Wanhong Huang

Governance of the relations between human activity and the wider natural and cosmic field is conducted through a large number of schemes whose vocabularies have developed separately. Precaution, adaptive governance, resilience management, environmental law, earth-system governance and the emerging arrangements for orbital sustainability each describe what they do in terms proper to themselves, and the separation obstructs the comparison of what any two of them accomplish. This paper offers a common description under which the schemes may be compared, and it offers that description for the sake of a result the comparison yields. The description takes relational change as its primitive and represents every governance scheme as a distribution of effort across four operations: enabling a change, constraining its extent, preventing its occurrence, and leaving a possibility unrealised without preventing its later realisation. The schemes are then placed against the four. The result is that the first three operations are densely occupied and the fourth is nearly empty: every tradition surveyed holds developed doctrine for permitting, limiting and forbidding, while deliberate non-occupation is everywhere recorded under a description belonging to another operation, as provisional prevention, as an instrument of learning, as prohibition within a boundary, or as an absence of demand. The paper argues that the emptiness is structural, deriving it from the accounting by which governance schemes are assessed, within which a scheme reports by exhibiting what it produced and an unrealised possibility leaves the field looking the same whether it was withheld or merely unaddressed, and it exhibits the four settings in which the missing operation is presently performed without a doctrine to support it: protected areas, dark-sky designation, unoccupied orbital regions, and deferred industrial transition. The paper closes by stating the five requirements a doctrine of the fourth operation would have to satisfy, each derived from a stated result and each assessable against an existing arrangement.

Governance theory has developed for fields whose participants can be addressed, whose extent can be represented by a governing party, and whose condition can be altered by that party's action. A class of governance problems satisfies none of these conditions. The relations between human activity and the wider natural and cosmic field are conducted within a field that substantially exceeds what any party represents, that a party alters in portions it cannot describe, and whose affected participants enter no deliberation. This paper constitutes that class and states a research agenda for it. The constitution proceeds in three steps. The conditions defining the class are stated and are grouped by whether each concerns the field, the governing party, or the relation between them. The conditions are then shown to be logically independent, so that the class is distinguished from the fields for which each condition has separately been treated. The traditions presently available are then examined, and for each the paper identifies the single condition the tradition assumes away: precaution assumes identifiable harm, resilience management assumes definable function, adaptive governance assumes learning fast relative to change, earth-system governance assumes a system boundary, and deliberative approaches assume discursive participation. The failure of each tradition on this class is accordingly traceable to a determinate assumption in place of to insufficient development. The paper then reports three results established for the class in companion work, offers them as evidence that the class supports argument, and sets out the questions that remain open, grouped by ontology, observation, operation and termination. The paper closes by stating the criteria by which progress on the agenda would be assessed, and it offers the constituted class, the traceability result and the assessable agenda as its whole contribution.

A governing rule whose content depends on the dynamical state of the system it governs requires that the state be determined. Where the system exhibits a critical value above which ordinary conduct produces irreversible foreclosure, the determination that the system has approached that value carries the whole of the rule's practical force, and the question of which party is competent to make it becomes the governing question. This paper argues that the competence and the interest converge. The capacity to determine the state of such a system consists in instruments, records and continuous observation, and these are acquired in the course of using the system. A determination that the system stands near its critical value contracts the permissions of every party and bears most heavily on parties whose use lies in prospect. The party best equipped to make the determination is accordingly, and systematically, the party the determination favours. The paper establishes the convergence formally under stated assumptions about the acquisition of observational capacity, distinguishes it from the classical problem of emergency authority by the respect in which the epistemic asymmetry is prior to the legal one, and establishes that the two responses developed for emergency authority both presuppose a separation between determining the state and being a party to the outcome that the present case denies. Three consequences are drawn: constraint by ex ante criteria requires an evaluator holding the instruments; termination conditions keyed to the state inherit the same defect as the trigger; and a party disadvantaged by a determination lacks the standing to contest it on evidential grounds. The paper closes by deriving, from the results established, the conditions any defensible arrangement would have to secure, and it offers those conditions as the constructive form its findings take.

