An independent nonprofit research institute in Austin, Texas.
We are deriving reality.
Physics describes what happens. We ask why it has to happen that way. We start from three facts that every question already uses and prove what follows, each result under its stated conditions. One public list holds what reality has to account for. Each result is marked on it as it is derived.
- Start with the overview
- Watch the film
- Read the foundation paper
The Forced Core of Physical Reality. Manuscript (PDF), not yet peer reviewed.
The list today One square for each thing reality has to account for.
681
of 4,280 derived, in full or given a stated premise.Counted from the public record, 11 November 2026, 12:53 AM CT
- 78 derived in full
- 603 derived, given a premise
- 725 partly derived
- 28 open walls
- 2,846 not yet derived
78 are derived in full and 603 given a stated premise.
The list runs outward in its own order, from its first domain at the centre to its last at the edge. Point at a square to see its name; select it to open it on the map.
Every square is placed and counted in your browser by 705 bytes of machine code. Read them
Our mission
Derive all of reality.
Every square is one thing the structure of reality has to account for, from counting and the golden ratio to proteins and minds. A square fills in when its result is derived from the foundation.
The institute’s objective is to derive reality and to use that understanding for the greatest human benefit.
One square for each thing reality has to account for, from counting to minds, in the order of the list. 15.9% are derived, in full or given a premise; grey squares are not yet derived.
A square counts as derived when it is derived in full or derived given a stated premise. Derived in full means proved in full from the foundation. Partly derived means part of the result is proved. An open wall is a question the foundation does not decide: two models agree on everything below it and differ there. The list grows as the work reaches new ground, so the share can fall when squares are added.
Open the mapFilm
The idea, in a film.
Where the derivation starts
Five answers, each the only one its conditions allow.
Recognition Science is the discovered architecture of reality. Reality has one forced shape. A recognition is one thing told from another: a comparison actually made. Recognition Science starts from three facts that every question already uses, adds the stated conditions of each part of that shape, and proves that under them only one answer is possible. We follow that shape into gravity, matter, morality and meaning.
The three facts
- Some things can be told apart.
- Comparing two readings needs both.
- Reading an old record is a new event.
The first answers, computed in your browser. The five answers below are computed now by this page’s own machine code, 705 bytes in all. The ratio, the dimension and the eight come from one function that takes no input: there is nothing in it to set. The cost is computed at the ratios shown, and the count is of the public list.
Run 1
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01 · Counting
4,280
squares on the list, counted one at a time.
Counting has one arithmetic.
Start empty, always add one more mark, reach every count in finitely many steps and never repeat one: every such system has the same arithmetic (Dedekind, 1888).
On the list: Natural numbers from iterated distinction · Derived in full
Its bytes
20 01 2d 00 80 20 41 02 74 22 02 20 02 28 02 40 41 01 6a 36 02 40 20 01 41 01 6a 21 01 41 00 20 01 36 02 54 41 00 28 02 40 41 00 28 02 44 6aThey walk the record of the list and add one for each square. Every count of the list on this page comes from them.
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02 · The cost
0.25
is J(2), and J(½) is 0.25: twice and half cost the same. J(1) is 0: only a match costs nothing.
A comparison has one cost.
J(x) = ½(x + 1/x) − 1
J is the only cost of a positive ratio x that obeys both the rule for combining comparisons, J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y), and the calibration at a match: near x = 1 the cost is ½(ln x)² to leading order. It follows that twice and half cost the same, the cost is never negative, and only a match costs nothing.
On the list: Uniqueness of the cost function J · Derived in full
Its bytes
20 00 44 00 00 00 00 00 00 f0 3f 20 00 a3 a0 44 00 00 00 00 00 00 e0 3f a2 44 00 00 00 00 00 00 f0 3f a1They take a ratio x and return x plus its mirror 1/x, halved, less one.
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03 · The golden ratio
1.6180339887
is φ, reached in 52 halvings. One step of that ladder costs J(φ) = 0.1180339887.
One ratio lets the levels join.
λ² = λ + 1
Positive levels that grow by one fixed ratio, with level 2 the sum of levels 0 and 1: the ratio solves λ² = λ + 1, whose one positive root is φ.
