Recognition PhysicsInstitute, ATX

Recognition Physics Institute: one rule, everything else follows.

We don't ask you to believe it. Every claim is open, and a computer checks the proofs.

PhysicsMathematicsConsciousnessMoralityEconomics

We found one simple rule for how the universe stays in balance. From that single rule (and nothing else) you can work out the particles, the forces, even what a mind is and what's right and wrong. We don't tune any numbers to make it fit, and a computer checks every step.

Fig. 01: The whole ideahover to re-drop

Being out of balance costs more.This is the one cost, J(x) = ½(x + 1/x) − 1. It touches zero only at perfect balance, a ratio and its flip (2:1 and 1:2) cost exactly the same, and it blows up at either extreme. The ball always rolls to the bottom.

0numbers tuned to fit
1rule it's built from
checked by computer, step by step
11peer-reviewed papers

01Who we are

A focused team, working in the open

Physicists, mathematicians, and a chemist building and checking the framework, paper by paper and proof by proof.

Jonathan Washburn

Lead Scientist & Director

Found the one rule, starting from a simple thought: nothing can't even notice itself, so something (a difference) has to exist. Everything else grows from there. Leads the research program and writes the theory, the proofs, and the code.

Emma Tully

Chief Operating Officer

Leads operations across the institute, from research planning and budgets to partnerships and the publishing pipeline. Turns open scientific work into finished, peer-reviewed papers and keeps the institute's people, funding, and timelines moving in step.

Dr. Elshad Allahyarov

Research Scientist

Dr. Sci. Physics & Mathematics, General Physics Institute RAS & Heinrich-Heine University Düsseldorf

Brings decades of expertise in many-body systems, plasma physics, and advanced materials science. Senior Scientific Researcher at the Joint Institute for High Temperatures of the Russian Academy of Sciences since 1988.

Dr. Sebastian Pardo Guerra

Research Scientist

Ph.D. Pure Mathematics, UNAM

Bridges abstract mathematical frameworks with Recognition Science principles. His work in category theory and graph theory provides foundations for understanding information flow and emergent behavior. Postdoctoral work at UC San Diego in applied mathematics.

Dr. Megan Simons

Research Scientist

Ph.D. Theoretical and Computational Chemistry, Southern Methodist University

Applies Recognition Science principles to molecular and chemical systems, integrating quantum chemistry with data-driven modeling. Explores how recognition-theoretic frameworks describe complex molecular interactions and spectroscopic phenomena.

Dr. Anil Thapa

Research Scientist

Ph.D. Theoretical Physics, Colorado State University

Investigates frontier particle physics through the recognition framework (connections between neutrino physics, dark matter, and beyond-Standard-Model phenomena), integrating effective field theory with first-principles structure.

Dr. Philip Beltracchi

Research Scientist

Ph.D. Physics, University of Utah

General-relativistic astrophysicist working on compact objects and black-hole mimickers: gravastars, dark energy stars, and rotating anisotropic relativistic stars. First-author papers in Physical Review D and Classical and Quantum Gravity, with collaborators including Paolo Gondolo and Emil Mottola. Earlier work: first-principles modeling of perovskite photovoltaics and fullerene superconductors.

Dr. Bhaskar Roy Bardhan

Research Scientist

Ph.D. Physics, Louisiana State University · Postdoc, MIT

Quantum information scientist with 15+ years across academia, industry, and defense: quantum error correction, quantum communication capacities, and near-term quantum algorithms. Led Ford's quantum computing team on optimization for mobility and manufacturing, held research roles at Xanadu and Raytheon BBN, and published in Nature Photonics, Physical Review A, and IEEE Transactions on Information Theory. Co-author of a forthcoming book on continuous-variable quantum computation.

Dr. Shannon Ray

Research Scientist

Ph.D. Physics, Florida Atlantic University

Theoretical physicist in quantum information, quantum photonic processing, and computational geometry, with a background in general relativity. Former Air Force Research Laboratory postdoc and National Research Council Fellow; first-author work in Entropy (featured), Physical Review A (Editor's Suggestion), and Classical and Quantum Gravity, spanning quantum entropy measures, photonic device characterization, and isometric embeddings for numerical relativity.

