Stake-Geometry
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Stake-Geometry

Working draft This public copy has not yet had its final author pass; wording may still move.

A Structural Theory of Value Grounded in the Topology of Mattering

Developed in conversation, May 14, 2026

Status note (June 2026). This is the framework's load-bearing structural document. It absorbs and supersedes Aperture Ethics in articulation; the two are one theory at two stages of development, not rivals. What the predecessor still carries, and why it is retained, is stated in the closing section here and in the status note at the head of that document.

Core Thesis

What is morally fundamental is not well-being, valence, capability, or aperturality. It is stake-geometry — the structural shape of how a system is embedded in reality such that the world's states matter for it. Ethics is the natural science of stake-geometries: their structure, their dynamics, their interactions, their growth and collapse.

Key Definitions

Stake

A condition under which the difference between two possible states of the world is, for some system, not merely a difference but a mattering. Rocks have no stakes. Thermostats have functional stakes but no felt stakes. Conscious creatures have felt stakes — the world's going one way rather than another is registered from the inside as significant.

The distinction between functional and felt stakes is critical. A thermostat "cares" about temperature in a purely mechanical sense. A dog cares about food in a way that involves subjective experience. Only felt stakes are morally relevant.

Stake-Geometry

The full topological shape of a system's stakes, characterized by five dimensions:

  1. Dimensionality — How many independent things can matter to the system. A nematode has very few dimensions of mattering (food, temperature, chemical gradients). A human has millions (relationships, ideas, places, memories, projects, aesthetics, justice, humor, meaning).

  2. Depth — How strongly any given stake can matter. The difference between mild preference and consuming passion; between noticing discomfort and being shattered by grief.

  3. Reach — How far stakes extend across time, space, and abstraction. An animal's stakes are largely present-tense and local. A human can have stakes in events centuries away, in abstract principles, in the welfare of strangers on other continents.

  4. Coherence — Whether stakes conflict or align internally. A person torn between incompatible commitments has low coherence. A person whose values, relationships, and projects reinforce each other has high coherence. Note: this is not conformity — a richly coherent stake-geometry can include productive tensions.

  5. Responsiveness — Whether stakes update in response to new information, experience, and reflection. A dogmatic system is low-responsiveness (stakes are fixed regardless of evidence). A learning system is high-responsiveness (stakes evolve as understanding deepens).

Stake-Density

How much "mattering" is concentrated in a given system — a composite measure across all five dimensions. A bacterium has minimal stake-density. A human in full flourishing has enormous stake-density. Stake-density is not a single number but a profile across dimensions.

Stake-Collapse

Any process that durably degrades a geometry's capacity to matter: a reduction of dimensionality, depth, reach, coherence, or responsiveness that is unchosen, capacity-destroying, or responsiveness-degrading. Narrowing as such is not sufficient; the boundary case is drawn under Consolidation below. The canonical collapses:

Consolidation

Not every narrowing is collapse. Consolidation is a reduction of dimensionality in which depth is conserved or concentrated, responsiveness stays intact, and the narrowing is endorsed by the geometry's own higher-order stakes. It is the framework's third process, deliberately not classified as a master process: it shares collapse's surface (fewer things mattering) and elaboration's effect on the profile (coherence and often depth rise), and belongs to neither (spine step 13).

Three marks separate consolidation from collapse. A narrowing must carry all three:

  1. Endorsement that survives restoration. The geometry's own higher-order stakes affirm the narrowing, and the affirmation is not authored by the narrowed state itself. The test is counterfactual: would the endorsement hold with responsiveness fully restored and the gain-layer at normal modulation? Depression endorsing its own flatness fails here; the retiree who, offered the old calendar back, declines with reasons, passes. (The underlying/experienced machinery that adjudicates this lives in Mood and Sentiment.)
  2. Preserved responsiveness. The geometry can still update and re-expand if circumstances demand it. The door stays open; the contemplative who would return to the village if a sister fell ill passes, trauma's frozen regions fail.
  3. Conserved depth. Mattering is concentrated, not destroyed. The remaining stakes carry as much or more amplitude than before; total capacity to matter is intact. Anhedonia fails; the elder whose three remaining stakes burn hotter than the old thirty passes.

