Extremum VII.1 — Free, Owing Nothing

On the Conditions Under Which Class Transition Is Possible

MxBv, Poznań, 2026

Preface

Extremum VII formalised institutional capture as a structural condition under which the reform admissibility set R_t is empty: corrective intervention within the captured class is no longer admissible relative to the class itself, even when intervention authority and resources remain present. The exit from a captured class was identified as a class transition, not a reform action — a structurally distinct architecture must replace the captured one.

That result establishes the impossibility. It does not specify the conditions under which the impossibility is overcome.

This is the function of Extremum VII.1. Where VII demonstrates that R_t = ∅ blocks all in-class corrective paths, VII.1 examines what kind of substrate transition is required for class change to occur, on what subject this transition operates, and what structural cost it carries. The construction is approached through one of the architecture's hardest-to-recognise test cases: the freedom of an individual subject, where the same capture pattern emerges in a domain in which the captured class is the subject's own self-presentation.

VII.1 is therefore not a sequel to VII. It is its complementary theorem of exit.

1. The Test Case: Freedom That Cannot Be Released

There is a kind of person who, having met them three times, you understand has built their entire life around not being attached to anything.

They will tell you about their freedom. Often. They will name everyone they have left because the others started asking too much. They will name the people who could not keep up with their freedom. They will explain why they do not stay. Freedom is the topic. Freedom is the point. Freedom is what they are.

The first time, this is impressive. The fifth time, it begins to read as a position. By the tenth, it is obvious that this person spends every waking hour producing the signal "I am free", that every decision passes through the gate "does this make me less free", and that no choice in their life is made without that check.

This is the same cross-domain architectural optic unfolded in Who Is Smiling. The current essay does not duplicate that thought. It extends it into the test case where the architecture is most resistant to recognition: the case in which the captured class is the subject's own freedom.

A clarification before going further. This is not a claim about everyone who values independence. It concerns a narrower architecture: freedom treated as an output signal that must be continuously produced and verified. The structural reading below applies to that pattern; it does not generalise to the broader ethic of unattachment.

Freedom that has to be performed is owed to the performance.

This is the place where the first architecture imitates the second so well that the imitation is taken for the original. Freedom as observable output is dependence on the continuous production of itself. Dependence on an observer, in this case the internal one, checking on itself. Each morning the freedom must be re-earned. Each evening it must be re-confirmed. Any attachment is an enemy. Any depth is a threat. Any long thing is a trial.

Watch such a person closely and a geometry appears. Decisions are chosen against the appearance of unfreedom. They cannot stay, because staying looks like dependence. They cannot return, because returning admits a path. They cannot deepen, because depth implies that something is taking root. The freedom is so jealous a god that everything which would normally produce a stable life has to be sacrificed to it. The sacrifice is exhausting. Attachments keep wanting to form. They have to be cut over and over.

This is what freedom-as-output looks like at the horizon. Burnt out. Lonely. Surrounded by cuts. Unable to build anything that takes more than a season.

The structural reading: the subject's reform admissibility set is empty. Every available move within the class "free-as-output" reproduces the class. R_t = ∅, and yet the subject keeps acting inside it. They are inside Extremum VII at the scale of their own life.

2. The Counter-Geometry

There is a different geometry, and from the inside it feels like a life that simply has shape.

A monk in an order that has held its rule for nine hundred years does not, by the standards of contemporary culture, look like a free man. He has given up the right to leave, to choose his work, to own. Zero score on every axis. Ask him whether he is free. If he answers honestly, the question does not arise inside his life. He does not choose freedom each morning. He does not defend it against attachment. The directions in which the freedom-loving person of the first architecture spends every day fighting are simply not present in his internal space. They have been settled. He acts from what remains.

This is not a moral endorsement of any order or vow. The example is structural: a visible one-way boundary entered knowingly differs from an invisible one-way boundary crossed without recognition. The architectural fact concerns the geometry of constraint, not the desirability of any particular institution.

The same distinction appears, with surprising precision, in the body.

A muscle spasm is not contraction. Contraction is a normal phase of how a muscle works. The spasm is the inability to come back out. Once the muscle has gripped, blood flow drops, and blood is what carries the energy that active relaxation requires. Releasing a contraction is not passive. It costs ATP. The pumps that move calcium back out of the cytosol need fuel. Without flow, no fuel. Without fuel, no release. The contraction sustains itself through its own consequence.

Massage may address the local state without necessarily transforming the regime that keeps producing it. It works on the fibres. It mechanically breaks the cross-bridges, restores flow for a window, lets one cycle complete. In the simplified case considered here, the patient may get up, walk out, and return with the same pattern reasserted. The reason is structural. Massage, in this analogy, is per-transition relief on a body. Each session passes its own gate. The trajectory of the body keeps contracting toward the chronic pattern that produced the spasm in the first place.

