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Law · Mathematics · Equality of arms
A machinedecided about youand nobody canexplain why.
You were denied a benefit, a loan, a job or a licence, and the explanation you received explains nothing. If an algorithm, a score or an automated process took part in that decision, there is a way to reconstruct it and to contest it. This firm exists for that. Only for that.
Assessing your caseNever charged, whether or not the case has legs.
72 hoursYou get a clear answer: we take it or we do not.
If you cannot payA fixed share of the firm's capacity is reserved for pro bono.
“The system calculated it that way.”
01 / Is this my case?
Start by recognising what happened to you.
Almost nobody arrives saying “an algorithm discriminated against me”. People arrive saying “they turned me down and I don't know why”. These are the shapes the problem usually takes.
Benefits and allowances
You are denied something you believe you are entitled to
A minimum income, a subsidy, a grant, an allowance. The decision cites provisions, but never says which of your data produced the “no”.
Credit and insurance
A score decided for you
A scoring model rejects the transaction, raises the premium or closes the account. Nobody at the institution can tell you what weighed, or correct it.
Employment
A filter ruled you out before the interview
Automated CV screening, video assessment, algorithmic allocation of shifts or gigs, dismissal driven by metrics.
Case files
You end up on a list and cannot get off it
Risk profiling, fraud control, model-selected inspection, revocation of a licence or of a place.
Justice
A tool intervened in your proceedings
Risk assessment, case allocation, assisted drafting or reasoning. The affected party can neither see nor contest that intervention.
Companies
Somebody else's system pushed you out of the market
Exclusion from a tender, suspension of a platform account, automated rating of solvency or reputational risk.
If none of these fits, write anyway. Assessing the case costs nothing, and telling you it is not ours is a useful answer too.
02 / Which cases we take
Three conditions. If one is missing, the case is not ours.
This is not a general practice and does not aspire to be one. Saying so up front saves your time and keeps us honest.
First
A system took part
An algorithm, a model, a score or an automated process played a relevant part in the decision. A computer being involved is not enough: it must have shaped the outcome.
Second
There is concrete harm
You lost something identifiable: a benefit, a job, a loan, a licence, a place, a freedom. Abstract cases are research material, not litigation.
Third
Ordinary law does not reach
The usual route is not enough because the decision cannot be seen, reproduced or contested with the ordinary means of evidence. If a conventional appeal solves your case, there are excellent firms that will do it faster and for less, and we will tell you so.
03 / What we will do with your case
Reconstruct the decision before contesting it.
A system is not challenged with adjectives. It is challenged by showing how it reached the outcome and at which point along the way a safeguard broke.
01 · 72 h
Intake
The case is tested against the three conditions and answered with a clear decision: taken or not taken. If not, we explain why and, where possible, point you to someone who can help.
02
Reconstruction
We identify which system intervened, with what data, under what criteria and with what degree of genuine human involvement. The decision chain is documented and the exact breaking point located.
03
Evidence
The finding is translated into something a court can weigh: technical expert evidence, reproducible proof, traceability of the intervention and comparison of your case against comparable ones.
04
Litigation and remedy
Administrative, judicial or supervisory-authority route, whichever restores the balance sooner. The aim is not only to win the case: it is to make the decision contestable again.
You do not have to understand any of thisBringing the papers and telling us what happened is enough. The technical part is ours.
Deadlines cannot be recoveredIf you have a dated notification, say so in the first line of your message.
Whoever drafts, signsOne senior and one junior carry your case from start to finish. No rotation, no anonymous work.
04 / Fees and pro bono
Someone who loses a benefit cannot pay for a lawsuit.
That is the underlying contradiction of this firm, and it is better said before you ask.
Assessment
Free, within 72 hours
Assessing the case and deciding whether to take it is never charged. If we do not take it, we explain why.
Pro bono
A share of our capacity, ring-fenced
A fixed percentage of the firm's time goes to cases without means whose public interest justifies it. This is not charity: these are the cases that set doctrine.
Companies
By the hour or by project
A closed, written quote before we start, with a detailed engagement letter. No surprises and no opaque billing: that would be incoherent.
Third parties
Funding and costs
Where appropriate, litigation-funding or outcome-sharing arrangements are considered, always within professional-conduct limits and explained in advance.
05 / Cases and testimony
What happens when nobody can explain the decision.
Our own cases where the client authorises publication, and public cases that show the same pattern. No identifying data without express written consent.
Video links open the source platform in a new tab. No player is embedded, so no third-party cookies load without your consent.
06 / Bring a case
Tell us what the system decided and what you lost.
You do not need to know whether an algorithm was involved. Tell us what you were told and we will find out.
If a deadline is about to expire, say so in the first line. Administrative and judicial deadlines cannot be recovered, and that is the only real urgency in this whole process.