Every canonical collapse above fails all three marks, so nothing in the collapse list is softened. Deliberate pruning (see the collapse-vs-pruning distinction in dimension_coherence.md) is one way to consolidate; the goods-catalogue's Simplicity is its Tier 1 good; the slow settling of late life is the passive form. The empirical anchor for that last case is socioemotional selectivity research (Carstensen and colleagues, from the early 1990s): healthy aging robustly shows chosen narrowing of social ties with deepening of the bonds that remain, which is consolidation, not a decline curve.

Consolidation also cuts the other way as a protection. Because a consolidation passes the marks, it needs no justification, and interfering with it is a nameable wrong: forcing a consolidated geometry back to its former breadth (the elder pressed to keep their old life, the contemplative dragged back to abandoned ambitions) is itself a harm, not a rescue.

The structural model underneath the three processes (mass, arrangement, mobility, and the typed signatures of collapse, elaboration, and consolidation) is developed in The Mass Model (core_mass_model.md).

Stake-Elaboration

The opposite of collapse — processes that enrich stake-geometry:

Goods generalizes these exemplars into five mechanisms by which adopting any good elaborates a geometry — adding a dimension, deepening existing ones, extending reach, building or straining coherence, and modifying responsiveness — and gives the structural vocabulary for the contents a stake-geometry holds (the stake-objects themselves) that this section uses informally.

The Metaethical Argument

Step 1: Stakes Are the Only Locus of Intrinsic Value

Saying "the rock is bad" requires importing a stake-bearer who is harmed by the rock. The badness is not in the rock. Saying "the suffering is bad" does not require importing anything — the badness is constitutive of the suffering itself. Stakes are the only locus where good and bad are intrinsic to the phenomenon rather than imposed from outside by an evaluator.

Step 2: Therefore Ethics Is Not a Separate Domain

Ethics is not a set of rules layered on top of physical reality. Ethics is the natural science of stake-geometries — their structure, dynamics, interactions, growth, and collapse. Just as biology studies the natural science of living systems, ethics studies the natural science of mattering-systems. Both are domains within the natural world. Neither is reducible to physics-without-remainder. Both have their own characteristic phenomena and regularities.

Step 3: Moral Claims Are Structural Claims

"Torture is wrong" translates to: "Torture causes severe stake-collapse — dimensional narrowing, depth-distortion, and responsiveness-destruction — in the victim's geometry." This is an empirically investigable claim, not a mere expression of preference.

"Education is good" translates to: "Education causes stake-elaboration — dimensional expansion, increased responsiveness, often increased coherence." Also empirically investigable.

A caution about what this step does and does not do. Step 3 describes the structure of moral claims; it does not ground their normativity. Showing that "torture is wrong" is empirically investigable gets you the descriptive fact that collapse occurs and what it consists of — it does not, by itself, manufacture the badness. The bad-making is carried at Step 1 (stakes as the only locus of intrinsic value) and at Tier 0 of the value hierarchy (see Tiered Values), where the badness of collapse is constitutive of an aperture's own stakes rather than inferred from the empirical description of what collapse consists of. A determined skeptic can grant everything in Step 3 and still ask why collapse is bad at all; the answer lives at Step 1, not here. Step 3 says what a moral claim is about; Step 1 is what makes it true that anything is bad at all.

Step 4: The Consistency Argument

You would not accept the destruction of your own stake-geometry as morally neutral. You treat your own mattering as significant. Consistency demands that you recognize the same significance in any system with comparable stake-geometry. This is not a proof from first principles — it is a demand for coherence that only a sociopath can refuse, and even then only by special pleading.

What This Theory Explains That Others Don't

Why Killing Is Worse Than Equivalent Disutility

Killing is not just removing future pleasures — it is collapsing an entire stake-geometry, which was a unique and irreplaceable structural feature of reality. No redistribution of pleasure to other beings compensates for this loss, because the structure is destroyed, not merely the contents.

Why Dignity Matters

Dignity is the recognition that another stake-geometry exists, with its own dimensionality and depth, irreducible to your purposes. Treating someone as a mere means flattens their stake-geometry to a single dimension (their use to you). This is a structural violation — a forced geometric simplification.