Dr. Margaret Johnston

Research Scientist

Ph.D. Physics, University of Nevada Las Vegas

Applies statistical methods to rigorously identify robust trends in population data. Their research in gravitational waves proposes a particle representation of gravity and identifies the resulting impacts to cosmological measurement.

Dr. Agnieszka Jaron

Research Scientist

Ph.D. Theoretical Physics, University of Warsaw

Brings 30 years of expertise in AMO physics, chemical physics, and computational physics. Associate Research Professor and PI at the University of Colorado Boulder (JILA) for 16 years, leading NSF- and DoD-funded programs and supervising 15+ PhD researchers. Recipient of the Alexander von Humboldt Research Fellowship, NATO Advanced Science Fellowship, and Max Planck Institute for Complex Systems Fellowship.

Dr. Roman Shugayev

Research ScientistFusion

Ph.D. Electrical Engineering, Purdue University

RF and plasma engineer whose work spans fusion reactor systems, semiconductor plasma equipment, and integrated quantum photonics. Built and operated the diagnostic neutral-beam ion accelerator at MIT's Alcator C-Mod fusion reactor, and has since led plasma-electromagnetics and quantum-sensing programs across national laboratories and industry.

Dr. Dylan Funk

Research ScientistFusion

Ph.D. Physics, Auburn University

Plasma physicist specializing in computational modeling, extended magnetohydrodynamics, and dusty plasma theory. Developed theoretical and simulation methods for dust charge in magnetized and strongly coupled plasmas.

Dr. Sajid Ahmed

Research ScientistFusion

Ph.D. Aerospace Engineering and Mechanics, The University of Alabama

Aerospace engineer and plasma scientist with expertise in magnetized low-temperature plasmas, diagnostics, and computational techniques. Designed computational models and integrated experiments to study instability-driven behavior and electron transport.

02The record

Published & peer-reviewed

The work isn't a blog. It's in journals other scientists vet, and posted openly for anyone to read and pick apart.

In peer-reviewed journals

Golden and Metallic Structures on Hessian Manifolds
Mathematics (MDPI) · accepted · 2026
Newly accepted
The peer-reviewed version of the golden-metallic preprint below. Proves the geometry the one cost carves out carries the golden ratio (and its "metallic" cousins) as built-in structure, so the framework's signature number is part of the shape itself, not an add-on. Co-authored with the institute's differential-geometry collaborator.
Admissible Reciprocally Symmetric Costs: Combiner Existence and Classification
Mathematics (MDPI) · 14(12):2157 · 2026
Catalogues every possible "fairness" score for how far a ratio sits from balance, and proves that basic consistency narrows them all to one simple family, with the framework's cost as the natural pick. The full proof that the starting point isn't arbitrary.
Multidimensional Cost Geometry
Axioms (MDPI) · 15(5):378 · 2026
Extends that single cost to many dimensions and shows the landscape it carves out always collapses onto one underlying direction. Why a system with many moving parts still has just one bottom line.
Coherent Comparison as Information Cost
Foundations (MDPI) · 6(2):17 · 2026
Begins from the plainest act there is, comparing two things, and shows it forces the framework's cost, then a self-balancing paired record where every entry has two sides, events that happen one at a time, and a repeating eight-step cycle in three dimensions. The bridge from comparison to time and space.
The d'Alembert Inevitability Theorem
Mathematics (MDPI) · 14(8):1386 · 2026
Proves the framework's core combining rule is not a choice: any simple, consistent way to add up comparison costs is forced into exactly this one form. The foundation is inevitable, not assumed.
A Discrete Informational Framework for Classical Gravity
Entropy (MDPI) · 28(4):477 · 2026
Recovers ordinary Newtonian gravity from the same rule, plus a small golden-ratio-shaped correction. Tested on 147 galaxies with no per-galaxy tuning, it tracks how fast stars actually orbit: a candidate way to explain galaxy rotation without dark matter.
Uniqueness of the Canonical Reciprocal Cost
Mathematics (MDPI) · 14(6):935 · 2026
Proves there is exactly one fair way to score how far any ratio sits from balance: the gap between its plain average and its balanced average. This single cost is the seed the whole framework grows from.
Recognition Geometry
Axioms (MDPI) · 15(2):90 · 2026
Builds space and geometry out of acts of observation rather than assuming them, and proves that what exists is fixed entirely by what can be told apart, with nothing hidden underneath. The framework's starting floor.
Reciprocal Convex Costs for Ratio Matching
Axioms (MDPI) · 15(2):151 · 2026
Uses the cost to decide which things "match," and proves the boundary between matches is always the balanced (geometric) average, and that matches stack up cleanly step by step. How pairing and meaning come out of the same cost.
Charged Lepton Masses from the Recognition Composition Law
Symmetry (MDPI) · 18(6):962 · 2026
Derives the masses of the electron, muon, and tau from the one rule with no adjustable dials. Fix the electron's scale and the other two come out right to a fraction of a percent, numbers physics normally can only measure.
A Noble-Gas-Centered Coordinate for Within-Period Atomic Property Trends
Symmetry (MDPI) · 18(7):1087 · 2026
Shows the same golden-ratio cost organizes four basic chemistry trends across a row of the periodic table (how tightly atoms hold and grab electrons) on a single axis. The framework reaching into chemistry.