On the list: Golden ratio forced by self-similar ladder · Derived in full
Its bytes
44 00 00 00 00 00 00 f0 3f 21 00 44 00 00 00 00 00 00 00 40 21 01 20 00 20 01 a0 44 00 00 00 00 00 00 e0 3f a2 22 02 20 03 41 01 6a 21 03 20 02 20 02 a2 44 00 00 00 00 00 00 f0 3f 20 02 a0 63 04 40 20 02 21 00 05 20 02 21 01 0b 41 00 20 01 39 03 00 41 00 20 03 36 02 1cThey try the ratio halfway between 1 and 2 and compare level 2 with the join of levels 0 and 1. If level 2 falls short the ratio is larger, and if not it is no larger; they halve the interval that way until it cannot be halved again.
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04 · Space
3
dimensions.
Two loops stay linked only in three dimensions.
In a closed space without one-dimensional holes, a lasting pair of loops can wind through each other a nonzero number of times, a count no bending changes while the loops stay apart, only in three dimensions.
On the list: Three dimensions forced by linking · Derived in full
Its bytes
03 40 20 04 41 01 6a 22 04 41 02 6b 41 01 47 0d 00 0b 41 00 20 04 36 02 10They count dimensions up from one. In D dimensions, what a loop can be linked with has D − 2 dimensions: a pair of points on a flat sheet, a closed surface in four dimensions. They stop where it is another loop.
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05 · Eight states
8
settings of 3 switches, each visited once, and home again in 8 ticks.
Three switches, eight states, eight ticks.
Give each of the three dimensions one on/off switch: 2 × 2 × 2 = 8 settings. Each tick flips one switch, so the shortest pass through all eight settings and home takes eight ticks.
On the list: Eight-tick cycle from the 3-cube · Derived in full
Its bytes
03 40 20 05 41 01 6a 22 05 68 22 07 20 04 41 01 6b 22 08 20 07 20 08 49 1b 21 07 20 06 41 01 20 07 74 73 22 06 41 01 20 06 74 20 09 72 21 09 0d 00 0b 41 00 20 05 36 02 18 41 00 20 09 69 36 02 14They flip one switch at each tick, mark every setting they reach, and count the ticks until every switch is off again.
Research
Peer-reviewed and published papers.
Each designed page shows one paper’s result working in your browser.
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.
Our Science
Feature pages.
Each of these pages states one part of the structure, shows it working live and names the conditions it rests on.
Featured
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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.
Watch the film and explore The Actuals
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Mathematics
δ is the mathematics that distinction forces.
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.
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Gravity
Gravity from a lattice of events.
Events are records on a four-dimensional lattice. At long wavelengths, its 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 metric at which each step runs at light speed.
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Simulation
Every lawful history of one recognizer, computed exactly.
A recognizer is any system that makes comparisons. We run the recognition law forward from the empty record, carrying every history the law allows.
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.
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 first answers, in 705 bytes of machine code.
This page does not only describe the derivation. It computes its first five answers in front of you, each from the condition that fixes it. The 705 bytes below compute those answers, find the golden turn from the ratio, give every square of the list its place and count the list, status by status. Each answer’s value in “Where the derivation starts” and every count of the list on this page comes out of them. The proofs that each answer is the only one its conditions allow are in the worked examples on the overview.
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 ratio, the dimension and the eight takes no input: its signature, the three bytes on black below, says no parameters and no results.
The page is laid out by what the bytes return. On a wide screen the words and the list share the width in the ratio 1 to φ. On every screen 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.
Dark bytes do the step named in front of them. Grey bytes are the frame: the file’s header, the loops and the ends.
Counting
One is added for each square, and one for its status.
The cost
For any ratio; and once inside the first steps, at the golden ratio.
The golden ratio
Halve the interval until level 2 meets the join of levels 0 and 1.
Space
Count dimensions up to the one in which a loop can be linked with a loop.
Eight states
Walk the settings of the switches, one flip per tick, and count the ticks home.
The golden turn
1/φ² of a full turn, built out of halved quarter turns.
A place for every square
Square k sits the square root of k from the centre, one golden turn on from the last.