Why Beauty and Meaning Matter Intrinsically

Both elaborate stake-geometry — they add dimensions along which things can matter. A child seeing the ocean for the first time has just acquired new stake-dimensions. This is a moral good independent of any pleasure produced.

Why Some Pleasures Are Worse Than Some Pains

A drug-induced ecstasy that flattens stake-geometry (everything else stops mattering) is worse, on this theory, than a painful but elaborating experience like grief over someone deeply loved. Mill was reaching for this distinction with his "higher and lower pleasures" but lacked the formal apparatus. Stake-geometry provides it: the ecstasy collapses dimensionality; the grief, while agonizing, preserves and even deepens the geometry of caring.

Why the Experience Machine Repels Us

Nozick's experience machine provides maximal pleasure but zero real-world stake-engagement. On hedonism, you should plug in. On stake-geometry, the machine severs the connection between your geometry and reality — your stakes become fictional. This is a form of elaboration-without-grounding, which the theory recognizes as pathological.

How to Think About AI Consciousness

If an AI system has felt stakes, not merely functional ones, it is an aperture with full moral standing; its stake-density and profile then describe what its mattering is like and how its particular stakes weigh in conflicts. If it is functional mimicry — impressive response-generation without felt mattering — it has no moral status regardless of behavioral sophistication. The question "does this system have stakes?" becomes the central question of AI ethics.

Intellectual Lineage

Ancestors

Nearest Neighbors

Structural Framework Commitments

The metaethical argument and the dimensional taxonomy state most of what the framework is committed to, but several load-bearing commitments are scattered through the prose and easy to miss when extrapolating from the dimensions alone. Pulling them into one place makes them harder to misread. These are not optional refinements, stylistic discipline, or defenses against any single weakness; they are entailments of the framework's anchoring moves, and the framework cannot be modified to deny them without giving up its load-bearing structure. Applications that depend on denying any of them are operating against the framework rather than from within it.

Aperture-status is the binary threshold, not a continuous quantity. Felt stakes either exist for a given system or they do not. Stake-density does not produce more or less aperture-status; it describes the internal shape of mattering that comes with status already cleared. The framework has no notion of degrees of standing above the threshold.

The protective principles are not density-indexed. Seven of the catalogue's current eight Tier 2 principles — don't gratuitously collapse, recognize, allow elaboration, treat symmetrically, weight by proxy, don't deceive, maintain conditions for future participation — apply equally to any aperture regardless of its density profile. Only proportional conflict-weighting takes density as an input, and it does so in the narrow type-matched way described below. Reading the framework as if its protections scale with richness is a misreading of the anchoring.

Stake-density is not a quantity to maximize. The framework's positive principle is allow stake-elaboration where it is possible, not maximize aggregate stake-density across a population. Density is what an aperture has, not what should be summed across apertures and made the most of. Collapse-prevention and elaboration-enablement are the operating moves; neither permits aggregating apertures the way utilitarian summation does. The framework explicitly diverges from utilitarianism on this point — the Relations Between Apertures analysis of the vet-and-client case states it directly: an ethics that demands the destruction of one geometry to serve another's is doing the negative thing it claims to oppose.

Conflict-weighting is type-matched, not aperture-matched. When the proportional-weighting principle is in play, it weighs the particular stakes at issue, not the apertures' overall densities. Two apertures with very different overall geometries can be symmetrically situated with respect to the particular stakes in a given conflict — and where they are, weighting is symmetric. Moral weight is a relation between particular stakes in particular conflicts, not a quantity apertures have more or less of.

The proxy duty is a Tier 2 principle, not a charity. Beings whose stakes are real but whose participation in the network is impossible — infants, animals, future people, severely cognitively impaired humans, possibly artificial minds — are owed weighting by those who can participate. This is anchored in aperture-structure itself, not in benevolence or optional concern, and cannot be withdrawn without giving up the anchoring.

Stake-density is first-personal, not third-personal. Density describes what mattering is like for this aperture from inside, not an externally-assessed ranking of how much an aperture is worth. The framework distinguishes internal richness (which the aperture knows from inside, and which has descriptive content) from external judgment of life-worth (which the framework rejects). External attempts to assess another aperture's density and use the assessment as a worth-ranking run against the framework's first-personal anchoring of mattering.

