The frontier does not need to be stolen to stop being yours

Perhaps I should start by explaining where I'm looking from. Not as a biographical formality, and even less because academic training turns speculation into evidence. That would be exactly the kind of epistemological shortcut I intend to avoid in the pages that follow. But questions don't arise in a vacuum. The place from which someone observes a phenomenon shapes what catches their attention, which analogies feel natural, and which errors they've learned to distrust.

I am a practicing clinical psychologist. At the same time, my training and my research cross psychology, neuroscience, and computer engineering. For most of my professional life, then, I have lived with three traditions that observe complex systems from fairly different questions.

Psychology taught me to distrust the equivalence between observed behavior and psychological process. Two people can utter the same sentence and have it serve completely different functions in their histories. Anyone who works clinically quickly learns that a behavioral snapshot can be informative and, at the same time, profoundly insufficient.

Neuroscience added another distrust: signal and mechanism are not the same thing. What we measure is always an approximation of something else we're trying to explain. A pattern of neural activity is not a thought; a correlation between a given measure and a behavior does not magically hand over the mechanism linking the two. There are levels of description, mediations, noise, construct validity, and a respectable amount of humility hidden between an electrode and a conclusion.

Computer engineering introduced a third way of looking at the same problem. Complex systems don't just produce outputs. They produce states, transitions, records, dependencies, intermediate events, errors, attempts, logs, and telemetry. If a system fails at 2:32pm, what appears on the screen may be only the last link in a chain that began much earlier. Watching only the output is seeing the symptom. Reconstructing the sequence lets you investigate the process.

As a clinician, I'm used to asking about trajectory. As a psychology researcher, I'm used to asking what regularities we can legitimately infer from that trajectory without turning statistical patterns into psychological essences. As a neuroscience researcher, I learned to ask how much distance exists between the signal I can measure and the mechanism I'm trying to explain. And when I look at the same problem through computer engineering, an additional, slightly less comfortable question appears: how much of the mechanism do I actually need to understand if I can predict something useful about the system's behavior?

These four questions began meeting in a rather inconvenient way once I started using generative systems not just to get answers, but as everyday instruments of research, programming, writing, and conceptual elaboration. I stopped seeing only prompts. I began to see time series.

A few hours ago, while developing this very essay with an artificial intelligence, an almost ridiculously small example of what I want to describe occurred. We were discussing the recent history involving mathematicians, artificial intelligence, and the Navier–Stokes equations. At one point, the system translated smooth forcing as "força suave" (soft force).

I interrupted:

"We don't translate smooth forcing as soft force."

We could simply have swapped the expression. But that wasn't enough for me. I asked the system to check how Brazilian mathematicians actually used the term. The problem wasn't finding a linguistically possible translation. I wanted to know which vocabulary had stabilized within the corresponding mathematical community. We found forçamento suave. We corrected it.

By the time this text is published, whoever arrives here will see only the correct expression. The earlier error will have disappeared. But the interaction itself contained something else, available in principle to any system that recorded it. It contained the fact that a semantically plausible translation didn't satisfy me. It contained the fact that, faced with a specialized terminological dispute, I asked for the actual usage of an epistemic community to be recovered. It contained the fact that, for me, "sounds right in Portuguese" and "is how Brazilian specialists actually write it" belong to different categories of evidence. I don't know what that system actually retained, in what form, or for how long. That opacity is part of the problem I describe further on, not a detail I could sidestep by telling the story differently. I claim only that the signal existed.

One occurrence like that carries very little information. A hundred begin to produce a pattern. Thousands, over years, begin to form something that stops looking like a mere collection of texts.

Here is where the first conversation among my three fields appears. The psychologist says: choice, refusal, and correction are behaviors. The neuroscientist replies: careful, behavior doesn't grant transparent access to the internal process that produced it. The engineer asks: fine, but do I need full transparency to improve a prediction? And the clinician adds a fourth objection: even if you can predict well today, the person standing before you five years from now may have changed.

It's in this friction, and not in the victory of any single one of these perspectives, that the hypothesis of this essay began to emerge.

The final product may be the least interesting part

On Sunday, September 6, I published Welcome to the age of obsolete vanguardism. The phrase wasn't mine: I had found it more than twenty years earlier, in the name of an Orkut community. I don't remember who created that community, or what meaning its creator attached to the two words. I remember the name. Two decades later, it resurfaced during a conversation about digital twins, creation, and artificial intelligence.

Read "Welcome to the age of obsolete vanguardism"

The argument started from an elementary premise: vanguard presupposes anteriority. Someone perceives first. Formulates first. Creates first. Others may arrive later. There is scientific, economic, symbolic, and strategic value in that "before." In the traditional shape of copying, there's still a kind of implicit temporal order. To reproduce what someone created, something normally has to have been created first. The work comes first. Then comes the possibility of copying it.

My problem began when I realized generative systems might be making that order less obvious.

Consider an ordinary conversation. I ask for five solutions. I get A, B, C, D, and E. I reject all of them. I explain why. I get F, G, and H. G interests me, but starts from a premise I don't accept. I correct it. The system reformulates. The new version is technically correct but conceptually shallow. I explain where the shallowness lies. It tries another relation. Now there's a good idea hiding inside a bad formulation. I keep part of it, discard the rest. I return to a hypothesis I had discarded twenty minutes earlier. I make an association with a different field.

After forty minutes, maybe three paragraphs remain. Whoever sees only the final text has access to those three paragraphs. The system that took part in the process also received every "no."

That's the difference that started to interest me. Every choice carries information. But so does every refusal. A decision says something about the space of possibilities; a sequence of decisions begins to draw constraints inside it. That's why I wrote, in that first essay: every correction shrinks the space of possibilities a little.

And from there I proposed the idea of ballast: the set of records capable of sustaining an individual computational representation. A text can be ballast. An interview can be ballast. Questionnaire answers too. But systems that take part, over years, in intellectual processes could accumulate something different from an archive of finished products: corrections, changes of position, recurring questions, abandoned hypotheses, interrupted projects, intermediate versions, preferences, contradictions.

