NINE FIELDS · NINE KNOWN ANSWERS · NINE PASSES

A number and a margin of error tell you nothing about the model that produced them.

Polytrion — digital twins
whose rules you can read and check

Polytrion builds two kinds of digital twin. A Static Digital Twin models an operation whose rules you can write down. An Open World Digital Twin models one you can only partly see, and repairs its own rules when the world disagrees. For the questions that need volume, a Monte Carlo simulator runs on a catalogue the engine has certified first. The engine underneath is our own, built and maintained in-house — internal technology, not a product — and it was qualified against nine published answers before it was allowed to answer yours.

What we offer → Open World Digital Twins → The qualification record → The QEC paper → The world-model audit →

1a · Static Digital Twin

A twin whose rules you declare

You describe the operation. The rules become declared artefacts, checked before a run and on every step of it, and every answer comes back with the evidence attached. Drift becomes something you are shown on a schedule instead of something you discover.

Running an operation

Test the policy you actually deploy. The same policy artefact runs in the twin and in the live system, so the twin cannot quietly diverge from the business.

Fewer runs to pick a winner. Stock levels, routing, staffing — the comparison is the question you care about, and it is the part this does cheaply.

Disruptions with the assumptions on the page. Outages and recovery times are named, versioned inputs, so any result traces back to the assumption behind it.

Doing research

Publish results a referee can replay. Four values beside a figure let a reader re-derive the number instead of taking your word for it.

Check the mechanism first. Establish that a reaction scheme or move set is consistent before spending months of compute on it.

Sharper comparisons on the same budget. Sensitivity studies are where the savings land, and they grow as the effect you are chasing gets smaller.

1b · Open World Digital Twin

An Open World Digital Twin assumes what it cannot see

A plant, a supply chain, a building, a market: each is observed only in part, and each changes in ways no one has written down. An Open World Digital Twin assumes the rest, acts on that assumption, and changes its own rules when the world disagrees. Frontier language models write the rules; an exact engine runs them; every rule can be read, checked and corrected, and the twin keeps what it has seen apart from what it has only assumed.

1 · ASSUME
Writes rules for what it sees, and lists what it believes exists but cannot see.
2 · ACT
Plans through its own rules and acts, exploring to test what it assumed.
3 · COMPARE
The engine’s prediction meets the world’s answer. A mismatch is exact and local.
4 · REPAIR
The language model edits the rule that failed. Assumptions are confirmed or reshaped.
5 · TRANSFER
Every repair is audited on layouts the twin never visited.

After one surprise, a language model writes the shortest rule it can, and the shortest rule names the one object that surprised it. Polytrion’s rule language is designed so the twin writes the lesson about the kind instead.

Preprints.org Article

A declared world model: language models write the rules of the scene they are shown

From one fully visible scene, every model tested wrote correct rules; the paper measures when those rules hold beyond the scene.

world modelsdeclared world modelJEPAlarge language modelsprogram synthesisgeneralizationidentifiabilityscene graphs

Jean-Jacques Dubray · Cognitive Fab LLC Posted 13 October 2026 doi: 10.20944/preprints202610.1139.v1

Read it on Preprints.org ↗

Open World Digital Twins: the full story → Watch the video → Talk to us →

2 · Monte Carlo on a certified catalogue

A fast sampler, on a model that was checked first

A sampler is only as good as the mechanisms it samples. Here the catalogue is certified before the sampler ever sees it.

MONTE CARLO

A Monte Carlo simulator, for the questions that need volume

Most of what a twin is asked is a sampling question. Sweep the parameters, rank the options, get the distribution.

AVAILABLE TODAY

The model it runs on is certified first

Before a catalogue of mechanisms is handed to the fast sampler, the engine establishes that it is complete and consistent — exhaustively, before a single trajectory exists. A defect is named by state and channel, not discovered in a wrong average.

The engine underneath all three

Four properties, and the combination is what is unusual

There is very little to say about the internals here on purpose — they are ours to maintain, not yours to learn. What matters to somebody deciding whether to use the platform is what holds, not how it is built.

Any result replays from four values

Engine version, scenario, seed, replication index. Quote those beside a figure and anyone re-derives it digit for digit on their own hardware. Nothing has to be shipped, stored or trusted.