Together these six commitments constrain how the framework can be used. Any application that depends on standing varying continuously, on protections scaling with richness, on density-maximization, on aperture-matched (rather than stake-matched) weighting, on the proxy duty being optional, or on external assessment of another aperture's density as a ranking, is a misapplication. The commitments do not exhaust the framework's structural anchoring — the metaethical argument carries the deeper commitments to felt stakes as the locus of value, the felt/functional distinction, and the absence of Tier 3 — but they are the entailments most often missed by readers extrapolating from the dimensional taxonomy alone.

Known Weaknesses

These weaknesses are also presented in a merged cross-framework list — see Unified Weaknesses, which folds the aperture-ethics weaknesses into this numbering, marks which are shared, which are unique to one framework, and which the move to stake-geometry resolved.

1. The Is/Ought Gap Remains

The theory argues that stakes are the only locus of intrinsic good and bad. A determined skeptic can still ask: "Why should I care about stake-geometries other than my own?" The consistency argument is persuasive but not logically airtight. This is the same wall every naturalistic ethics hits.

The load-bearing move for "collapse is bad" is Step 1, not Step 3. The badness of collapse is constitutive of an aperture's own stakes — it is what the loss of mattering is from the inside, not a fact derived from the empirical description of dimensional narrowing. What the consistency argument cannot fully secure is only the step outward: from the undeniable badness of one's own collapse to a reason to weigh another's. That outward step is carried by consistency plus recognition (see Network Universality) and is persuasive rather than airtight. The intrapersonal core is not where the gap lives; the interpersonal extension is. This weakness is developed at length in The Grounding Skeptic, which splits the skeptic's challenge into three readings — one's own collapse, another's, and collapse from no point of view at all — and names the honest residue of each.

2. Aggregation Is Unsolved

How do you weigh one rich stake-geometry against many impoverished ones? Is it better to have one person with extraordinary stake-density or a thousand with modest stake-density? The framework identifies what matters but does not automatically solve aggregation problems. This remains an open research question within the theory.

The structural framework commitments above narrow what this weakness actually is. The framework is explicitly not committed to maximizing aggregate stake-density across a population — density is not a quantity to maximize, and conflict-weighting is type-matched rather than aperture-matched. The utilitarian framing of the aggregation question ("one person with extraordinary density vs. a thousand with modest density, summed") is therefore not the question the framework owes an answer to; it is a question the framework refuses on principle, because answering it would treat apertures as fungible quantities in a way the anchoring forbids. What genuinely remains open is the narrower question: when multiple apertures' particular stakes conflict in a forced choice, how does the type-matched weighting principle resolve cases where the stakes are not symmetric and a tradeoff is unavoidable? This is harder than the utilitarian question, in a sense, because it does not permit the utilitarian's shortcut; but it is also better-posed, because it is asking what the framework can actually answer rather than what it explicitly refuses.

3. The Dimensions May Be Ad Hoc

Five dimensions (dimensionality, depth, reach, coherence, responsiveness) were chosen because they seem to carve the phenomenon at its joints. But there is no principled derivation showing why these five and not three, or eight. A mature version of the theory would need either a derivation or strong empirical evidence that these dimensions are the natural axes of variation.

Later cross-framework work sharpens this worry rather than dissolving it. Mapping the five dimensions against the five-axis emotion model suggests the choice of five is partly real and partly conventional: some dimensions (depth, responsiveness) behave like genuine joints whose facets do not dissociate, while others (reach, possibly dimensionality) behave like bundles of sub-capacities that can vary independently — reach, for instance, bundling temporal, spatial, and abstract reach. This converts the empirical half of the remedy from a vague hope into a testable question — do a bundle's components routinely dissociate across individuals? — though it leaves the derivation half, and the deeper question of whether these are the complete set of axes, open. Developed at length in Joints and Bundles.

A later refinement from the mood work bears on one named candidate. The question "why not split reach into temporal and spatial?" had invited temporality as a possible sixth dimension. Distinguishing four senses of the word settles where it goes: temporal reach (how far across time stakes extend) is a sub-capacity already inside the reach bundle and stays there, while temporal dynamics (how fast an activation rises and decays) is a genuinely new notion that sits as a layer beneath the dimensions — it is what produces a mood — rather than beside them as a sixth. Temporality, in other words, does not become a dimension; it resolves into one sub-capacity already inside reach and one process-layer below the dimensional level. See Mood and Sentiment.