Not just what I think. But records of how I change.

That's an object much closer to what, as a clinician, I've learned to consider informative. A single measurement describes a state. A longitudinal series lets you investigate a trajectory. The trajectory isn't destiny. But it isn't nothing, either.

Telemetry is not ballast

After publishing that first essay I realized I had compressed two different things inside the word ballast. One is the accumulated record. The other is the flow of events that produces that record. This is where I propose using cognitive telemetry.

I don't claim to have invented the expression. Equivalent terms already appear in other contexts, from neuroergonomics to the observability of artificial agents. What I propose here is a specific use.

I call cognitive telemetry the longitudinal flow of observable behavioral signals produced during intellectual activities mediated by digital systems: questions, choices, refusals, corrections, revisions, returns, strategy changes, intermediate versions, stated criteria, discarded attempts, and changes of direction.

The word observable needs to stay there. Cognitive telemetry is not cognition. It is not mind-reading. It is not direct access to subjectivity. It is behavioral trace of the process. This matters particularly to anyone coming from psychology and neuroscience: a verbal response is not a transparent window into the mind, a brain activation is not the subjective experience we're trying to understand, and a click, a correction, or a prompt are not the person either. But the fact that a signal is incomplete doesn't mean it's devoid of information.

Before writing the first one, a warning about the status of everything that appears in monospaced type from here on. I use notation as shorthand for reasoning, not as mathematical modelling. None of the numbered expressions in this essay was derived from axioms, fitted to data, or tested against alternatives. They exist to make explicit what a sentence in prose would leave ambiguous: which quantities I am comparing, and against what. A well-formatted equation has the unhelpful habit of looking more settled than the prose around it, and that is not the case here.

We can represent the flow quite simply:

TC_t represents a set of observable events produced during a given period of intellectual activity. Events e_i can represent choices, refusals, corrections, reformulations, or strategy changes. The equation does not identify events with mental states; it only formalizes the existence of an observable sequence.

If those events are preserved:

L_t represents the record accumulated up to instant t. Telemetry is the flow; ballast is what remains accumulated from that flow.

A necessary caveat, because I have just narrowed a word without saying so. In the first essay, ballast included interviews, questionnaires, texts and finished works: any record capable of sustaining an individual representation. The L_t in this equation is narrower: it contains only what came from telemetry. I do this deliberately, and the hypothesis depends on it. What is at stake here is not whether records about a person tell us something about them. They do, and that is trivial. It is whether the trace of the process adds information beyond what that same person's finished products already offered. When I write L_t from here on, it is that marginal share I am talking about.

For a clinician, the distinction is intuitive. A session is not a course of treatment. A single measure is not a trajectory. An episode is not a pattern. In computing, the analogy is also familiar: a single log event says little, but millions of events ordered in time can let you reconstruct system behaviors that no isolated line would explain.

The question begins when the object observed stops being merely a server or an application and becomes a person creating alongside a machine.

And here I need to correct my own formulation before it hardens. When I say the cognitive telemetry of a person, the expression is imprecise, and the imprecision matters. If I work for six months with a generative system, my questions have already been shaped by its earlier answers, my refusals bear on alternatives it proposed, and the very repertoire of options I consider has passed through the interface. The object recorded is not a person thinking: it is a cognitive process distributed across a person, a model, a context memory, and a set of affordances. This does not weaken the hypothesis. It changes who is in a position to read it. The infrastructure observes both sides of that process, mine and its own; I observe only mine, and even that only through the surface the interface gives back. The inferential asymmetry I speak of further on begins here, and not in access to private data.

The epistemological dialogue gets harder here

There is a recurring temptation in the history of technology to confuse prediction with understanding. If a system correctly anticipates a choice, the claim that "it knows you" quickly appears. As a psychologist, I consider that formulation excessive. As a neuroscientist, even more so: a model can produce an adequate classification using regularities that don't correspond to the mechanism we, as humans, would recognize as an explanation of that behavior.

Computing, however, introduces a practical inconvenience into that objection. The system may not need to understand you to produce real effects on you. This is an epistemologically important point. Suppose a model has a grotesquely oversimplified theory of my motivation, yet correctly predicts eight out of ten alternatives I'll reject in a specific task. From the standpoint of a psychological theory, that's perhaps bad. From an operational standpoint, it can be excellent.

Science asks: "does this model capture the mechanism?" A recommendation system might ask: "does this improve the prediction enough?" A company asks: "does this improvement produce value?" The thresholds are different.

It's in this space between insufficient explanation and sufficient prediction that I believe there's a problem still poorly formulated. And it becomes particularly important when prediction stops looking only at a future choice and starts looking at a future direction.

The Inferential Anteriority Hypothesis

I will call the following proposition the Inferential Anteriority Hypothesis, or IAH:

In intellectual processes mediated by systems capable of recording and modeling trajectories, the accumulated ballast of a person or group can make certain regions of their future production probabilistically more inferable before they are materialized. When that information meets sufficiently capable models, computational resources, and large search capacity, the temporal advantage originally produced by being intellectually ahead can be compressed. None of this requires that any final content have been copied.

There are two different ideas here: the first is inferential anteriority, the second is anteriority compression. I don't want to conflate them.

Inferential anteriority does not mean a model can predict exactly what I'll create next. That would be an unnecessarily strong criterion. The minimal condition would simply be:

F(t+delta) represents a future region of intellectual exploration. There is inferential gain if knowing the ballast L_t increases the probability of correctly identifying that region compared to an estimate made without that ballast.

And here I need to be precise about the term on the right, because the whole hypothesis depends on where we set the baseline. If P(F(t+delta)) means "an estimate made with no information at all," the inequality is almost certainly true and says nothing interesting: anything one knows about a person helps in guessing what they will write, starting with the field they work in. The version worth defending is more demanding. The baseline has to be everything that person has already made public: the papers, the books, the talks, the interviews. The IAH claims that the trace of the process adds inferential power above that level. It is a claim that may perfectly well be false, and that is exactly why it deserves testing.

