Decision and measurement engineering, with a professional API and engagements by written quote.
Decisions your business can defend
We build the systems behind the decisions you keep having to make: what to spend, what to schedule, what to prioritise. Then we hand them over with the reasoning attached, so your team can run them without us.
Start a conversation Request a quote Ask our consultant See how engagements work
Behind that practice is one product. We turn the things your business actually runs on into a model you own, and that one model answers four questions: what to do, what you already know that is closest to this, what you are holding, and what has changed. Certified, audited, and billed per answer. The professional API is how that is bought, and every product is listed with its door and its price.
The type of AI · quantum-inspired optimisation
How we solve your problem
Most AI learns patterns from a pile of examples and predicts what is likely. That is the right tool when you have the examples and no rules. Our work is the other case: you have the rules, and you need the arrangement that satisfies them best.
So we lay your decision out as a web of tiny compass needles — one needle for every choice in front of you. Your rules and priorities become the forces between them: what belongs together pulls together, what clashes pushes apart, and what matters more pulls harder. Then we let it settle the way nature settles, downhill, until the needles come into alignment — and that alignment is the recommendation, with the reasoning attached. It is quantum-inspired, and it runs on ordinary processors you already own.
And we will tell you when the answer is not good enough
We say how far from the best possible the recommendation could be — a margin, in writing, beside it. When the rules you have given us cannot all be met at once we say so, name the ones that are fighting, and come back with what relaxing each of them would be worth to you. A consultant who only ever agrees with the brief is not worth hiring, and an engine that always produces an answer is the same problem in a lab coat.
The optimisation API → · The longer version, on embark.day →
Day, the consultant we run ourselves
Ask Day about a system and two things come back: an answer, and the sources it came from — a list of what he still needs from you next is available on request through your engagement. He is the instrument behind the engagements below. He answers with sources and says when the sources do not carry the answer: on 29 September 2026 the first source Day named was the right page for 23 of 26 questions about our services, and on a public test set he still answers too often when he should say he cannot — we publish that number too, on the evaluation page.
On this site there is one box, Ask: it settles a question over our published pages and names each source. In an engagement, Gaps turns it around: given a business context, Day returns the questions that would need answering next, each tied to something measurable.
We publish his score rather than describing him. Measured on 29 September 2026, through this site’s own question box, on 26 questions we wrote about our services: 19 answers carried the fact asked for, the first source named was the right page for 23, and all 13 questions about things we do not publish were declined; the median answer took 0.22 seconds. We say the answer number because it is the weaker one: seven answers did not carry the fact asked for, and closing that is the work.
Day reads our systems, not yours, and he is not a self-serve product. He is how we work; the engagement shapes on how we work are how you buy it.
What we are actually good at
One thing, applied in several places: taking a decision that is currently made by instinct, spreadsheet or habit, and turning it into something measurable, repeatable and arguable.
Marketing measurement
Know which spend actually moved the number.
Decision systems
Turn a recurring judgement call into a system that explains itself.
Scheduling & logistics
Rosters, routes and capacity that hold up on contact.
Industrial vision
Count, track and flag what the cameras already see.
Data & ontology
One vocabulary your systems and your people both use.
Edge & hardware
When the decision has to run on the machine itself.
Third-party review
An independent review of someone else’s AI or system.
A second line: the Day QIO
Alongside the engagements above, we also sell direct, ongoing access to the optimisation engine behind them — the Day QIO API — to development and consulting companies building their own optimisation work. It is a separate offer with its own model: it is sold to firms under a written agreement; for calls on your own key, embark.day sells prepaid credit. See the optimisation API and how it is sold. Beyond running the solver, the professional API is where you build and own the models themselves, not just run them.
The experts behind the ecosystem
Three layers, one firm behind all of them, and it is worth being plain about which is which. We run the engine and its API ourselves, metered in tokens. We build models in the studio for the clients who want us to build theirs, engagement by engagement. And where a need is matched automatically to a model someone else built, we stand behind what the market routes — the certificate travels with the answer either way.
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Layer 1
Run
The public engine and its API are ours, end to end.
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Layer 2
Build
Engagements are the studio applied to your problem, done for you.
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Layer 3
Stand behind
A matched model still carries our certificate and our audit trail, whoever built the piece it routed to.
The docs, the proof and the independent evaluation behind all three sit at embark.day/docs.
Who this is built for
The buyer we are built for is the one who has to defend a decision afterward, not just make it: a CTO answering for a system that spans a large enterprise, the person who owns a supply chain’s routing and capacity calls, or an operator running infrastructure that cannot go down — a power grid, a communications network. If your job is to stand behind a decision when someone asks you to justify it, that is the conversation we are built to have.
What you get is not advice on a slide: it is a model, its certificate, and the report that explains what it does and why — see how an engagement delivers all three.
embark.day is where the models and the community that build them live — see what already exists at the three layers, measured. This is the studio: who you hire when you want one built for you.
Who Agile Integrations is for
Agile Integrations is the demand side of the market embark.day runs: operators who buy answers rather than build the model themselves. embark.day is the supply side, where a domain expert builds and owns the model instead.
Our advantage, measured
Five numbers, each reported with where it loses as well as where it wins — that is the discipline, not a slogan:
- Certified bound · 40 variables A certified error bound that lands exactly on the true answer. On a 40-variable planted test problem, the certified bound equalled the true gap on 100 of 100 seeds. Where it loses: on a harder, more tangled problem the same bound is honest but looser — a real number, not a flawless one. Record: our certified-bound test on 100 planted problems, 13 September 2026.