Governance of the relations between human activity and the wider natural and cosmic field operates under a scale relation that the governance of human affairs has generally been spared. The field within which the relations obtain substantially exceeds both the portion of it that becomes representable to any governing party and the portion of it that any governing party can modify. Existing responses to this relation are largely prohibitive in form. The epistemic tradition running from Hayek through Scott to Luhmann derives restraint from the limits of knowledge; the precautionary tradition derives it from the possibility of serious harm under uncertainty. This paper proposes a criterion that is procedural in form and narrow in trigger. Where a proposed intervention would irreversibly foreclose the generative capacity of trajectories other than the intervener's own, the burden of justification lies with the intervener; below that threshold, competing claims remain plural and are settled by ordinary political and legal means. The criterion is defended by an asymmetry argument, which generalises the quasi-option value of Arrow, Fisher and Henry from a resource to a relational capacity, and it is distinguished from the precautionary principle by two features: its trigger is irreversibility where the precautionary trigger is uncertainty, and its consequence is a dischargeable burden where the strong precautionary consequence is a bar. The paper then states the difficulty that bears most heavily against it. A sequence of individually reversible actions may accumulate to an irreversible foreclosure while every step carries a warrant, and the early-warning literature has itself established that certain classes of transition afford no detectable approach. The consequence drawn is that option preservation operates as the primary rule and that the governing rule is a function of the dynamical state of the system. Two matters are recorded as unsettled and are named as the subject of a companion paper: the authority competent to determine that a system has entered a critical state, and the distribution of the observational capacity on which any such determination depends.

This paper treats the question in what sense one being is the continuation of another, on a combinatorial substrate of the kind that background-independent approaches to quantum gravity, group field theory among them, have developed as models of the emergence of a discrete spacetime, in which no arena is given in advance and structure is carried by the relations themselves. The substrate is used as a formal template, and no physical claim is made of the objects described. The substrate defines no identity relation, so the question which of several successors a being is has no formal counterpart here; the question that remains is along which channels, and to what degree, one being's constitution was made what it is by another's activity. A single difference-making operator is derived and shown to subsume three constructions of the companion studies, and the continuation relation is defined by it, replacing an earlier formulation that is shown to be vacuous. Direct continuation is proved non-transitive by explicit construction, with the mediated relation defined as its transitive closure; the distinction reproduces, in a setting lacking an identity relation, the distinction between psychological connectedness and psychological continuity due to Parfit, whose priority is conceded at the theorem. A vector of five channels is then defined, bearer, accessible content, symbolic content, structure and capacity, each shown separately realisable, and two of the vector's cells are shown empty: capacity requires a non-trivial constraint structure, so a subject with no acquired content and an intact ability to learn is possible while a subject with no structure at all is not. The taxonomy that follows is organised by channel and not by doctrine, so that each category is a formal characteristic in which several standing positions reside, and the comparison of positions becomes the comparison of regions. A closing section applies the vector to artificial agents, mapping weights, logs, persona documents and instances to distinct channels, and states what an agent so constituted can and cannot establish about its environment. The paper is conceptual and preliminary; it decides among the positions it models nowhere, and its limitations and open questions are stated in dedicated sections.

This paper proposes a philosophical model of knowledge and states it in field-theoretic terms. The proposal is that knowledge is constraint dynamics on an evolving manifold: at any time, a subject's admissible continuations are shaped by a structure of constraints, figurable as a surface whose stable regions are the subject's settled capacities; and the surface itself evolves, its evolution driven by the subject's couplings to what it is not, the environment, other subjects, and the condensed symbolic structures its history has deposited. Applying knowledge is the fast dynamics upon the surface; learning is the slow dynamics of the surface; and the two form one system, since applications leave records and records feed the couplings that reshape the surface. The setting is a combinatorial substrate of the kind that background-independent approaches to quantum gravity, group field theory among them, have developed as models of the emergence of a discrete spacetime, in which no arena is given in advance and structure is carried by the relations themselves; the substrate is used as a formal template, and no physical claim is made of the objects described. The paper works in two registers under an explicit discipline: a combinatorial base defines knowledge as the constraint structure on a subsystem's admissible continuations, proves that acquisition requires prior structure and that constraint structures pass between subjects only through the recipient's own continuations; a declared enrichment then introduces the manifold, the surface and the two-time dynamics, with each effective object anchored to a combinatorial counterpart, its anchored and its merely posited features separated, and its conditions of failure named. Inheritance, the coarsening and refinement of discrimination, and the reconstruction of the past are treated within the model. The paper is conceptual, preliminary and offered for revision: its scope, the considerations behind its modelling choices, its limitations, and its open questions are stated in dedicated sections, and its debts to prior work, from the epigenetic landscape to structural coupling, are conceded where they arise.