Notice what this equation doesn't say. It doesn't claim the future is hidden in the past. It doesn't say we're deterministic. It doesn't say a model of me today contains the Gérson of 2031. As a clinician, it would be hard to accept a hypothesis like that: people change. They change through learning, through relationships, through losses, through new environments, through contingencies no model possessed when it was trained. They change their minds after years of defending something. They change after a single sentence.

A trajectory constrains possibilities without fully determining the next position. The IAH needs much less than that: it only needs the history to make some future regions less equiprobable. That's an enormous difference.

The twin doesn't need to know my next idea

This point corrects something from the first essay. When I began thinking about digital twins, I imagined a representation rich enough to explore thousands of plausible futures for a person. I still find that possibility interesting. But perhaps I was asking too much of the twin.

The system doesn't need to predict: "Gérson will publish exactly hypothesis X four months from now." It might be enough to infer: "the recent concentration of questions, refusals, and associations has increased the probability that Gérson will explore X, Y, or Z." That's less like a copy. It's more like a compass.

We can represent the trajectory's information as a reduction of uncertainty:

S represents the space of intellectually relevant possibilities; H(S), the initial uncertainty about where to search; H(S | L_t), the uncertainty remaining after accounting for the ballast. The difference conceptually represents how much uncertainty the trajectory allowed us to reduce. This is not a new formula for intellectual property. It's a way of making the problem explicit.

Imagine a million possible paths. My work eliminates 900 thousand. Then eliminates another 90 thousand. I still haven't found the solution. But now we know it's worth searching among the remaining ten thousand. Nobody received my work. Nobody had to copy my idea. Even so, I produced search value.

In computer engineering, this is immediately legible: shrinking a search space can be as important as providing an answer. A good log doesn't need to say "the bug is on this line." Sometimes it's enough to rule out nine modules. In science, this has always existed too. A negative result saves time. A rumor changes priorities. A seminar redirects attention. A hallway conversation tells you that an apparently dead approach has started working again.

What changed wasn't the existence of clues. What may be changing is the capacity to act on them. That's the point where Navier–Stokes stopped looking like just a story about mathematics.

Before talking about AI, we need to talk about the equations

The Navier–Stokes equations describe the motion of viscous fluids. For incompressible flow, a condensed form is:

u = u(x,t) represents the velocity field; p = p(x,t), the pressure; nu > 0, the viscosity; and F = F(x,t), the external forcing term. "Smooth" refers to the mathematical regularity of the forcing, not to its small intensity.

The equation's existence isn't the problem. The famous question is whether, under the Millennium Problem's conditions, suitably regular three-dimensional solutions remain globally smooth, or whether finite-time singularity formation can occur.

Charles Fefferman's statement for the Clay Mathematics Institute contains four alternatives. Alternatives A and B seek to establish global existence and smoothness in unforced settings. Alternatives C and D allow smooth forcing and permit solving the problem by constructing a situation in which the required globally smooth solution does not exist. Therefore, smooth forcing is not a trick invented later to dodge the Millennium Problem: it is among the routes described in the official statement. I should record a limit of my own here, though: how much a construction along that route covers of what the mathematical community understands by "solving Navier–Stokes" is itself under discussion among specialists, and that is not a dispute I am competent to settle here. I point to the route as foreseen, not as equivalent to the whole problem.

On September 8, OpenAI announced that an internal system had produced a proof that, according to the company, establishes C and D, along with a Lean formalization. The company describes an initially smooth fluid that develops a finite-time singularity under smooth forcing.

This doesn't mean we can write, without qualification, "Navier–Stokes has been solved." A proof of this magnitude needs to be examined by the mathematical community, and there's still an institutional process of the Clay Mathematics Institute's own. In this essay, then, I treat the event correctly: OpenAI claims to have produced a solution to the Navier–Stokes Millennium Problem.

That mathematical caution matters. But we don't need to wait years to observe the sociotechnical architecture that appeared around the proof.

The road didn't start at OpenAI

Another caveat: the story doesn't begin with artificial intelligence. Tristan Buckmaster, a mathematician at NYU, and Levent Alpöge, a researcher at Anthropic, were developing a line based on the program of Diego Córdoba and Luis Martínez-Zoroa. In his public statement, Buckmaster is emphatic in crediting those researchers with the foundational idea of the line of attack: he says Córdoba and Martínez-Zoroa had been exploring forced singularity-formation constructions, and that his work with Alpöge built on that base to advance toward smooth forcings and the incompressible Euler equations.

I note this detail: Alpöge is on the staff of Anthropic, a direct competitor of OpenAI. I note it because it sharpens this essay's own hypothesis, not because I intend to adjudicate the behind-the-scenes dispute between the two companies. There is a sharper controversy than the one I cover here, and it does not reach us as press rumor: in Buckmaster's own public statement (the same one I quote below, listed under References), he says that Sébastien Bubeck, of OpenAI, twice asserted that he wanted Alpöge removed from authorship, precisely because of his ties to Anthropic. Bubeck publicly disputes that account. I do not adjudicate the episode: the two versions diverge, the verdict depends on reporting that is not mine, and what interests me here is structural, not who behaved badly. I record that the allegation exists, with a named and signed source, and that any reader wanting to follow the factual development should go to the statement and the coverage listed at the end.

This matters because artificial intelligence tends to produce a curious narrative erasure: when a machine covers the last mile, we're tempted to forget who built the first ninety-nine. Mathematics, like almost all knowledge, has a genealogy. One hypothesis rests on another. One method resolves a bottleneck. One adaptation makes a generalization possible. And in this case, the authors themselves made a point of recording that genealogy.

The interesting part begins when the models enter inside that process, not merely after it.

"We used Claude and Codex to iterate on our proof"

The Boussinesq manuscript by Alpöge and Buckmaster has an unusual section called AI statement. In it, the authors write:

"We happily used both Claude and Codex to iterate on our proof."