Open preprints (arXiv)

Curvature-Induced Smectic-C Order of Tangentially Anchored Hard Spherocylinders on a Sphere
arXiv · 2606.24961 · 2026
Packs hard rods on a curved spherical surface and shows the curvature alone forces them into a tilted, layered arrangement that flat space never produces. The framework's cost predicts the tilt angles and the sphere size where this kicks in with no fitted constants, and particle simulations of fifteen geometries confirm it. The framework reaching into the physics of liquid crystals.
Nested Walsh Parity-Check Filters on a Cloud Photonic Processor
arXiv · 2606.18408 · 2026
A first hardware test, on a commercial quantum-photonics chip, of the framework's eight-slot three-dimensional balance structure: the chip kept balanced states balanced and routed the imbalance signals to the right channels, as predicted. A clean test of the structure, not error correction.
A Finite-Lattice Model from a Reciprocal Cost Action: Spectral and Reflection-Positivity Properties
arXiv · 2606.07922 · 2026
Treats the framework's cost as a physical action on a three-dimensional lattice with the eight-step clock and tests whether it can seed a genuine quantum theory. Proves the plain continuous version hits a precise, rigorously certified obstruction, while a version with field values pinned to a finite grid passes the key consistency test. An honest map of how far the cost reaches toward quantum field theory and where the open problems begin.
Golden Metallic Hessian Manifolds
arXiv · 2606.02150 · 2026
Shows the geometry built from the cost carries the golden ratio (and its mathematical cousins) as built-in structure. Ties the framework's signature number to the shape of its cost. The peer-reviewed version now sits in the journal list above.
A Finite-State Gibbs Construction from a Recognition Cost
arXiv · 2605.15667 · 2026
Shows that once the framework's cost is in hand, the standard laws of heat and probability (the Boltzmann distribution and free energy) follow on their own. Connects the one rule to thermodynamics.
A Noble-Gas-Centered Coordinate for Within-Period Atomic Property Trends
arXiv · 2605.00028 · 2026
Open preprint of the periodic-table result above: one golden-ratio cost lines up how atoms across a row hold and grab electrons on a single axis.
The Coercive Projection Theorem for Canonical Reciprocal Costs
arXiv · 2603.20205 · 2026
Gives a single guaranteed-correct procedure to certify, from only a few measurements, whether a system is perfectly in balance, and proves no other sound method can do better. The framework's mathematical balance test.
Matching Rules as Cocycle Conditions
arXiv · 2603.13553 · 2026
Proves that local fit-together rules (the kind that force the ordered patterns in quasicrystals) are the very same thing as a globally conserved quantity. Local consistency and a global conservation law turn out to be one structure.
A Complete Derivation of the Fermion Spectrum from the Recognition Composition Law
arXiv · 2506.12859 · 2025
An earlier, wide-net preprint predicting the full table of Standard-Model particle masses from the framework's golden-ratio scale and simple whole-number steps, close to the measured values. The peer-reviewed lepton paper above is its rigorous core.

