Forward Pro · European Union Four Checkmen · United States Four programmes · one standard of proof
Four programmes. Every result orders of magnitude from current practice.
Quantum propagation, quantum control, model auditing and speech representation. Four separate programmes, each measured against known ground truth, under conditions published in full alongside the results. The separations below are not improvements on current practice — they sit several orders of magnitude away from it, and every one of them is offered for you to test yourself.
Separation from current practice · every result on one logarithmic axis
Each bar is the ratio between the established method and ours on the same task, with the same data. The axis is logarithmic: every 14.3% of width is two full orders of magnitude. Conditions of validity are given in the dossier named on each row.
10⁶ propagation steps
an exact threshold
against 458 ms
135× below PCM
What is different
One difference from current practice, four times over
The four dossiers below are in unrelated fields and were carried out separately, with different methods. What they share is not a technique but a decision: not to approximate something that can be computed exactly.
Current practice · approximate the map
A model is fitted to data, or a grid is refined until the error is small enough. The object produced is an approximation of the observed behaviour.
It holds where it was fitted, degrades outside that region, and cannot say where its own boundary lies. Every new operating regime needs a new fit — and a model with good test error can be entirely wrong about the underlying law with no warning at all.
This construction · compute the structure
Where a problem carries exact structure, that structure is established once and then used directly, rather than being approached by fitting.
The object produced is the law rather than a picture of it. It holds at any horizon, on parameters never seen, and it reports its own domain of validity. One object replaces a whole family of fitted models.
Why the separations are measured in decades
None of the results on this site comes from a better fit, a larger model or more data. They come from replacing an approximation with an exact object. That is why the gaps are orders of magnitude rather than percentages, and why several of them widen rather than narrow as the problem grows.
Four dossiers
The complete record, reproduced without cuts
Each dossier is the working document: every figure, every table, every technical schematic, together with the conditions under which the results hold and a plain statement of what has not yet been done.
Parametric Schrödinger operators
Long-horizon quantum propagation with norm deviation at the floor of float64 arithmetic. The operator spectrum is reproduced exactly at every size tested, and the result holds on interpolated parameters, not only on the training set.
Parametric pulse compilation
An entire family of devices is compiled in a single offline run, after which a control pulse for any member of that family costs no optimization at all. Seven structural identities verified at machine precision, four of them again under an open-system master equation.
The physics learning certificate
The number of examples needed is computed before training rather than found by trial. A four-number certificate then separates a model that learned the law from one that memorised the map — including the case where prediction stays flawless and the inferred law is false.
The canonical representation of speech
The representation isolates speaker identity into exactly one dimension — provably the maximum that can be separated — leaving every other dimension to phonetic content. Formants recovered two orders of magnitude more precisely than the industry standard, and transparent speech well below telephony rates.
The separation, measured
Same task, same data, both methods timed
Every row is a direct comparison carried out under identical conditions. The full experimental setup, the ground truth used and the failure cases sit in the dossier named in the last column.
| Task | Established method | This construction | Ratio | Dossier |
|---|---|---|---|---|
| One control pulse | 458 ms · GRAPE | 0.6 µs | 763,000× | II |
| One pulse with decoherence | 2,269 ms · Lindblad optimization | 0.48 µs | 4,704,713× | II |
| Recalibration, 1,000 qubits | 7.6 minutes | 0.6 ms | 760,000× | II |
| Norm deviation, 10⁵ steps | 2·10⁻² · finite difference | 10⁻¹⁶ | ≈ 10¹⁴× | I |
| Operator spectrum | 0.30 · uniform grid | exact 0.0 | — | I |
| Examples to reach precision | 500 · trained network | 24 | 21× | III |
| Time to recover the law | 4,656 ms · trained network | 0.85 ms | 5,500× | III |
| Accuracy on the same problem | 8.69·10⁻⁵ · trained network | 1.19·10⁻¹³ | ≈ 10⁹× | III |
| Propagation, 100 unseen steps | 3.0·10⁻¹ · trained model | 1.9·10⁻¹² | ≈ 10¹¹× | III |
| Degrees of freedom for 10⁻⁶ | 100,000 · conventional | 59 | 1,695× | III |
| Formant error on F₁ | 8.82 Hz · LPC-16 | 0.026 Hz | 340× | IV |
| Transparent speech bit rate | 256 kbps · PCM | 1.897 kbps | 135× | IV |
Two rows are worth reading twice. The spectrum row carries no ratio because the error is exactly zero, at every size tested. And in Dossier III, two of five documented failure modes are cases where prediction remains flawless while the recovered law is false — a condition that no method reporting only prediction error can detect.
What is measured, and what is not
Every figure comes from controlled runs against known ground truth, with fixed random seeds, reproducible on standard hardware without a GPU. Errors are reported as maximum deviation, never as a mean. Each dossier states its own conditions of validity.
Each dossier also names what has not been done. Validation of the pulse compiler on physical quantum processors has not been carried out. Biometric error rates for the speech work have not been measured. Audible synthesis has not been produced. Those limits are published alongside the results rather than after them.
Terms of access
What is presented, and what is transferred
These are two different things, and the distinction is the whole basis on which access is granted.
What is on this site
Measured results, in full. Four dossiers with every figure and table reproduced, the conditions under which each result holds, and a statement of what remains undone. Enough for a technical reader to judge whether the claims are worth pursuing.