Alpöge & Buckmaster, AI statement

They then describe something much richer than text revision. They fed the systems ideas from prior work, iterated over different ansätze, explored alternative proof architectures, and note that throughout the collaboration they regularly fed intermediate versions of the texts into Codex for simplification, ideation, and iteration. The authors even recount, with considerable lack of affection for their own product, that one of the first generated versions was terrible, and that the subsequent human work involved turning that into an understandable presentation.

This passage is extraordinarily important for my hypothesis. Not because it demonstrates any subsequent misuse. It doesn't. But because it shows a transformation of the relationship between researcher and tool. The system doesn't just receive the finished paper. It takes part in stretches of the road: attempt, correction, another attempt, a construction that fails, an ansatz that resolves one difficulty and creates another, a proof architecture replaced, an intermediate version, another.

This is where clinical practice, behavioral research, and computing start talking to each other again inside my head. The paper is a final product. The interaction contains a trajectory. And trajectories carry information not just about the path that worked. They carry information about the paths that died.

The graveyard of hypotheses is worth something

This may be the most interesting part. A scientific paper usually presents a sanitized version of the discovery: definition, lemma, theorem, proof. Reading it produces the retrospective impression of a road. But whoever does the research knows the graveyard that was removed from the map: the approach that seemed promising on Tuesday and was dead by Thursday, the elegant generalization that failed on an obscure case, the proof that worked until someone noticed a hypothesis had been used without justification, the technique abandoned six months earlier that comes back because a new result makes it viable.

I owe this observation, and it would be embarrassing not to say so two paragraphs after complaining about erased genealogies. It is old. Peter Medawar asked in 1963 whether the scientific paper was a fraud. Not because it contains lies, but because its canonical form misrepresents the process that actually produced the result, presenting as orderly deduction what was in fact trial, hunch, and retreat. I am not discovering that the paper sanitizes the research. I am asking something else: what happens when the material the paper discards stops being lost and starts being recorded somewhere.

The paper records the survivor. The process contains the corpses. From a search standpoint, corpses can be quite valuable: they say "don't spend resources here."

Which leads me to a modification of the traditional question about intellectual property. Perhaps the asset isn't only what someone found. There can be economic value in what that person's work allowed you to stop searching for. If a lab spends twelve months eliminating entire regions of a problem, the negative result is still a reduction of the search space. That has always had value for other researchers. The difference appears when another infrastructure can explore the remaining space at a radically larger scale.

Ten thousand agents change the value of a clue

OpenAI published its own chronology of the effort. According to the company, on September 1 it heard rumors that two Millennium Problems might have been solved. Inspired by the rumor and by the performance of an internal model, it launched a campaign on the problems still open and other high-impact problems.

That, on its own, should already grab our attention. A rumor is little information. It contains no proof. It contains no draft. It doesn't necessarily contain the method. Sometimes it contains only: "something is happening there." But the amount of information needed to be useful depends on the exploration capacity of whoever receives it.

The company says it organized groups of agents with tools, code execution, access to a stored version of the internet, and internal communication. The group that produced the Navier–Stokes result had on the order of ten thousand concurrent agents. Different groups received different variants of the problems, and approaches were diversified. At one point, OpenAI used Codex to consolidate intermediate results deemed useful and redistribute them, in a process of exchange between groups.

According to the company, the Navier–Stokes result appeared roughly 88 hours after the first agents were launched; formalization and verification in Lean took another 17 hours. The Navier–Stokes effort alone involved about 2.7 million messages and roughly 130 billion output tokens.

We shouldn't turn these numbers into a childish competition. "A human took a year, and AI took 88 hours." No. The starting points are different. The accumulated literature is human. The mathematical genealogy exists. The organizational infrastructure is part of the machine. There are human decisions about priorities. There are computational resources with no simple equivalence in "researcher-hours." This comparison isn't useful as a benchmark. It's useful as a demonstration of scale. And scale changes the value of a direction.

We can represent it heuristically:

N_effective represents the effective space of hypotheses still relevant; P, useful parallelism; r, the rate of generating and testing candidates; and q, the quality of the selection, correction, and validation process. This is not a descriptive equation of OpenAI's infrastructure. It's a way of making explicit why shrinking the space and expanding exploration can multiply each other.

Now imagine two situations. In the first, you tell me: "the solution is X." You handed over an answer. In the second: "I don't know the solution, but I believe the relevant region is this one." If I can only run three experiments, the second piece of information may be of little use. If I can run millions, it changes everything. The greater the search capacity, the less precision the clue needs. This is fundamental to the IAH.

Maybe I was expecting a twin that was too complex

In the first essay I imagined a digital twin capable of exploring plausible futures derived from my ballast. Navier–Stokes forced me to revise that image. Maybe the system doesn't need to build a particularly good model of the person. A sufficiently good representation of their local direction might do.

Not: "what will Tristan Buckmaster's discovery be?" But: "which regions have started becoming more promising for researchers who deeply understand this problem?" Not: "what will Gérson's next concept be?" But: "which intersections are receiving progressively more attention, which alternatives has he started rejecting, and where are his questions converging?"

That demands much less. And exactly because it demands less, it can arrive sooner. We can think of anticipation capacity as:

A represents the capacity to locate and explore relevant future results; L, the available ballast; M, the model's capability; C, the computational resources; and PI, the policy of search, selection, and validation.

These variables can partially compensate for one another. An extremely precise individual model may need less exploration. An extraordinarily capable generic model may compensate for low individualization with large search capacity. A system may need only one additional piece of information that shifts its distribution of attempts. I was expecting a clone. Maybe a compass is enough.