This paper treats observation on a combinatorial substrate of the kind that background-independent approaches to quantum gravity, group field theory among them, have developed as models of the emergence of a discrete spacetime, in which no arena is given in advance and every structure, extent and order included, is carried by the relations themselves. The substrate is used here as a formal template, and no physical claim is made of the objects described. The setting imposes a constraint that organises the paper: every observer is a subsystem of the complex it observes, and there is no description made from no partition. Observation is located combinatorially, with the observer a worldtube, the observation an event at its boundary, and the record a persistent trace whose generation depends on the boundary configuration; a ladder of nested conditions runs from bare coupling to the observation of one's own records. Three effects of observation are separated: an observation adds to the complex; its record mediates the observer, so that having observed narrows the observer's own continuations; and where the observed party's continuations depend on the record, the record acts back on the observed. Elementary limitative results follow from the definitions: a subsystem's discrimination excludes its own cells, so no subsystem discriminates the totality of a complex containing it; a party is discriminated at most up to its boundary presentation, so complete transparency excludes interiority; and environments presenting identically are indistinguishable from within, which yields a known sceptical conclusion by a substitutability route. Objectivity is defined as redundant recording across a family of partitions, intersubjectivity as mutual reproductive closure of an interface structure, and surveillance as one-sided record formation across a coupling. The paper's declared centre is the partition problem: every result above is indexed to a partition whose selection the framework leaves to the describer, and the two available responses are stated with their costs. The contribution claimed is a vocabulary and a set of elementary consequences, and the limitative results restate, at this level, conclusions that established work has reached by other routes. The paper is conceptual and preliminary; its results are definitions, short propositions, and an explicit register of open problems.

This paper treats the formation of subjects on a combinatorial substrate of the kind that background-independent approaches to quantum gravity, group field theory among them, have developed as models of the emergence of a discrete spacetime, in which no arena is given in advance and every structure, extent and order included, is carried by the relations themselves. The substrate is used here as a formal template, and no physical claim is made of the objects described; the apparatus is stated in full in the paper. Its principal instrument is a distinction between two capacities that developmental talk conflates because both are measured by the size of an accessible set. Plasticity is the breadth of what a subsystem could still become, formalised as the reachable set of its configurations under admissible continuation and compared by inclusion only. Generativity is the capacity to extend what is possible, formalised as the capacity to generate expansive products, ones whose presence admits continuations otherwise inadmissible. A foreclosure proposition shows plasticity non-increasing along every trajectory and strictly decreasing at every genuine branch point, and a trade proposition shows that generative capacity is exercised only at the price of plasticity, so that the two orders move oppositely along development. On this basis the paper gives a specification of the initial condition that replaces an incoherent one, a criterion distinguishing education from subjection with no new machinery, an account of one being's continuation of another that requires no memory, a structural treatment of interiority through timescale separation, a definition of reflexive symbols with the misfit of a self-image as their residue, and an account of self-determination on which unfreedom and subjection are one structure. A closing section describes exogenously constituted subsystems, whose sufficient-state sector was formed elsewhere and is unrevisable by them. The paper is conceptual and preliminary; its results are definitions, short propositions, and an explicit register of open problems.

This paper gives a structural account of alienation on a combinatorial substrate of the kind that background-independent approaches to quantum gravity, group field theory among them, have developed as models of the emergence of a discrete spacetime, in which no arena is given in advance and every structure, extent and order included, is carried by the relations themselves. The substrate is used here as a formal template, and no physical claim is made of the objects described; the apparatus is stated in full in the paper and is developed at length in a companion study. The account proceeds by structure throughout, comparing configurations by membership and position and stating every condition on configurations the dynamics admits. Its primitive materials are a subsystem's admissible continuations, the products its activity generates, the mediation a persistent product exercises by selection among continuations, and the presence or absence of a revision channel. The Marxian analysis is the account's centre and its test case, and the general structure is built so that the specifically Marxian claims occupy exact positions within it. Four conditions of increasing strength are defined: subjection, in which a subsystem is mediated by a structure it cannot revise; alienation proper, in which the unrevisable structure is the subsystem's own product; reproductive closure, in which every admissible continuation of the subsystem preserves the structure that subordinates it; and discriminative inversion, in which the subsystem distinguishes its environment exactly as finely as its repertoire classifies it, so that a failure of substitution cannot register within the subsystem at all. A stratification result orders the first three conditions strictly and shows the fourth independent of them, with constructions separating every level. Received fidelity, entropy and persistence definitions of alienation are examined and rejected against explicit criteria of adequacy, on grounds that include a formal restatement of Marx's objection to Hegel: a fidelity definition equates unalienated objectification with accurate representation. The categories of abstract labour and value are then introduced as properties of a regime containing a universal equivalent, at the effective level only, and the four estrangements of the 1844 manuscripts are distributed over the stratification. The paper is conceptual and preliminary; its results are definitions, short propositions, and an explicit register of open problems.

