An independent nonprofit research institute in Austin, Texas. Our science, Recognition Science, derives the forced structure of reality.
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.
- Start with the overview
- Read the foundation paper
The Forced Core of Physical Reality. Manuscript (PDF), not yet peer reviewed.
Every question already uses three facts
- Some things can be told apart. “The light is on” and “the light is off” say different things.
- Comparing two readings needs both. Yesterday’s reading has to be held until it is compared with today’s.
- Reading an old record is a new event. A log of everything up to noon does not contain your reading it at one o’clock.
Our mission
Derive all of reality.
We have listed everything the structure of reality has to account for, from counting and the golden ratio to proteins and minds. Each square below is one of them, and it fills in as its result is derived.
Derived so far
11.7%of the list derived
1.4%derived in full
Newly derived squares
+0today0in the last 7 days
- things to derive
- 3,999
- derived in full
- 28
- derived, given a premise
- 281
- partly derived
- 440
- open walls
- 19
Updated 8 November 2026, 8:48 AM CT
One square for each thing to derive, in the map’s order and grouped by domain. Grey squares are not yet derived. Point at a square to see its name; select it to open it on the map.
Open the mapResearch
Peer-reviewed and published papers.
Each designed page takes one paper’s central result: the question it answers and who asked it first, the result working in your browser, and what it means for the structure of reality.
Publication record, 2026
- Peer-reviewed journal papers
- 24
- Papers on arXiv
- 25
- Journals
- 11
- Publishers
- 4
Two of the 24 are accepted and in production.
Journal of Statistical Mechanics: Theory and Experiment, 2026Counting at a fixed average cost gives Boltzmann’s law.A Finite-State Gibbs Construction from a Recognition Cost
Mathematics (MDPI), 2026A connected network has one resting state for each twist its loops hold.Finite-Volume Stability and Flux Sectors in a Reciprocal Ratio Gradient Model on Graphs
Entropy (MDPI), 2026Gravity is the books balancing.A Discrete Informational Framework for Classical Gravity
Foundations (MDPI), 2026The universe keeps double-entry books.Coherent Comparison as Information Cost
Mathematics (MDPI), 2026Nobody set these numbers.A Coherence Theorem for Conserved Comparison Ledgers: Structural Axioms Pin Down the Scale, the Cost, and the Ratio
Axioms (MDPI), 2026Many things, priced along one direction.Multidimensional Cost Geometry
33 designed pages · 13 with films · 63 papers in all, with books, preprints and manuscripts
Long-form manuscripts
Book-length works from Recognition Science. Each follows one question at length 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 in your browser 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. That value is identified, not derived, and a massless quantum graviton is still open.
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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, in exact arithmetic, 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.
The forced shape in one view
Five answers, each the only one its conditions allow.
- 01 · Counting 0 → 1 → 2 → 3 → … 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).
- 02 · The cost J(x) = ½(x + 1/x) − 1 Given the rule for combining comparisons, F(xy) + F(x/y) = 2F(x)F(y) + 2F(x) + 2F(y), J is the only continuous cost F of a positive ratio x that is never negative and has unit curvature at a match. Twice and half cost the same; only a match costs nothing.
- 03 · The golden ratio φ = (1 + √5)/2 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 = 1.618…
- 04 · Space Three dimensions In a closed space without holes, one loop can wind through another a nonzero number of times, a count no bending changes while the loops stay apart, only in three dimensions.
- 05 · Eight states 2 × 2 × 2 = 8 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.
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Bring a question worth solving.
We welcome researchers and partners with a problem our science could help address, or an experiment that could put it to the test.
Research together
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Gifts from individuals and foundations fund research fellowships, experiments, open-access publication and independent critique of our work.
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