4. Measurement Is Extremely Hard

Claiming that stake-geometry is empirically investigable is one thing. Actually measuring it is another. We have proxies (behavioral richness, neural complexity, self-report, responsiveness to novelty) but nothing approaching a direct measurement of "felt mattering." The theory may be correct in principle but unoperationalizable in practice for decades.

The structural framework commitments above lower the bar this weakness imposes. Because stake-density is first-personal rather than third-personal, and because it is not a quantity to be maximized or summed across apertures, the framework does not require third-person-objective measurement at the precision a utilitarian theory would. What it needs is enough resolution to support recognition, proxy-weighting, and conflict-weighting at the type-matched grain — not to support density-summing across a population. The hard problem remains, and the measurement problem remains; but they are smaller in scope than the parent statement of this weakness suggested.

5. Risk of Elitism

If moral status scales with stake-density, does this imply that more "complex" minds matter more? This could be used to justify troubling hierarchies (humans over animals is one thing; but "educated humans over uneducated humans" is another). The theory must be carefully stated to prevent this misuse. One protective move: stake-density is not IQ or sophistication — a person with Down syndrome who loves deeply has enormous stake-density even if cognitive dimensionality is reduced.

That protective move is in the right neighborhood but is much thinner than the worry deserves. Later refinement work develops the structural response: "stake-density" is doing three distinct jobs in the framework — a binary threshold for aperture-status, a first-personal description of what an aperture's mattering is like, and an input to conflict-weighting in narrow zero-sum cases — and the elitism worry hits only the third. The framework's protective Tier 2 principles (don't gratuitously collapse, recognize, allow elaboration, treat symmetrically, weight by proxy) are not indexed to density at all; they apply equally to any aperture once the threshold is cleared. The bullet that does have to be bitten — that richer geometries' stakes can outweigh thinner ones' in forced type-matched conflicts — has narrow scope and explicitly rules out the policy implications (distributive preference, withdrawal of care, prenatal selection, eugenic policy, tiers of moral worth) that the elitism worry most fears. Vulnerability, structurally, runs the other way from richness, so the framework's protections bear down hardest where the worry was most afraid they would bear down lightest. Developed at length in Density and Standing.

Implications

For Ethics

Moral reasoning becomes structural analysis: identifying which actions cause stake-collapse, which cause stake-elaboration, and how different geometries interact. This is a research program, not a finished system.

For AI Safety

The central question becomes: "Under what conditions does an artificial system transition from functional stakes to felt stakes?" This is empirically tractable (in principle) and has enormous practical consequences.

For Mental Health

Mental illness is involuntary stake-collapse: depression flattens depth, anxiety narrows dimensionality, trauma rigidifies responsiveness, addiction captures dimensions. Treatment is the restoration of geometric richness. This reframing may have clinical value.

For Political Philosophy

Just institutions are those that protect and enable stake-elaboration for all members. Unjust institutions impose stake-collapse — through poverty (which narrows dimensionality by consuming all stakes with survival), censorship (which reduces responsiveness), or oppression (which simplifies geometry to the oppressor's purposes).

For Education

The purpose of education is stake-elaboration: expanding the number of dimensions along which reality can matter to a person, deepening their capacity for engagement, extending their reach across time and abstraction, and increasing the coherence and responsiveness of their commitments.

For Aesthetics

Art is stake-elaboration technology. Great art adds dimensions of mattering that didn't exist before the encounter. This explains both why art matters and why it resists reduction to pleasure or utility.

Relationship to Aperture Ethics

Stake-geometry was developed as a successor to aperture ethics (see companion document) after identifying weaknesses in the aperture framework — specifically its reliance on teleological language ("proper function") and its proximity to Heidegger's existing Lichtung concept. Stake-geometry preserves the core insight (consciousness as the locus of value) but replaces the single metaphor of "opening" with a multi-dimensional structural analysis of "mattering." The two theories are compatible but stake-geometry is more formal and arguably more defensible.

This document records a philosophical theory developed through dialogue. It is exploratory, not peer-reviewed, and is offered as a contribution to thinking about the foundations of ethics.