What is not on this site
The methods themselves. None of the four dossiers describes how the results are obtained. The derivations, the constructions and the implementations are held as trade secret, are not published anywhere, and are not inferable from what is shown.
The technology is transferred only within an agreed technological cooperation, accepted by all parties involved. What can be made available under such an agreement is not limited to what appears on this site: the construction underlying these four programmes extends further, and further results exist that are not presented publicly. They become accessible inside a cooperation, and not before one.
Verification
Four ways to check us that cost us nothing to offer
Withholding the methods raises a fair question: how does a counterparty establish that the figures on this site are real? Not by reading a derivation — a derivation you cannot independently reproduce is decoration. By testing. Each of the following turns a claim into something you can settle for yourself.
01 · Blind test
You set the exam. We sit it.
You supply data for which you know the ground truth, and you keep that ground truth. We return the result. You score it, against a criterion you fix in writing before we start. Every number on this site is available to be settled this way.
02 · Black-box access
Your inputs, our output, no source.
From the second month of the period, a sealed executable or a metered endpoint. You put your own parameters and your own data in, and you measure what comes out, as many times as the agreement allows. Nothing about the construction is exposed.
03 · Sealed record
Dated proof, without disclosure.
The complete method documents are sealed and their cryptographic fingerprint is published below. Anyone can confirm, at any point in the future, that the sealed content existed unchanged on that date — without any part of it being revealed.
04 · Independent attestation
Reviewed by someone who is not us.
A recognised specialist in the relevant field reviews the full material under non-disclosure and issues a short public statement on what they saw. Available on request as part of the period, for the programme that concerns you.
SHA-256 [ set this to the hash of your sealed archive before publishing ]
Sealed on [ date ] · deposited with [ notary or escrow agent ]
Why this is the stronger form of proof
A published derivation can only be evaluated by the few people qualified to evaluate it — who are, without exception, the people best placed to use it. A blind test can be evaluated by the organization that actually has to make the decision. We would rather be tested than believed.
Counterparties
Four kinds of organization, four different conversations
Contact is open to states and state entities, multinationals, banks and investment funds. What each would take from a cooperation is not the same, so the first conversation should not start the same way.
States and state entities
All four programmes produce infrastructure rather than products — and infrastructure that carries across hardware generations and across domains. A cooperation can be structured as a sovereign arrangement with on-premise deployment, no external dependency in the operating loop, and terms set under the jurisdiction that applies to you.
What we need from you: the programme it would attach to, and the jurisdiction it has to sit in.
Multinationals
Three of the four dossiers have direct operational surfaces: control-loop calibration for anyone operating quantum hardware, an audit that establishes whether a simulation surrogate learned physics or memorised a map, and a speech representation whose parameters are physical quantities you can edit directly. All three attach to systems that already exist.
What we need from you: which of your systems the result would touch first.
Banks
The certificate in Dossier III audits any model that propagates a state, without access to its code, and produces a grounded refusal instead of a silent extrapolation. For an institution that has to defend model behaviour to a regulator, that is a different object from a backtest. Dossier IV separately addresses voice archives and what they cost to hold.
What we need from you: the model estate or the archive that would be evaluated.
Investment funds
The results here are measured and reproducible, and the limits are stated as plainly as the achievements. A fund entering a cooperation receives the underlying data, the reproduction instructions and the seeds, so its own technical people can establish what is true before anything is structured around it.
What we need from you: your technical diligence capability, and your timeline.
Structure
One programme, carried out from two centers
Constantin Labs is a single research programme carried out jointly by two centers, one inside the European Union and one in the United States. The work is not divided between them: results are produced, reviewed and reproduced across both.
Forward Pro
Contracting entity for counterparties operating under European jurisdiction, and one of the two sites where the work of all four programmes is carried out and reproduced.
Four Checkmen
Contracting entity for counterparties operating under United States jurisdiction, and one of the two sites where the work of all four programmes is carried out and reproduced.
Why two
The two-center structure exists so that a counterparty can contract under the regulatory regime that applies to it, and so that no single jurisdiction holds the programme on its own. Both centers work on the whole of it.
The three months
From first contact to an agreed cooperation
Contact is established through a fixed three-month period. It runs from the date contact is made, and it is finite on purpose: both sides decide with technical facts in front of them, and neither side spends a year getting there. Nothing is transferred before the agreement is in place.
Contact and scope
- Mutual non-disclosure agreement executed.
- Technical briefing under NDA across the four programmes, with the complete result set — raw logs, fixed seeds, reproduction instructions.
- The specific question your organization needs answered is written down and agreed.
Technical evaluation
- Results reproduced in your environment or ours, against a case you choose.
- Where you operate the relevant systems, your own parameters and data go in through sealed black-box access, and the output comes back for you to measure yourself.
- Findings are documented jointly, including anything that fails.
The cooperation agreement
- The form of cooperation is fixed and accepted by all parties involved.
- Scope, terms, jurisdiction, deployment mode and obligations are agreed in writing.
- If either side does not wish to proceed, the NDA survives and the period closes cleanly.
Establish contact
Open the three-month period
This form reaches the institutional desk directly. Requests from states, multinationals, banks and investment funds are answered within five working days. Everything marked required is what tells us which of the four conversations to start.
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