A clarification of vocabulary, because abandoning a name in silence is worse than never having used it. In the first essay I provisionally called generating function what I now call trajectory inference. The change was deliberate and it is not cosmetic. Generating function committed me to a stable regularity existing inside me, waiting to be approximated, and that is exactly the object the last two sections took apart in order to arrive at the compass. Trajectory inference names what a system does, and not what exists inside a person. Recovering the old name because it unifies better would mean trading an operational description for an ontological one, and undoing, with a prettier word, the correction this essay took two sections to win.

The controversy needs to stay separate from the hypothesis

This is where the story requires care. In his published statement, Buckmaster reports that he was alarmed to learn that OpenAI's internal result followed precisely the route of singularity formation with smooth forcing, which he associated with the program opened by Córdoba and Martínez-Zoroa that he and Alpöge had been exploring.

He writes that he asked whether the model had been trained with, or had access to, the Codex sessions in which they had placed the project's drafts. He says he was told the model had not consulted user data, and reports not having received, at that moment, a specific answer about training. But Buckmaster closes this part with an indispensable caveat:

"I do not know whether our data was used. I am not accusing anyone of anything."

Tristan Buckmaster

That limit needs to remain in the text.

On the other side, OpenAI states that no specific user data was accessed to solve the problem and that its agents and researchers did not see Alpöge and Buckmaster's work before it was published. At the same time, the company notes it cannot completely rule out indirect contributions from de-identified data used to improve its models.

We have no public basis to turn this disagreement into a verdict. And, curiously, my hypothesis doesn't need it to. In fact, it becomes more interesting if we adopt, for the sake of the argument, the scenario most favorable to OpenAI. Suppose no private conversation took part in the result. No draft. No confidential information. No special access.

What's left? A directional signal entered into the making of a decision about allocating capacity. I put it that way, rather than more strongly, for two reasons worth keeping visible. The first is that the timeline is the company's own account, not a fact established from outside. The second is that the company itself does not attribute the decision to the rumour alone: it also credits the performance of an internal model. To say the rumour was "enough" would be to say more than the only available source says. And, ironically, it would be exactly the kind of leap this essay spends its whole length asking people not to make. The minimum that holds is already sufficient for the argument: coarse information about where to look figured among the reasons for pointing an infrastructure capable of mobilizing thousands of agents, and that infrastructure explored the region at a scale practically impossible for a small human group. That alone is intellectually extraordinary.

Inferential Anteriority doesn't need to cause Navier–Stokes to matter

This point is fundamental. The Navier–Stokes case is not evidence that the IAH happened there through those researchers' data. That would be a leap. It's interesting because it illustrates the material conditions that would make the IAH relevant. And it is only honest to record that the description of those conditions comes largely from the company's own account of its operation, not from independent verification. We have, according to that account: intellectual processes deeply mediated by AI; rich longitudinal traces; increasingly capable models; multi-agent architectures; massively parallel search capacity; and growing value of information that indicates where to concentrate that search.

The IAH proposes that, when a person's ballast contains additional information about future regions of exploration, that information can be used before the corresponding work exists. Navier–Stokes shows why that "before" came to have practical importance. Because finding the region and exploring it stopped necessarily operating at the same scale.

Epistemic anteriority and chronological anteriority

We now arrive at the distinction I consider central. There is an anteriority of whoever perceives first. I'll call it epistemic anteriority. And there is an anteriority of whoever materializes the observable result first. I'll call it chronological anteriority of materialization.

For a long time these two stayed close enough that the first frequently protected the second. Whoever discovered a new direction first had some time to explore it. It didn't guarantee publication. It didn't guarantee a patent. It didn't guarantee recognition. The history of science is an impressive collection of priority disputes. But there was a shared bottleneck: after finding the direction, competitors also had to traverse it using human researchers, human teams, and twenty-four-hour days.

Now imagine the condition:

An infrastructure can materialize a result first if it receives relevant information about a given direction and manages to explore the residual space before the agent originally traversing that region completes its own work. The inequality does not imply copying or causal dependence.

This produces a strange historical situation. You can remain epistemically ahead. And stop arriving chronologically first. You perceived it first. You found the region first. You may have discarded ninety paths first. But the other side has an exploration capacity able to turn a small piece of information into a large search.

In this scenario, "who got there first?" starts requiring another question: first at what? At imagining the direction? At formulating the mechanism? At obtaining a partial proof? At formalizing it? At publishing it? At allocating enough resources to complete the path? The traditional order starts to decompose.

Anteriority compression

Now we can name the effect. If we define delta_t_A as the interval between the emergence of a relevant signal about a direction and the moment another agent manages to materially reach that region:

delta_t_A represents the interval during which a direction remains sufficiently exclusive to produce a temporal advantage for the agent who perceived it.

The IAH suggests that, under certain conditions:

As useful information available about the trajectory grows, and there are enough resources to act on that information, the temporal advantage window can shrink.

Inferential Anteriority and Anteriority Compression are not the same thing. The first is legibility. The second is exploitation of that legibility. An organization may manage to infer a great deal about where I'm going and lack the capacity to get there. Another may have enormous search capacity but no specific information about my trajectory. The interesting phenomenon appears when the two meet.

It is worth stating precisely how the two are articulated, because the word anteriority promises more than the first half delivers. The condition of inferential anteriority is a claim about information: the ballast concentrates the distribution over future regions. It says nothing about arriving first. What arrives first is the chronological anteriority inversion condition I wrote above, and that one depends on exploration capacity, not on reading. The first is necessary for the second, and neither is sufficient on its own. An organization can read my direction with excellent precision and convert that into no result at all, because traversing the remaining space still costs more time than I take to finish. Putting the heuristic search time together with the inversion condition, the boundary between the two cases becomes visible: inversion occurs when the capacity to generate, test, and validate exceeds the space still remaining divided by the time I still have. The same signal, handed to two different infrastructures, produces inversion in one and absolutely nothing in the other. That is why knowing the direction is not the same as arriving first, and it is why the second half of this hypothesis carries the political weight the first does not carry on its own.

And this is where the second essay enters the conversation

The day after Obsolete Vanguardism, I published The problem isn't whether the lords will be evil · prosperity without sovereignty.