- Unattended consultant · 24 problem classes A consultant that works the whole problem, unattended. Given 34 written problems across 24 different problem classes, it screened, identified the class, modelled the constraints, solved, certified and reported on 23 of 34 — with a shadow price on every constraint it solved against, so you can see what relaxing any one rule would be worth. It never invented a number none of the 34 requests stated. Where it stops: eleven of the 34 it did not carry all the way. We publish the denominator because the denominator is the claim. Record: the consultant battery as it stood on 15 September 2026, when it held 34 problems.
- Scale · 2,500 variables 2,500 decision variables, built from 125 exactly-solvable blocks of 20. Recomposed, the blocked answer lands within 0.77% of the certified bound. Where it loses: on a densely-tangled version of the same size a single whole-problem pass wins instead, by 8.1%, with no certified bound available at all. We publish both results, not just the one that flatters the method. Record: the 2,500-variable benchmark, 15 September 2026.
- Real video · fixed camera Real camera footage, not a demo clip. On 120 frames of real pedestrian-camera video, our background detector agreed with a large reference detector's labels at 0.973 recall and 0.893 precision, at 157.8 frames a second on a single CPU core. Where it stops: a fixed camera only, and agreement with another detector is not accuracy against people counted by hand. A moving camera invalidates the comparison by construction, and we will not quote this figure for one. Record: the real-video benchmark, July 2026.
- First cloud run · six job kinds A first real cloud run, priced honestly. Six different job kinds, run end to end on one worker: 535 seconds at $0.35 an hour of machine time, $0.052. Where it stops: that is one run on one worker, not a price list. Ongoing work is quoted in writing. Record: the first cloud run, 15 September 2026.
Each measured number here names its record; $0.35 an hour is a stated rate, not a measurement. If we cannot show you the number, we say so instead of rounding up.
Why us, honestly
We are a small firm, and the useful thing about us is not a client list — it is that we built the engine underneath this work and we sell it as a product in its own right at embark.day. Our own marketing and pricing decisions run through the same measurement loop we would build for you. That has two consequences worth caring about:
- You are not paying us to learn. The methods arrive built and tested rather than assembled on your budget.
- The result is not a slide deck. An engagement ends with something that runs, plus the numbers it was checked against. If we cannot show you a number, we will say so.
We do not publish the names of our clients
We do not publish client names, logos or engagement details — including yours. If you want a reference, we will ask a past client directly rather than list them on a website.
Where we are a bad fit
Said up front, because finding out in month two is expensive for both of us:
- Staff augmentation. We take responsibility for an outcome, not a seat on a board.
- Decisions nobody wants measured. If the answer is already fixed politically, measurement makes things worse, not better.
- Regulated financial advice. We build decision tooling; we are not advisers and we do not manage anyone's money.
Start small on purpose
Most engagements begin as a fixed-scope pilot: one decision, a few weeks, a defined deliverable and a number we agree on in advance. If the pilot does not earn the next phase, it should not get one.
How we write about the work
We publish short working notes on how we measure what we do — why our receipts carry how much uncertainty a run removed rather than how long it stayed up, and why we treat our own consultant's refusals as a report on our documentation. Beside them are eight papers on the engine and the model behind it. Every figure in a paper traces to a recorded measurement, both authors are credited, and each paper says how the work was divided and what it does not claim.
- The unit of work: a receipt for one settled problem, booked on a hash-chained ledger, and what it is not, with the economy's measured losses first.
- HOPE: recall in a library of Hilbert spaces: recall as settling to the nearest stored state, in a library of small spaces kept one per model, with the measured answer that they do not make one large space.
- The Earth as a two-state recorder: the Earth's dipole read as a two-way choice from public records, with a prediction written before the data, and the planet's clocks.
- The halo of a decision: a two-way choice, the partner it is tied to and the event that tied them, in textbook terms, with what an experiment could measure.
- Sense, remember, act: what the engine senses, remembers and learns.
- Closing the gaps: four sustainability problems an engine can schedule, and what it cannot do about them.
- The periodic table as a ground-state ladder: each element read as the lowest-energy filling of its electrons, with every answer NIST lists checked against it.
- The Operational Unit: the model behind the engine, and how it was built.
Who's behind the math — Day AGI
Day answers your questions on embark.day, works as the consultant at Agile Integrations, and draws each figure on our Mission page from a committed record.
The name states a goal, not a result. A kind of problem counts as done when Day solves every registered case of it and each answer is checked against a reference Day did not produce; the name is earned when that holds across kinds of problem and others can check it.
Mechanized, not promised.
- Hands over a certificate with every solved model: how far from the best possible answer it could still be, which you can re-check on your own machine with no network. At 20 choices or fewer, the service checks every arrangement and says the answer is exact. The open client re-checks every arrangement on your own machine up to 18 choices by default, and above that checks only that the answer is consistent. Above 20, the service searches without checking every arrangement, and says so. Record:
deploy/compute_page.py EXACT_BITS; sdk_dist/cottage_sdk/result.py MAX_EXACT_VARS. - Puts one gauge on every certified answer, its entropy in bits: low means one answer clearly won; high means the problem itself is undecided, not that the software failed.
- Answers from our published pages and names the section each answer came from, so you can open it and check. Draws each figure on our Mission page from a committed record and captions it with that record's status word.
- Failed tests in the Mission page's table: 11, each published with its number and the line it had to clear. Record:
deploy/mission_objects.json#refuted.rows. Questions written to look answerable from a document we hold, but not answerable from it: answered confidently 111 of 200 times instead of declining. Record:deploy/chatbot_eval_measured.json#measured_heldout.
- Day AGI
- What Day does for you, and what Day has been measured to do and not to do, failures first.
- Roles
- Who does what behind our numbers and our work, and what each role gives you.