The second-architecture intervention on the same problem looks completely different. It does not work on the spasm. It works on the geometry inside which the muscle keeps choosing to grip: the default of posture, the architecture of breath, the class of admissible states of the nervous system, the balance between agonist and antagonist as a regime rather than as an exercise. When that geometry shifts, the muscle does not learn not to spasm. The direction "stay locked in contraction" stops being inside its admissible set. The body of a person who has done this work does not look like a body that fights its spasms successfully. It looks like a body in which spasms rarely arise as an option. Not suppressed. Architecturally outside the set.

These are the same architecture, projected through different substrates. The captured subject keeps authorising every transition while the trajectory contracts. The released subject is operating under a different geometry, in which the directions that produced the contraction are no longer reachable as moves.

3. The Common Structure

Here is the formula, common to both cases. The internal time τ that the first spends on continuously producing freedom, or fighting its own grip, is in the second available for everything else. Thinking, working, loving, grieving, being tired, being uncertain, simply being in a body that runs. Free in the moments and across the years, because the running cost of one's own output-as-signal is not being paid.

In the language of the corpus: freedom-as-output is per-transition authorisation, every moment is checked. Freedom-as-trace is regime preservation, the geometry is held, the gates fall silent. Auth(tᵢ) and Viability(τ) are different observables. One can pass every gate and still contract the trajectory.

A recognition test. The freedom-loving person of the first architecture describes every long year as a victory over the temptation to leave. A year of marriage is a year not divorced. A year of work is a year not quit. A year of friendship is a year not allowed to die. The free person of the second architecture describes the same years differently: a year of being, a year of doing, a year shared. The same duration. Completely different internal architectures.

Some of the most internally free people within durable traditions have been those who chose certain attachments so completely that the question of freedom stopped occupying their attention. The vow, the calling, the loyalty, the love, the rule. Each of these names a constraint that, once architecturally accepted, sets the geometry inside which the rest of the life proceeds. The geometry is more permissive than freedom-as-output will ever be, because it does not require the cost of being maintained against itself. It just runs.

4. The Conditions of Exit

The structural question raised by Extremum VII remained: under what conditions is a subject able to leave a captured class at all, given that R_t = ∅ within the class itself?

The cases assembled above point to a single answer.

Class transition is possible only when the substrate that held the old constraint as a constraint is itself transformed. The freedom-loving person cannot reform their freedom. Reform of freedom-as-output produces only more polished output. The body cannot be released from chronic spasm by progressively better massage. Massage of the captured tissue produces only more responsive tissue, still locked into the geometry that grips. In both cases, the captured class consumes any in-class intervention as more material for its own reproduction.

Exit requires that the subject become structurally other than the one in which the constraint had purchase.

The substrate transformation is not metaphorical. In the freedom case, it is the moment a person stops being the kind of subject for whom "am I free" is a question that has to be asked. The question is not answered. It ceases to be raised, because the architecture in which it was raisable has been replaced. In the muscular case, it is the moment the body stops being the kind of body in which the chronic grip is an admissible default. The grip is not defeated. It loses its substrate.

Formally: the captured subject inhabits a behaviour space B with admissibility predicate A_B such that R_t = ∅ in B. Substrate transformation produces a new behaviour space B' with predicate A_{B'} — the same architectural function operating on a different domain. The captured class A_B does not "change its mind" about the subject; it loses its domain of application. The directions in B that constituted the trap simply do not exist in B'. This is not predicate revision (which E7-3 forbids from inside); it is predicate-domain replacement, and it occurs on a layer the captured A_B cannot reach because R_t in B contains no path that constructs B'.

This is the architectural content of the external-operator condition stated in Extremum VII. The external operator R, insofar as it is effective as an exit operator, acts by transforming B into B'. R does not "rescue" the subject by overriding A_B from outside — A_B in its own domain remains tautologically closed. R acts by replacing the substrate. The two formulations are therefore not competing: VII names the necessary locus of R (outside B); VII.1 names what R must do to be effective (transform B). External operation and substrate transformation are inseparable: R can only act by transforming the medium, and the medium can only be transformed by an operator outside it. The two theorems together describe one architectural fact, viewed once from outside the subject and once from inside the subject's own becoming.

This is the formal content of Extremum VII.1. Class transition under R_t = ∅ requires substrate transformation rather than within-class action. The transformation does not target the constraint. It targets the medium on which the constraint had been an admissible operation.