In review

Finite-Volume Rigidity and Flux Sectors in a Reciprocal Ratio Gradient Model on Graphs
Mathematics (MDPI) · in review · 2026
Treats the framework's cost as the energy of a network of connected points. In each twist class there is exactly one balanced configuration, and it is rigid: a clean energy gap sits above it. On repeating lattices the lowest-energy pattern is the simple uniform one, and its energy per site does not depend on how large the lattice is. A rigidity result for the cost on graphs.
Recognition-Operator Dynamics from Reciprocal Cost and an Eight-Tick Kernel
Physics (MDPI) · in review · 2026
Shows that the one cost plus the eight-step clock single out a specific reversible operator and the energy that generates it, with a single unit carrying a rigid four-level spectrum. Couple a few units and you can represent any finite quantum dynamics. A direct route from the framework's two core ingredients to standard quantum mechanics on a fixed finite stage.
A Golden-Ratio Ladder and a Delocalisation-Saturated Participation Bridge for the Hydrogen-Bond Network of Liquid Water
Molecules (MDPI) · in review · 2026
Lines up liquid water's fastest hydrogen-bond timescales and its terahertz vibrational bands on a single golden-ratio ladder fixed by one measured anchor time. Molecular-dynamics simulation then supplies the law for how many molecules share each motion, showing the slow modes spread over about one coordination shell. The framework reaching into the physics of water.
An Eight-Slot Operator Bridge for Reciprocal-Cost Ledgers, with Finite-Amplitude Born Corrections
In review · 2026
Treats the framework's eight-slot ledger as a finite operator system and proves the one closed update is forced to be a specific shift whose Fourier transform is exactly unitary, recovering the quantum-style structure on a seven-channel carrier. Keeping the next term in the cost predicts tiny corrections to the usual quantum probability rule, including a small but nonzero three-path interference coefficient. Flagged carefully as a calibration target conditional on its stated assumptions, not a direct experimental claim.
Logic, Identity, Existence, and the Recognition Composition Law
In review · 2026
Starts from the framework's single composition law and derives the unique cost, then traces what follows: identity is the zero-cost state, the blow-up of the cost as a ratio goes to zero pushes dynamics away from nonexistence, finite recognizer resolution forces discreteness in what can be observed, and ledger balance yields conservation laws. Every step is written as a machine-checked Lean 4 theorem. Co-authored with the institute's astrophysics collaborator.
d'Alembert's Functional Equation and a Globally Convex Free-Action Principle on Positive Paths
Axioms (MDPI) · in review · 2026
Proves that the kinetic action forced by d'Alembert's functional equation on positive paths is strongly convex, so its fixed-endpoint minimizer is the global one, not merely a stationary point. Global minimality follows from a one-sided chord condition, the minimizer runs at uniform log-velocity, and the energy gap obeys an exact Bregman identity, none of it needing an Euler-Lagrange equation. The bridge to Newtonian and relativistic mechanics is stated as conditional, with the extra structure it requires spelled out. Co-authored with the institute's pure-mathematics collaborator.
Rigidity of Conserved Comparison Ledgers: Structural Axioms Force the Scale, the Cost, and the Ratio
In review · 2026
Shows that a short list of structural axioms forces a conserved comparison ledger to fix its own constants: the scale ratio is driven to the golden ratio, the cost to the framework's J, and the internal ratio to one, which collapses everything a measurement can distinguish to a single class. The axioms are sharp, since dropping any one admits an explicit counterexample that keeps the rest. Co-authored with the institute's pure-mathematics and soft-matter collaborators.
Certificate-Based Verification of Derivation-Graph Structural Properties in Lean 4/Mathlib
Journal of Automated Reasoning · in review · 2026
A Lean 4 method that turns development-wide audit claims into compile-time certificates: a structure whose one verified field bundles named obligations, so the build succeeds only when every one is reproved. Applied to a 175-file, 1,490-theorem, zero-sorry formalization to track that results depend only on declared inputs, that the advertised chain is actually connected, and that uniqueness claims hold under their stated premises. The former smoothness axiom is now proved internally, so the artifact uses no custom axioms beyond Lean's kernel and Mathlib. Co-authored with the institute's computational-chemistry collaborator.