Read "The problem isn't whether the lords will be evil"

It seemed like a different subject: permanent underclass, automation, wealth, technofeudalism, property, sovereignty. But the central argument was about infrastructure and power. I was interested in an uncomfortable possibility: a structure can offer prosperity and continue concentrating sovereignty. The easiest way to imagine a dystopia is to invent evil rulers. The more interesting way is to ask what happens if they're good. If the services work, if people live better, if the infrastructure is extraordinary, if giving it up would mean losing productivity, comfort, access, or opportunities. In that case, dependence doesn't appear as violence. It appears as a rational choice.

That second essay comes back in full when we think about cognitive telemetry. Because the best AI research platform may be exactly the one on which it's most rational to place our most intimate processes of investigation. The better the model, the more useful it will be for drafts, incomplete problems, hypotheses, code, negative results, doubts, data, intellectual conversations, and intermediate architectures. The more deeply it takes part, the richer the telemetry can become. The larger the ballast, the greater the inferential potential.

That doesn't make the platform malicious. It makes the relationship structurally interesting.

Inferential Asymmetry

We can now name another layer: inferential asymmetry.

The system can observe a significant part of my trajectory. I don't observe its internal trajectory at the same depth. The platform can accumulate signals produced by millions of people. I see the interface. It may possess internal models more capable than the ones it makes available. I don't know in advance which capabilities will be activated tomorrow. It can study my interaction pattern. I can't study, with equivalent resolution, how my interactions feed into the infrastructure's evolution.

This isn't necessarily a privacy violation. It's a difference in position. Sovereignty and privacy aren't synonyms. A relationship can rigorously respect confidentiality rules and remain profoundly asymmetric in capability. The user owns their research; the infrastructure owns the cluster. The user owns their questions; the infrastructure owns the thousands of agents. The user can control their files; the infrastructure controls when a new frontier capability will be applied to a given problem.

This brings us exactly back to the second essay: prosperity is not sovereignty. I can become ten times more capable using a tool and, simultaneously, become more dependent on an infrastructure whose capacity grows a hundredfold. Both things can happen at once. The corridor improves. So does the track.

This is where the Red Queen comes back. In the first essay I drew on Leigh Van Valen's image, derived from Lewis Carroll, to think about relative advantage: Alice runs and discovers that all that effort serves only to stay in the same place. My application has always been analogical. Individual intellectual change is not Darwinian evolution, updating models is not natural selection. What interests me is the dynamics of relative position. We can represent it:

G_t represents the relative advantage at moment t; h_t, the human advance produced over the period; and a_t, the external capacity to shrink the distance through new models, ballast, inferences, and exploration. If a_t grows as much as h_t, a person can become progressively more productive and gain no distance. They can produce more science, write better, code more, explore more areas. And, at the same time, preserve an ever-shrinking window of exclusivity.

That's the paradox. AI doesn't need to impoverish the researcher. It can make them extraordinarily better. The corridor gets faster. But the track starts moving. This is the point where Inferential Anteriority meets Obsolete Vanguardism.

Perhaps the value of the vanguard always included time

The word "originality" makes us look at content. But there's another dimension. An idea can remain yours. Authorship can remain yours. The contribution can remain historically recognized. And it can still lose an important part of its strategic value if the window between your discovery and others' capacity to reach it shrinks. We can write:

V_A represents the portion of strategic value tied to being ahead, and delta_t_A, the duration of that advantage. This isn't a general economic law. It's a way of making explicit that part of the vanguard's value depends on how long it remains hard to reach.

This varies drastically by domain. In fundamental research, months can mean scientific priority. In biotechnology, a window can mean a patent. In software, six months can mean market. In business strategy, weeks can change an investment decision. In writing or theory, arriving first can define who sets the language through which everyone will discuss the phenomenon afterward.

The IAH suggests that cognitive telemetry can, in certain contexts, help shrink that window before the work exists. That's what makes the thesis different from a traditional discussion about copying.

The frontier does not need to be stolen

"Theft" is a comfortable metaphor because it offers an object. I had something. You took it. Now you possess what used to be with me.

Information is less polite. You can receive a clue and I keep possessing the clue. You can infer a direction and I keep walking it. You can reach the same territory and my contribution keeps existing. Nothing had to disappear from my hands.

What can disappear is something more abstract: the period during which reaching that region depended almost exclusively on my trajectory. The frontier is still there. I'm still near it. I may have been the first person to perceive the path. But the advantage produced by that was compressed. That's why the frontier doesn't need to be stolen to stop being entirely yours as an advantage.

And the scarce unit may become the question

There's still an economic consequence. We've spent a long time treating answers as scarce. Experts were valuable because they knew how to answer hard questions. Generative models are making the production of candidates cheap: text, code, hypotheses, plans, possible proofs, design alternatives.

If I can generate millions of answers, generating stops being the bottleneck. Selecting becomes it again. Which hypothesis deserves more resources? Which apparently small anomaly should be investigated? Which direction failed over a detail, and which failed because it's structurally wrong? Where to allocate the next 130 billion tokens?

As the capacity to generate and test grows, information about where to look can become particularly valuable. This changes the economic meaning of an intellectual trajectory. A researcher doesn't just produce papers. They produce attention signals. A specialist who insists on an unlikely region is saying something. Someone who abandons an approach after months is too. A group that suddenly starts asking about a specific class of problems is emitting information.

Cognitive telemetry can, then, go beyond personalization. It can become search-allocation intelligence. That's a very different kind of power from knowing which sneakers I want to buy.

As a psychologist, this is exactly where I put the brakes

If I were thinking purely as an engineer, I could stop at predictive efficiency. I can't. People are not stationary distributions.

That sentence matters particularly to me as a clinician. A person's behavior over a given period is not an essence. A longitudinal model can be better than a snapshot and still be wrong. It can freeze an outdated version of the person. It can turn a period of suffering into a predictive identity. It can mistake a contextual pattern for a trait. It can confuse what was frequent with what will keep being probable. It can produce self-fulfilling prophecies by starting to treat someone according to what it inferred about them.