Keep everything you have: the decision, the emails, the screenshots, the file number. The sooner the information is requested from the system, the more remains to be reconstructed.
07 / The perplexing case
Two texts from the same year, by the same twenty-year-old.
In 1666 Leibniz published the Disputatio de casibus perplexis in jure and the Dissertatio de arte combinatoria. One asks what to do when the law cannot close a case. The other proposes breaking knowledge down into simple elements and enumerating all their combinations.
That second idea — that one can compute with concepts — is the direct ancestor of what an automated system does today when it scores, classifies, ranks or decides. Enumeration worked: these systems are right most of the time, which is why they have settled into granting a loan, selecting a candidate, allocating a benefit, processing a file.
But a system that optimises the average does not answer for the individual case. And the individual case is a person. A casus perplexus of the twenty-first century is no longer an ambiguous inheritance: it is a decision nobody can explain, issued by a procedure the affected party cannot see, understand or contest on equal terms.
That is where equality of arms breaks. One side knows the system, controls the data and has technical capacity. The other only receives the result.
The injustice
An unbalanced decision
Technology shapes a decision on rights without sufficient safeguards, introduces a bias, or turns an inefficiency into a real disadvantage for one party.
The asymmetry
Technology without equality of arms
One party knows the system, controls the data or holds the technical capacity; the other only receives the result. That difference limits defence and contradiction.
The work
Law, evidence and control
Investigate how the process works, locate the breaking point, and combine legal argument, technical evidence and control measures that restore the balance.
08 / Who signs
Carlos Ibáñez Sánchez
Lawyer since 2011, founder of legal-technology companies since 2013, researcher in law and artificial intelligence.
I began in public and planning law, in the years when the property crisis left many people facing decisions they did not understand. In 2013 I turned a legal inefficiency into my first legal-technology product. Since then I have built systems that automate legal and administrative work: case management, case-law analytics, document extraction, agent architectures.
That is the reason for this firm. I know from the inside how the systems that now decide on rights are built, what can be demanded of them and where they tend to fail. The same competence that builds them serves to take them apart when they get someone wrong.
Research runs alongside litigation and feeds it: meaningful human oversight, traceability of intervention, reasoning under uncertainty and institutional evaluation of artificial-intelligence systems.
Legal Innovation Technology2015 — hoy
AIDEA INTAR · Grupo Planeta2020 — 2025
University of Seville2023 — hoy
KPI Enterprise · Kairos Int.2024 — hoy
IDFOR.AI2026 — hoy
Casibus Perplexis2027 — hoy
Full academic record at ORCID 0009-0005-9997-4466.
09 / The founding compendium
A firm born the day a doctoral thesis is defended.
Casibus Perplexis is not merely incorporated before a notary. It is founded by a deed signed by the thesis supervisor and by the members of the examining board. That document is the first piece of the compendium and the only one that cannot be rewritten.
The compendium gathers the rules of the house: how one enters, how one works, what is accepted and what is not. It is written to outlast its founder. A firm that litigates against decisions nobody can examine must itself be open to examination.
Entry
Doctors only
To practise here you must hold a doctorate in law, in mathematics, or in both. This is not elitism: these matters demand reading a model and a judgment with equal ease, and that competence is evidenced by a thesis defended before a board.
Form
One senior and one junior
Teams are of two, in the manner of Wachtell & Lipton and, before that, of the tutor and the disciple of antiquity. No pyramid, no rotation, no anonymous work. Whoever drafts, signs.
Subject matter
Complex cases, and only those
Automation of administrative and judicial decisions, scoring systems, profiling, and any AI-assisted decision affecting rights. Low volume, high difficulty, public impact.
Spirit
The human being at the centre
The cultural reference is not a law firm: it is Adriano Olivetti and La ciudad del hombre. Technology as a tool in the service of people's lives, and the firm as a counterweight when it stops being one.
Publication planned for January 2027, the day after the thesis defence.
10 / Writing and templates
The templates we use, published.
Briefs, templates and academic work. Part of it is free because those who need it most cannot pay for it; the rest sustains the work that produces it.
11 / Voices and content
Podcast, talks and interviews.
In-house production and appearances in third-party media. Anything that helps this be understood outside the profession.
12 / Work here
We hire very few people, and we hire them carefully.
One senior and one junior per team, for years. You come in with a doctorate in law or mathematics and you leave knowing how to litigate against a system. If volume is what interests you, this is not the place.
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Send a CV, one piece of your own writing you are proud of, and a paragraph on the case you would like to run. The writing counts for more than the CV.
13 / Channels
Where all of this is published.
The newsletter is the main channel: the firm's writing arrives there before anywhere else. The rest are mirrors.