03What's new

News

New papers, accepted results, milestones, and the occasional experiment that worked. The record as it happens.

Paper accepted: Golden and Metallic Structures on Hessian Manifolds
Jul 2026 · Publication
Accepted in Mathematics (MDPI), co-authored with the institute's University of Niš collaborator. Proves the geometry the one cost carves out carries the golden ratio, and its "metallic" cousins, as built-in structure. Now listed under the peer-reviewed record above.
Recognition-cost control validated on a tokamak
Jul 2026 · Fusion
On Columbia University's HBT-EP tokamak, the framework's imbalance cost tracked the plasma's instability mode as predicted (Block A), and a programmed drive moved that cost with the predicted sign (Block B); the closed-loop reduction (Block C) is partially validated. One drive setting was the most consistent operating point in the whole dataset, sitting at or below the baseline cost on every run day. Work carried out with plasma physicists from Auburn University.
The whole publishing roadmap is public
2026 · Milestone
Every paper, published or planned, laid out as one dependency graph: what's proved, what's in review, what's being written, and exactly what each result rests on. An upstream node on the act of distinction itself now anchors the foundation.
The fusion team has grown
2026 · People
Three plasma physicists (Roman Shugayev, Dylan Funk, and Sajid Ahmed) joined to push the recognition-cost control program on real hardware.

04Where we're pushing

Open research

Beyond the published record, here's where the work is live right now. Some of these already have results; all of them keep an honest line between what's proved and what's still open.

01

Fusion

An active line of work applying the framework to plasma control for fusion, in collaboration with university groups.

02

Protein folding & drug design

An active line of work on protein folding and therapeutic design from the framework.

03

Native intelligence

An active line of work building a recognition-native intelligence.

04

Recognition gravity

Einstein's equations recovered from the ledger in the slow limit, plus a small golden-ratio correction that tracks how galaxies actually rotate with no dark-matter dials. The strong, quantum version is being written.

05

The Bekenstein–Hawking coefficient

Why a black hole's information is exactly a quarter of its surface area. In three dimensions the number of corners around a pixel is four (proved); pinning the absolute scale is the open part.

06

The baryon-to-photon ratio

Why the universe holds roughly a billion photons for every atom. Three independent routes land on the same golden-ratio rung and a proved band around the measured value; the exact prefactor is open.

07

The δ framework

All of mathematics rebuilt from one move: telling two things apart. Counting and logic come out as two constructions on the very same object, which is the distinction → recognition step the roadmap now starts from.

08

Holography

The thin slice a mind actually reads versus the full ledger that exists: how much of reality a recognizer can access, and the area law that bounds it. Shares its floor with the black-hole result.

Nature does not have free parameters, so our theories should not either. If you have to turn twenty dials to make an equation fit the data, you are describing the universe, not explaining it. We built this institute to find out what happens when you leave yourself no escape hatch. One rule. Zero tuned numbers. If a telescope sees an anomaly, the mathematics must answer for it. To keep ourselves honest, we write every derivation in a formal language and let a computer check the proofs. The machine does not care about reputation.

Jonathan Washburn, founder

05Don't take our word for it

It's all public. Check it yourself.

Every proof lives in the open. If you read code, you can run it on your own machine and watch a computer accept each step, or find a hole and tell us. Either way, that's the point.