The model is checked before it runs

Because the mechanism is data rather than buried in the code that scans the state, an independent checker establishes structural properties of it exhaustively — before a single trajectory exists.

Everything that must hold is checked on every step

Not sampled, not checked at the end. Between eight and eleven invariants per world, evaluated over 10⁵ to 10⁸ journal rows per study. A breach names the node, the tick and the rule, and stops the run.

Where a study cannot answer, it refuses

This is the rule that costs something. Two studies in the suite report underpowered with the exact value they could not estimate and the replication count that would have been needed — one after four thousand replications returned exactly zero.

Qualification

Nine published answers, in nine fields, none of them another simulator's output

Every entry was selected on one rule: the right answer must already be known to more digits than the engine can deliver, and it must not be a simulation. A closed form, an exactly solvable finite system, or a linear solve over a finite chain — in that order. A heavily replicated numerical constant is second best; another code's output is not accepted at all. That rule excludes most of the simulation literature, and it is what makes agreement informative — if the reference is somebody's program, reproducing it means reproducing their conventions, and disagreement localises nothing.

9 / 9

entries passed, against tolerances written down before the run that scores them

findings in the engine's semantics

Wave 3

two of three scored; the suite's last entry is built and running

Field	The known answer it was run against	What happened
Wave one — is the suite viable at all? · complete
Epidemiology	Reed–Frost final-size distribution, exact rationals	Every point within 0.0030, against tolerances of 0.0044–0.0085; the mean covers at three transmission rates
Queueing	Jackson product form and Gordon–Newell, solved exactly	Occupancy 1.2976 against 857090/660203; joint deviation 0.0020 against a 0.0124 budget
Traffic	Nagel–Schreckenberg at v_max=1, exact	Five randomisation rates, each against the finite ring's own exact current; all covered
Wave two — the substantive claim · complete
Non-equilibrium physics	Open TASEP, J₅₀ = 26/101	0.257276 ± 0.000130 — −1.15σ. The value a defective tie-break would produce is excluded by 57σ
Stochastic chemistry	Schlögl network: birth–death sums and an absorbing chain's Green's function	First passage 0.16σ; occupation histogram 0.42σ; the driven cycle behaved as predicted
Operations research	Zheng–Federgruen (s, S) optimum, three published triples	All three to the digit — −0.92σ, +0.52σ, −0.41σ
Computer networks	Bianchi's 802.11 DCF fixed point	Within 0.7% at every station count; RTS/CTS flat at 1.98% against Basic Access's 34.3%
Wave three — the suite's last entry is running
Rare events	M/M/1 first passage, gambler's ruin	γ₂₀ = 9.670×10⁻⁷ ± 1.5×10⁻⁸ against 9.537×10⁻⁷
Statistical mechanics	2D Ising on an L×L torus, against Kaufman's exact finite-lattice partition function — differentiated analytically, and cross-derived from the exact density of states	Fifteen points, thirty scored quantities, zero findings. Energy and heat capacity inside the declared rule at every temperature; two starts two units of energy per site apart met at −0.02σ
Market microstructure	zero-intelligence continuous double auction — the deep book as an exact infinite-server law, Exponential(δ) share lifetimes, and the dimensional collapse that makes the spread scorable without anyone's fitted prefactor	Built — 34 tests, zero findings across runs. The deep-book law is CLEAN at both order sizes: variance-to-mean 2.30 against an exact 2.5 at σ = 4, the statistic that separates per-share from per-order cancellation. The three collapse arms read 0.4228 / 0.4360 / 0.4325 against Smith et al.’s ≈0.45. Production runs in flight: the deep study at 12 replications, then the ε-collapse on a 120-level ladder.

Every row's acceptance rule is a rule, not a number — “three standard errors of the ensemble mean at this replication count, plus the declared tick-quantisation allowance,” written into the experiment document before any run exists. “Within one per cent” is a number that can be chosen after seeing the answer. Every completed study reports zero invariant findings.

Beyond the exact-answer suite

Four more fields, where the reference is a mechanism or a reference tool

These are where the construction's other claim — that a mechanism can be checked before it is sampled — was exercised.