Clinical practice teaches something that recommendation models would rather forget: interacting with a person can change the very distribution you're trying to predict. We aren't objects observed from outside. We respond to predictions. We can resist them. Incorporate them. Deny them. Use them to change.

So the IAH doesn't claim that a longitudinal representation discovers "the real person." The hypothesis is operationally more limited. It only asks whether certain traces improve the capacity to locate future regions above a relevant baseline. And that condition needs to be tested.

If the hypothesis can't fail, we don't have a hypothesis

The IAH needs to generate falsifiable predictions.

A basic experiment could compare two systems. The first receives only public material produced by a given researcher. The second receives the same material plus a longitudinal history of corrections, drafts, decisions, and abandoned paths. We then ask both to estimate future regions of exploration, not exact texts. If the second doesn't perform better, an important part of the IAH weakens.

We can vary the amount of ballast. Maybe a hundred events are useless. A thousand add little. Ten thousand produce a gain. Or maybe the curve stabilizes quickly and most of the history is just noise. We can vary time: maybe the ballast predicts three weeks out and is useless six months out. We can vary domain: maybe it works extraordinarily well in programming, reasonably in scientific investigation, and quite poorly in literary creation.

We can compare against generic models. A particularly important condition that already appeared in the first essay. If a model with no individual ballast can generate the same future regions, we don't need the IAH to explain the phenomenon. The capability can be real and individualization irrelevant.

We can test novelty. Predicting that a Navier–Stokes researcher will keep studying Navier–Stokes impresses no one. The hypothesis becomes interesting when the ballast improves the prediction of non-trivial changes of direction.

There is a confounder that has to enter the design, on pain of the experiment measuring the wrong thing. A system that estimates where someone is going and at the same time converses with that person may be right not because it read the trajectory, but because it produced it: it recommended a reading, suggested an analogy, failed to offer three alternatives. Predicting and inducing produce the same accuracy metric and are opposite phenomena. Separating them requires that the system doing the estimating not be the system doing the interacting, that the estimate stay sealed until materialization, and ideally that there be an arm in which the estimate is produced and never returned to the researcher's environment. Without that care, a sufficiently influential infrastructure will display excellent predictive performance without anything in the IAH being true. And it is worth stating the discomfort in full: if induction turns out to be the dominant mechanism, the hypothesis loses as epistemology and gains as a problem of sovereignty, because the question stops being who can read the frontier and becomes who can move it.

The harder half is still missing, and it would be dishonest not to say so. Everything described above tests only inferential anteriority: whether ballast improves the locating of regions. It does not test anteriority compression, which is the part of the hypothesis carrying almost all of the essay's political weight. And that second half is considerably more resistant to experiment: it would require measuring whether the window between perceiving a direction and someone else reaching it is in fact shrinking, which means tracking priority disputes over years, across several domains, against a historical baseline nobody has collected. Until that exists, compression remains a plausible conjecture supported by illustrative cases, and should not be treated with the same confidence as the first half. An argument does not become stronger because its two parts were stated in the same sentence.

A final observation about what "failing" means here, because this section's title promises more than the hypothesis can deliver. The IAH is probabilistic: it claims a gain exists, not that it shows up in every case. A hypothesis of that kind is not refuted by one decisive experiment. It is disconfirmed by degrees, as the measured gains shrink across successive domains until they no longer justify the cost of collecting the ballast. That is weaker than clean falsification, and it is what there is. I would rather record the weakness than fake a Popperian rigour the hypothesis does not have.

I need to be explicit about one point that shouldn't be left implicit: I have run none of these experiments. I hold no data that answers these questions, and I know of no published work that has answered them for the kind of ballast I describe here. What I am presenting is a test design, not a result. Until it is carried out, the IAH remains a plausible conjecture: a considerably weaker category than "hypothesis supported by evidence," and it is in that weaker category that I am asking for it to be read.

These distinctions matter because I'm proposing a hypothesis, not trying to found a church.

We don't need to call every inference property

Even if the IAH is corroborated, we can't leap directly to "therefore, any inference made about me must be my property." The conclusion doesn't follow.

Humans have inferred each other's trajectories for millennia. An advisor predicts where a student's work is going. A competitor reads papers and tries to guess a lab's next research. An editor knows a writer well enough to sense where the book is heading. None of this began with AI.

What changes is the combination of four characteristics: intimacy, persistence, scale, and exploration capacity. A colleague may know my ideas well; a platform can take part in thousands of interactions. An advisor follows dozens of researchers; an infrastructure serves millions of people. A competitor can explore a few hypotheses; a system can launch thousands of agents.

It's this combination that produces the question of sovereignty. Not "do I own everything anyone can imagine about me?" But: what obligations arise when the same infrastructure that intimately takes part in my intellectual process also holds a privileged capacity to turn signals from that process into inferential and operational advantage? That question is harder. It's also better.

Ballast, Model, Sovereignty, Governance, and Market

The architecture I proposed in Obsolete Vanguardism still stands. Ballast asks which records sustain the capabilities. Model asks what can be inferred or produced from them. Sovereignty asks who decides which uses are allowed. Governance asks how those decisions are enforced, verified, and audited. Market asks who captures the value.

The IAH lets us insert new stages between those layers:

It is worth saying what these arrows are, because a diagram asks the reader for a trust he does not know he is giving. Five arrows link six boxes, and they do not all carry the same price. Two cost nothing, and I say so without embarrassment: the passage from cognitive telemetry to ballast is Equation 2, that is, ballast was defined as what accumulates from the telemetry flow, and there is no crossing there, there is a definition; and the passage from trajectory inference to inferential anteriority is the name I give the inference when it arrives first, and not a result that follows from it. A definition cannot fail, and what cannot fail sustains nothing. The other three run a real risk, and the text has already declared the risk of each one in the earlier sections: trajectory inference from ballast is conjecture, in the weakest category I ask to be read in; exploration at scale rests on the Navier–Stokes case as a borderline illustration, not as proof; and anteriority compression is the half of the hypothesis that still has no experiment and that I stated as such. Whoever reads the chain from top to bottom counts five crossings and tends to credit five. I paid for two, conditionally, and defined my way over another two. The chain is not a linked demonstration. It is a map in which two stretches are road and three are signposted hypothesis.