356,000lines of Lean proof code
17,929theorems, every one machine-checked
0unfinished proofs
0assumptions of our own

What's in the library

  • 01
    The whole chain. From "two things differ" to logic, the cosmic balance record, the one cost rule, the golden ratio, three dimensions of space, and the 8-beat: every link a theorem, none of it assumed.
  • 02
    The one rule, proved unique. Not "a rule that works," but a proof that no other fair way to price imbalance can exist.
  • 03
    The constants. The fine-structure constant pinned inside a window of less than a hundredth of a percent, and the measured value sits inside it. Planck's constant and Newton's G in the theory's own units.
  • 04
    Matter and gravity. The mass ladder for particles, and gravity strong enough to trace how galaxies actually rotate, with no invisible-matter dials.
  • 05
    The observer. A precise account of what it is to recognize something, and a proof that plain logic comes free with any recognizer.

What it claims, and how hard

  • The laws of physics are forced, not chosen. Pull out any link and everything below it falls.
  • It rests on zero assumptions of ours. Every theorem traces back to the same three foundations the rest of modern mathematics stands on, and you can run the audit that proves nothing else snuck in.
  • Its numbers are predicted, not fitted. There is no parameter anywhere you could turn to make an answer come out right.
  • And it's staked in public: if any one of the 17,929 theorems breaks, the build fails for everyone watching.
github.com/jonwashburn/shape-of-logic

2,473 Lean files and 356,000 lines of proof, built on Lean 4 + Mathlib. One command rebuilds the library and re-checks all 17,929 theorems from scratch. A public audit script guards the whole tree: zero unfinished proofs, zero axioms of our own, on every change.

Open repo ↗
for the curious: run a proof
# check that the one rule is the only one that works
build  the-one-rule

# check the chain from "something exists" to 3-D space
build  the-whole-chain

# check that right and wrong is balance conservation
build  the-moral-law

# re-check the entire library for gaps and hidden assumptions
audit  everything            # → no gaps, nothing of ours snuck in

06The engine, running

Watch reality build itself

Reading the argument is one thing. Watching it run is another. We built the rule into an engine and pressed play on an empty universe: one difference posts, the cost lights up, the golden ratio falls out, then the 8-beat, then three directions, then structure. Nobody draws any of it. It's forced.

This is not an animation. The screen is only allowed to draw numbers the engine actually computed. Click any cell in the real run and it shows its receipt: the tick it appeared, what it cost, the rule it obeyed.

Two needles keep it honest. The balance needle must sit at zero forever. The cost meter may only climb. There's even a button that tries to violate the balance law, so you can watch the universe refuse.

Also: join the engine running live · stand inside it in VR · try to break it · every instrument →

Fig. 02: the idea, sketchedhover to re-run

Space gets drawn only where it's forced.A flat sketch of the idea. The real instruments replay the engine's own per-tick record. The picture holds no physics of its own.

07What things actually are

The same one rule, asked about seven different things

Once you have the rule, you can ask it almost anything. Here's what it says, in one plain sentence each.

08Where to find us

Events

Seminars, conference talks, lectures, and meetings. Upcoming and recent appearances land here.

09Everything else to read

Library

Resources beyond the journal papers: plain-language explainers, the proof code, technical notes, a book, and the instruments you can run yourself.

01

Plain-language reads

The framework without the mathematics: what math really is, what economics is and its shared blind spot, and what stories really are.

02

The proof library

Every derivation as machine-checked Lean 4 code, plus a plain explainer of what "a computer checked it" actually means.

03

The publishing roadmap

The whole program as one dependency graph: what's proved, in review, or still to write, and exactly what each result rests on.

04

Big questions, answered plainly

The twenty biggest questions the framework takes on, each in a paragraph, and a look at what a calendar counted from the framework's start would mean.

05

Manifestos & notes

Short technical pieces: the algebra-of-distinction manifesto, and the meaning manifesto that sits under the stories work.

06

The simulation lab

Run the rule yourself: watch an empty universe build itself from one difference, or try to break the balance law and watch it refuse.

07

Signed reviews (Pith)

Referee-style, signed reviews of every arXiv preprint, so you can see the work being picked apart in the open.