An independent nonprofit research institute in Austin, Texas.
We are deriving reality.
In the film Select a part to play it with sound.
Physics describes what happens. We ask why it has to happen that way. We start from a fact that every question already uses, that some things can be told apart, and prove what follows, each result under its stated conditions.
961
of the 4,310 things on our public list are derived, in full or given a stated premise.
Counted from the public record, 13 November 2026, 11:23 PM CT
58 are derived in full and 903 given a stated premise.
About this count
The count. The list holds every thing the structure of reality has to account for, from counting and the golden ratio to proteins and minds. A thing is counted as derived when its result is proved in full from the foundation, or proved given a stated premise. Open the list · What the colours mean, on the map
- 58 derived in full Proved in full from the foundation.
- 903 derived, given a premise Proved, given a stated premise.
- 1,574 partly derived Part of the result is proved.
- 26 open walls The foundation does not decide this. Two models agree on everything below it and differ here.
- 1,749 not yet derived The work has not reached this item yet.
The stamp. The round stamp beside the count is the whole list drawn as squares, one for each thing, in the colours above. It runs outward in the list’s own order: its first domain, Foundations and mathematics, is at the centre and its last, Mind and society, is at the edge.
Every square is placed and counted in your browser by 735 bytes of machine code. Why machine code: so that nothing is hidden. The bytes are printed in full at the foot of this page, and this count comes out of them. Read them
Four charges and four masses go in. The measured number comes out.
The four particles are settling into their lowest state. The number is counted once they have.
What went in: four charges and four masses. What was fitted: nothing. What came out: the hold between two atoms, on the value that was measured.
How this is computed, and the measured values
Two protons and two electrons, with Coulomb’s law between every pair and nothing else. All four are treated as quantum particles, the nuclei included, and their lowest state is found by diffusion Monte Carlo, a method that is exact for this molecule apart from its statistical interval (shown, at 95%) and a time step whose effect here is smaller than that interval. Heavier nuclei sit lower in the same hold, which is why the bond of heavy hydrogen is stronger. Measured values: the dissociation energies of H₂, HD and D₂ by laser spectroscopy (Liu and co-workers 2009 and 2010; Sprecher and co-workers 2010). The corrections this law leaves out (relativity and the radiation field) move these numbers by about 0.002 kcal/mol.
Recognition Science starts from one fact: some things can be told apart. Coulomb’s law, the only law in this computation, is on the map of what follows from that fact, derived given a premise the map names. Here the law runs on the smallest molecule there is, with nothing fitted, and it lands on the measurement.
Research
Peer-reviewed and published papers.
Each designed page shows one paper’s result working in your browser. It also tells you the question the paper answers and who asked it first, and says what the result means for the structure of reality.
The journals: The Journal of Chemical Physics, Journal of Statistical Mechanics: Theory and Experiment, AIP Advances, Entropy, Mathematics, Advances in Pure Mathematics, Symmetry, Molecules, Axioms, Mathematical and Computational Applications and Foundations.
Where the work meets measurement
Each of these four pages sets what a paper computes beside measurements.
Symmetry (MDPI), 2026
Matter and mind run on one cube.
A peer-reviewed paper puts the electron, the muon and the tau on one golden ladder and reads their steps, in whole rungs, off a cube: its eleven idle edges, then its six faces. Measured, the steps are just over eleven rungs and just under six.
arXiv, 2025 (preprint)
Twelve masses on one golden ladder.
Mass is the price of holding a pattern. This preprint extends the lepton ladder to all twelve masses, counted from a cube, and shows where the count holds and where it fails.
Symmetry (MDPI), 2026
Every noble gas sits at balance, where the one cost of reality is zero.
One coordinate, measured from the noble gases; one cost curve, zero at every noble gas; four atomic properties checked against NIST and Pearson data.
Entropy (MDPI), 2026
Gravity is the books balancing.
The price every comparison pays, added up across space. A peer-reviewed paper gets Newton's law from double-entry books with one price for a mismatch, with G taken from measurement.
Long-form manuscripts
Book-length works from Recognition Science. Each follows one question and keeps the conditions of its results with them.
Cambrian
Our program for discovering new theorems, which ran until 6 November 2026. It joined pairs of proved results from the institute’s library of theorems into new claims; in its last week it settled ten problems the library had listed as open. That library is the institute’s machine-checked library of mathematics and physics; on 6 November 2026 Cambrian drew on 421,993 proved statements from it.
Our people
Different disciplines. A shared ambition.
Our work connects mathematical foundations with molecules, plasmas, light and computation. The team brings the expertise needed to move between a formal result and a physical experiment.
Our Science · Feature pages
One part of the structure on each page, working live.
Eight pages. Each takes one part of the structure and shows it at work.
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A lattice of events
Gravity
Every event is a record, the records form a four-dimensional lattice (a grid of sites), and gravity is the shape of that record.
At long wavelengths the lattice’s weak waves obey Einstein’s linearized equations and travel on the light cone: proved at κ = 1, the value of the one free number in the lattice’s bond lengths (what general relativity calls its metric) at which each step runs at light speed.