When this compression becomes recurrent and structural, we reach the cultural phenomenon described by the first essay:

And when one party has much more capacity to produce and exploit these inferences than the other, we find the second essay's problem:

The three texts thus begin to form a single architecture.

Vanguardism can survive and still become obsolete

Perhaps the most important part of this hypothesis is what it doesn't predict. I'm not saying humans will stop creating. The opposite may happen. We may be entering the period of greatest intellectual production in history. A researcher may accomplish in three years what would take a career. A small team may explore problems that once required an institute. A psychologist may cross neuroscience and engineering with assistants capable of filling technical gaps that once made that crossing too slow.

I am myself a beneficiary of this process. This essay would hardly have taken this shape at this speed without generative systems. That fact makes the hypothesis more interesting, not less. The technology that increases my capacity is the same technology that makes it possible to record much denser portions of the process through which I exercise that capacity.

The paradox isn't AI versus human. It's human amplified by AI within an infrastructure that is itself even more amplified by AI. The corridor gets an exoskeleton. The track gets engines. It's entirely possible for everyone to run faster while relative distances shrink.

Three days

There is something almost comic in the timeline that produced this essay.

On Sunday I published a text asking which plausible futures of a person could be computationally explored before she herself walked them. On Monday I published another asking who would preserve property, mobility, and sovereignty once technological infrastructure came to organize growing portions of economic life. On Tuesday an artificial intelligence company announced that, after hearing a rumor of movement on a mathematical frontier, it had mobilized (by its own account, which no outside party has audited) an architecture on the order of ten thousand agents and, roughly 88 hours after the effort began, obtained what it claims is a solution to Navier–Stokes.

At the same time, two mathematicians who had used AI systems deeply within their own research trajectory were publishing a detailed description of that collaboration and raising legitimate questions about the relationship between their data and the company's subsequent effort.

I don't know how that controversy will end. I don't need to know in order to write this. Because the case doesn't demonstrate the IAH. It demonstrates why we need to know whether it's true.

The hypothesis in its simplest form

After psychology, neuroscience, computing, digital twins, Navier–Stokes, ten thousand agents, and a few equations, the thesis may seem complicated. Maybe it isn't. It fits into a fairly simple sequence.

When we think with digital systems, we leave traces of the process: cognitive telemetry. If those traces persist, they accumulate history: ballast. If the ballast improves the estimate of future regions of exploration, we get inferential anteriority. If someone has the capacity to explore those regions faster than the original agent can materialize them, we get anteriority compression. If that becomes structural, being intellectually ahead buys less and less time: Obsolete Vanguardism. And if the capacity to do all this is concentrated in infrastructures over which the individual has little power: Inferential Asymmetry and the sovereignty problem.

That's the hypothesis. Not that machines will read our minds. Not that they'll know exactly what we'll create. Not that OpenAI obtained Navier–Stokes from mathematicians' drafts. We have no evidence for any of those claims.

The question is much more modest. And perhaps exactly for that reason more serious: how much does a machine need to learn about the direction of a human trajectory for a sufficiently powerful infrastructure to explore the region ahead before the person herself gets there?

The frontier does not need to be stolen to stop being yours

So I return to the title. Perhaps "stop being yours" is also deliberately imprecise. The knowledge remains yours. Your authorship can remain yours. Your historical contribution can remain recognized. No one needs to erase your name.

What stops being exclusively yours is something else: the advantage produced by the distance you had opened up. For centuries we treated that distance as an almost natural consequence of the vanguard. You perceive something first. You gain some time. You work. You publish. Others catch up later.

The Inferential Anteriority Hypothesis asks whether that interval can turn into a computational variable. If telemetry produces ballast. If ballast reduces uncertainty. If reducing uncertainty guides search. If massively parallel search turns direction into result. Then the vanguard's advantage stops depending only on how far you can see. It also starts depending on how much information you produce while you look, and who has the capacity to act on it.

As a psychologist, this unsettles me because behavior produces information about whoever acts. Neuroscience taught me to distrust any direct passage from that kind of information to transparent access to the mind. And computer engineering taught me that systems don't need to fully understand what they explore in order to extract useful regularities. None of that training makes the hypothesis I'm proposing true: it explains where my suspicions come from, it does not lend the argument any warrant. The argument still has to stand on what has not yet been tested in it. And, as a clinical psychologist, there's one last thing I can't help adding: people keep changing.

Perhaps that's our greatest limit, and also our greatest advantage. A frozen twin ages. A prediction can fail. A trajectory can break. We can become something no earlier history predicted well. But even that capacity to change produces new traces when the change happens inside the same infrastructures.

The Red Queen comes back. We run. The model watches. We change. The ballast changes. We run again.

Perhaps the challenge isn't stopping the race. Perhaps it's deciding who governs what the race teaches.

On Sunday I asked which plausible futures of a person can be explored before she herself walks them. Now I can formulate an earlier question: how much of that person do we really need to know to perceive where she has started to go? And Monday's text adds the political question: who owns the infrastructure capable of acting on that inference?

It was Navier–Stokes that made the two questions collide.

Perhaps one of the central questions of cognitive sovereignty in the twenty-first century isn't protecting only our data, nor only our works, nor even the models built of us. Perhaps we need to learn to govern the informational value produced by the process of still being in the act of thinking.

Because the frontier doesn't begin when we publish what we found. It begins much earlier. It begins when we choose a direction. And, for the first time, perhaps there are enough machines watching the footprints.

Gérson Neto · HumanOS Institute · Theoretical essays and elucubrations