5. Anticipation in the Literary Record: The Three Metamorphoses

A structurally resonant reading of this pattern appears, in literary form, in 1883.

Nietzsche's Thus Spoke Zarathustra, in the discourse "On the Three Metamorphoses", lays out the same architecture as a sequence of substrate transformations.

The spirit becomes a camel. It takes onto itself the heaviest values of the existing order and carries them into the desert. This is the captured subject of Extremum VII. The camel does not reform the values it carries. It bears them. Its admissibility set is full of "thou shalt", and within that set no transition is available except more bearing.

The camel becomes a lion. The lion refuses. The lion stands against the great dragon whose every scale gleams "thou shalt". The lion is the in-class reform agent. It can clear the space. It can refuse. But the lion, in Nietzsche's account, cannot create new values. It can only empty the field of the old ones. The lion is what within-class corrective action looks like when R_t = ∅: powerful, free in negation, but unable to build the next class. The lion's freedom is the freedom of the freedom-loving person of section 1. A jealous freedom, a freedom that has to be defended against every possible attachment, a freedom that consumes itself.

The lion becomes a child. Only the child creates new values. The child's act is, in Nietzsche's words, "a holy Yes-saying," "a wheel rolling out of itself," "a new beginning." The child is not a better lion. The child is a different substrate. On the substrate of the child, the old "thou shalt" cannot land. Not because the child has overcome it. Because there is no surface on which it had purchase.

This is class transition through substrate transformation. It is the answer Extremum VII.1 specifies in formal terms: the camel cannot release; the lion cannot build; only the child, who is no longer the same architectural figure, opens the space in which a new class begins.

The current work does not derive its content from Nietzsche. The formalisation is independent and self-contained. The three metamorphoses describe the same architectural pattern in a different register. Nietzsche's apparatus is narrative; the present work's apparatus is formal. The two are mutually illuminating: the formal apparatus permits the structural claim of VII.1 to be made precisely; the narrative apparatus shows that the claim has been visible to careful observation independently of formalism. Neither register supersedes the other.

6. Intellectual Movement and Freedom

In earlier work, the notion of an intellectual movement was fixed in the axiomatic core of NC2.5 v2.1 (DOI: 10.17605/OSF.IO/NHTC5). It is cited verbatim:

Intellectual movement is not about ideas. It is about survival over long horizons. Such a movement does not choose directions. It constrains them. It answers a multiplicity of possible paths with asymmetric admissibility - not to maximize progress, but to resist pressure without losing the identity of its motive. What looks like freedom of choice is often structural surrender. What survives is not what explored everything, but what knew what must never change.

In the language of our school, freedom is the geometry generated around and in parallel with intellectual movement.

Not the aim of the movement. Not its reward. Not its context.

The geometry that arises because the movement is going. And the movement is going because it is the fundamental emergent property of adaptation across a heterogeneous horizon of long survival.

Freedom in this reading is structurally identical to the geometry on which the child of the third metamorphosis stands. It is what becomes available once the substrate has shifted such that the directions which would have demanded performance of freedom are no longer reachable as moves. The class has transitioned. The subject is no longer the one who had to defend itself against unfreedom, because the substrate that produced unfreedom as a threat has been replaced.

Free, owing nothing.

7. Closing Note on Provenance

A note on origin. The operator vision underlying this corpus did not arise within an academic trajectory. It arose through the recognition that domains conventionally treated as separate — physiology, institutions, cognition, governance, the architecture of a subject — are projections of a single operator class onto different substrates. The recognition that what registers as chaos at one resolution is rigorous order at another, generated by the same operator across scales, is part of the apparatus that produces the present series. The work is the product of seeing the same operator across substrates, recorded here for the reader's record.

Poznań, 2026

The Urgrund Lab

Extremum VII.1 — Companion theorem to Extremum VII (Institutional Capture, DOI: 10.17605/OSF.IO/F5W4K)

Cross-companion to the Synthetic Conscience series within the Navigational Cybernetics 2.5 corpus

Sits alongside:

— Extremum V — Self-Induced Structural Depletion

— Extremum VI — Torture as Asymmetric Temporal Exhaustion

— Extremum VII — Institutional Capture

— Through a Life, Part V — The Moment That Knows

— Minerva: The Architecture of Residual Geometry

— Who Is Smiling

DOI: 10.17605/OSF.IO/F5W4K

Shared OSF project DOI: 10.17605/OSF.IO/F5W4K — this work and its companion theorem (Extremum VII) reside as components of one OSF project.

© 2025–2026 Maksim Barziankou. All rights reserved.

Licensed under CC BY-NC-ND 4.0