Watch the film and run the simulations
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From the empty record
Simulation
Earlier simulations of nature started from measured numbers, or from rules someone chose. This one starts from a law that could not be otherwise.
It runs that law forward from the empty record, the record before the first event, and carries every history the law allows. After eight ticks there are 1,679,616, and every one is drawn on the page.
Watch the film and open the simulation
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Mathematics · Morality · Meaning
The Actuals
Mathematics, morality and meaning are built into reality: physical structures forced by the same act that forces physics.
That act is telling two things apart. What is forced has exactly one form, and nothing else can do its work. That is what earns it the word the.
Watch the film and explore The Actuals
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Before the first event
Universe Formation
If the universe began, it began from balance, not from nothing.
Under one premise, the start is the empty books: every account at zero, because nothing is written yet. The page follows how the universe forms from there, step by step, and says what is proved, on which premises, and where the derivation stops.
Watch the film and follow the steps
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δ · Actual mathematics
Mathematics
δ is the mathematics that distinction forces.
Recognition Science derives physics from distinction. δ derives, from that same distinction, the mathematics physics is written in. From one repeatable act, telling two things apart, it builds arithmetic, the integers, the ratios and the line of real numbers. Every proof in it carries its price: the principles it uses beyond what distinction forces.
Watch the film and explore δ
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From a circle to everything
The Shape of Logic
Reality has one shape, and it is forced. The same structure that makes a circle round is the structure of everything there is.
In ten steps, each the only answer its question allows, it runs from a single circle out to the whole of what exists. The film puts those ten steps in the recorded voices of the people who first asked them.
Watch the film and walk the ten steps
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A ride · Three minutes, with sound
Recognition Boundary Theory
You are not your body. The past still exists. One record, many windows.
This page is a ride through those three statements, not an article about them. It runs for three minutes, with sound, on your own device. It can use your camera, and nothing leaves the device.
Take the ride
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The moral law, running live
Morality
Right and wrong are physics. The moral law is part of the structure of reality, as real as gravity and light.
Every wisdom tradition saw it. It can now be written down exactly, and it says they were right. The page runs the law on a working record of 144 people, and you are inside it.
Watch the film and run the law
Where the derivation starts See the five answers work
Collaborate with us
Bring a question worth solving.
Research together
Bring a mathematical idea or an experiment that could advance the work.
Discuss a research ideaExplore a partnership
Find where our work in medicine or quantum computing could connect with yours.
Start a conversationThe engine of this page
The count at the top of this page, in 735 bytes of machine code.
In plain words: these are the bytes that count the list for the top of this page, printed in full so that nothing is hidden. The count beside the film comes out of them, and so does the place of every square in its stamp.
The 735 bytes below compute the first five answers of the derivation, each from the condition that fixes it, find the golden turn from the ratio, give every square of the list its place and count the list, status by status. The page is laid out by the ratio they find. The five answers are shown working, one at a time, on a page of their own. The proofs that each answer is the only one its conditions allow are in the worked examples on the overview.
More about the bytes: how they are written, the two values typed into them, and how they lay out the page
They are written directly as WebAssembly bytes, the machine code of the virtual machine built into every modern browser, with no compiler and no library. Your browser runs exactly these bytes. The function that computes the first answers takes no input: its signature, the three bytes on black below, says no parameters and no results.
Two values are typed into the instructions: a 0 and a 1. They are the five bytes on black where that function begins: put a 0, put a 1, do they differ? They are compared once and never used again. The unit, two, the half, every count and every ratio are made from the answer. Every other number an instruction carries is an address, where to read or write, or part of the instruction’s own form.
The page is laid out by what the bytes return. On a wide screen the words and the film share the width in the ratio 1 to φ. In the stamp beside the count each square of the list sits one golden turn, 1/φ² of a full turn, on from the square before it, at a distance that grows as the square root of its place in the list. Both φ and the turn are found by the bytes before the page is drawn.
A short script on this page, with no library, can carry out these same bytes one instruction at a time. It takes over on a device that declines WebAssembly. Otherwise your browser’s own engine runs them at full speed.
- 282bytes: the first answers, one function with no input
- 28bytes: the cost of a comparison
- 121bytes: counting the list
- 219bytes: a place for every square
- 85bytes: the frame, which is the file’s header, the four signatures and the names
- 735bytes in all
Dark bytes do the step named in front of them. Grey bytes are the frame: the file’s header, the loops and the ends. Bytes on black are the signature that says no input, and the two typed-in values.
The eight annotated listings: every instruction of the 735 bytes, with what it does
00 · The distinction
Two things, a 0 and a 1, told apart. The answer is the mark.
01 · Counting
Two, the unit, two units and a half, all made from the mark.
02 · The cost
For any ratio. The run takes it at two, at a half and at a match.
The cost itself
03 · The golden ratio
Halve the interval until level 2 meets the join of levels 0 and 1; then the cost of one step, and the golden turn.
04 · Space
Count dimensions up to the one in which a loop can be linked with a loop.
05 · Eight states
Walk the settings of the switches, one flip per tick, and count the ticks home.
Counting the list
One mark is added for each square, and one for its status.
A place for every square
The golden turn, built out of halved quarter turns; then square k sits the square root of k from the centre, one golden turn on from the last.