every export is auditable, route by route, rather than asserted.
Dark matter and dark energy treated as two roles the same capacity budget plays, rather than two new substances — carrying a parameter-free equation-of-state prediction the program stakes itself on against current and coming surveys.
Temperature, entropy, and the laws of thermodynamics for a system whose distinctions are finite and costly to maintain. The bounded-ledger thermodynamics that sits between perfect symmetry and the empty void — including the regime that admits negative temperature.
Black-hole and cosmological horizons read as ledgers of continuation — where horizon entropy, the Page-curve turnover, and the status of the interior all follow from how a finite horizon books what crosses it.
The full, self-contained derivation that the weak mixing angle is not free: sin²θ_W = 3/13 from the capacity ledger — the sharpest standalone statement of the result and its ~0.2% match to measurement.