Field	What it was run against	What happened
Surface chemistry	a published diamond CVD reaction catalogue	Five structural properties of the mechanism checked exhaustively before any trajectory existed. Eight deliberately introduced defects, eight rejected — each with the offending state or channel named.
Mathematics	Dhar's abelian sandpile theorem	Four different orderings produced four different executions and one identical answer, exactly as the theorem requires.
Quantum error correction	surface-code decoding, against Stim	Agrees with the reference tool in that field.
Quantum optics	a continuously measured two-level system, against QuTiP	Agrees.

Case study · world models

How do you know a world model is good enough to plan with?

JEPA world models are usually selected by two proxies: whether a probe can read the true state from the embedding, and how low the prediction loss is. We checked both against planning, in a world where everything is known.

If the video does not load, watch it on YouTube ↗

The world is built from declared state machines in Polytrion: two rooms, a wall, a door. It knows every state, every refused move and every shortest path. That answer key lets each module of the planner be audited on its own. Every decision rule was fixed before its data existed.

What the audit found, on a scaled-down LeWorldModel:

Readable is not plannable

The position is recovered almost perfectly from the embedding, yet planning succeeds on 2 to 26% of tasks, against 100% with the true dynamics.

The cost points away from the door

The latent distance used as the planning cost leads the agent away from the door. A small critic on the same frozen latents adds 60 points. The information is there; the cost does not read it.

A label-free critic gets most of the way, once

A critic learned without labels recovers about 60% of that gain, but the recipe did not replicate on new encoders. It fails exactly on paths through the door.

The predictor breaks first

Narrow training data, or a moved door, breaks the predictor, not the representation. And prediction loss barely predicts planning failure.

The representation can be sound while the cost and the predictor fail. A declared world can tell them apart.

The study stops at latent size 16. The grid is scripted end to end, and we would gladly run it at 64 and 192 with anyone who can provide the computation.

The work builds on LeWorldModel and LeJEPA by Yann LeCun, Randall Balestriero and Lucas Maes, and relates to the structured world models of Jiajun Wu.

Request a copy of the paper → Offer compute for the 64 and 192 runs →

Polytrion — digital twins
whose rules you can read and check

Two kinds of digital twin, and a Monte Carlo you can certify

You declare the rules

The twin writes the rules, and repairs them

For the questions that need volume

A twin whose rules you declare

Running an operation

Doing research

An Open World Digital Twin assumes what it cannot see

A declared world model: language models write the rules of the scene they are shown

A fast sampler, on a model that was checked first

A Monte Carlo simulator, for the questions that need volume

The model it runs on is certified first

Four properties, and the combination is what is unusual

Any result replays from four values

The model is checked before it runs

Everything that must hold is checked on every step

Where a study cannot answer, it refuses

Nine published answers, in nine fields, none of them another simulator's output

Four more fields, where the reference is a mechanism or a reference tool

Where the engine was pointed at an open question, not a known answer

Backlog Metastability in Windowed Quantum Error Correction Decoding

How do you know a world model is good enough to plan with?

Readable is not plannable

The cost points away from the door

A label-free critic gets most of the way, once

The predictor breaks first

Soft launch — by invitation

Polytrion — digital twinswhose rules you can read and check

Two kinds of digital twin, and a Monte Carlo you can certify

You declare the rules

The twin writes the rules, and repairs them

For the questions that need volume

A twin whose rules you declare

Running an operation

Doing research

An Open World Digital Twin assumes what it cannot see

A declared world model: language models write the rules of the scene they are shown

A fast sampler, on a model that was checked first

A Monte Carlo simulator, for the questions that need volume

The model it runs on is certified first

Four properties, and the combination is what is unusual

Any result replays from four values

The model is checked before it runs

Everything that must hold is checked on every step

Where a study cannot answer, it refuses

Nine published answers, in nine fields, none of them another simulator's output

Four more fields, where the reference is a mechanism or a reference tool

Where the engine was pointed at an open question, not a known answer

Backlog Metastability in Windowed Quantum Error Correction Decoding

How do you know a world model is good enough to plan with?

Readable is not plannable

The cost points away from the door

A label-free critic gets most of the way, once

The predictor breaks first

Soft launch — by invitation

Polytrion — digital twins
whose rules you can read and check