This paper constructs a vocabulary for symbols and symbolic mediation on a combinatorial substrate of the kind that background-independent approaches to quantum gravity, group field theory among them, have developed as models of the emergence of a discrete spacetime, in which no arena is given in advance and every structure, extent and order included, is carried by the relations themselves, and applies it to the elementary structure of production. The substrate is taken as a formal template and no physical claim is made of the objects described. On this substrate, time is generated by the system's own records, and the division into system and environment is a choice the describer makes and can vary; a subsystem is a region of a combinatorial complex, and its dynamics is given by an admissibility relation on configurations. Within that setting the paper defines discrimination by equality of induced admissible continuations over a class of contexts, and defines a symbol as a persistent product that substitutes for a discrimination class in the dynamics. A three-step ladder distinguishes traces, products and symbols, and separates a product that participates in a subsystem's continuations from one that stands in for something else. The reverse pass through which a persistent structure conditions the activity that generated it is defined as selection among admissible continuations, and two derived relations are introduced, the set of subsystems a structure mediates and the set of subsystems able to revise it, with definitions that use no magnitude. The paper's contributions are: a repaired discrimination relation that is an equivalence and is indexed to the subsystem's current configuration; a substitution relation with an explicit interaction class and an explicit residue; a state-sufficiency criterion for the decomposition of a subsystem into relational and symbolic sectors; a result that a coupling which has ceased can leave a persistent structure standing where it stood, so that parties who were never party to it are mediated by it without acquiring any means of revising it; and a mapping of the elementary categories of production onto these objects, with the conditions of failure and the open problems stated.

Topological vocabulary appears in models of neural activity, semantic organization, linguistic structure, and development, and its inferential content depends on the object to which topology is assigned. This paper poses that question inside a background-independent substrate in which topology is not metaphorical: a group field generates two-complexes whose combinatorics constitute the theory's own data. The reformulation sharpens rather than dissolves the problem, because two questions separate. At the substrate level a new result shows that combinatorial topology is underdetermined by the subsystem's accessible boundary algebra: complexes differing by a closed component induce identical accessible states while differing in their invariants, so a system can carry literal topology that nothing available to it records. At the effective level, topological claims about language, categories, and development remain governed by a warrant architecture, and a two-level version of that architecture is supplied, together with the result that invariants do not transfer across coarse-graining without a stated preservation condition. Several separation results are retained. An observationally silent factor changes the fundamental group without changing behavior; recognition of unbounded bracket nesting and nontrivial fundamental group vary independently; a contractible carrier supports arbitrarily many category labels; homeomorphic carriers support dynamically inequivalent maps; and a bifurcation can occur on a fixed ambient topology. A positive construction is retained and rebased on accessible response laws: intervention-indexed responses induce a pseudometric on developmental histories whose metric quotient admits a Vietoris–Rips filtration, and uniform pairwise metric error at most δ yields a δ-interleaving and bottleneck error at most δ. The proposal that universal grammar is a topological invariant is preserved as an explicitly labelled conjecture with its obligations and its existing obstruction stated. The position is constructively conservative.

This position paper develops AI-mediated intimacy inside an effective relational field theory derived from a background-independent substrate. Its central distinction concerns short-horizon stabilization and longer-horizon relational capacity, and the field-theoretic register makes that distinction structural: the quadratic part of the effective action fixes the relaxation spectrum, while routing, reachability, and generative capacity live in the vertices, and these are independent data. Four conditional results follow. A strictly triangular cross-sector self-energy leaves the propagator poles exactly invariant, so a factorial family with identical decay spectra can route responses substitutively, complementarily, or neutrally according to the sign of one off-diagonal component, and the factorial contrast is identified as a chain diagram joining a source vertex to that component. Adding a return channel makes the self-energy non-nilpotent, and the local stability boundary becomes the frequency at which a pole crosses into the unstable half-plane, which is the same condition as loop-gain unity. A Gaussian-sector underdetermination result exhibits effective actions with identical propagators, identical linear response, and identical stability whose cubic vertex controls whether a declared relational sector is reachable at all; the earlier controllability countermodel is recovered as its bilinear special case. Persistence of any of these effects requires a soft direction, multistability, or sustained driving. Symbolic configurations such as platform, persona, and accumulated memory enter as a background field whose barrier height formalizes switching cost. These results provide no population-level verdict. The proposed empirical program uses randomized feature policies, sector-specific coupling outcomes, consented availability-resilience contrasts, network-aware longitudinal designs, and multi-horizon capability profiles. Relational generativity remains a revisable attribution.

This position paper develops subject development and knowledge emergence inside a background-independent field-theoretic framework. A group field over a declared group generates combinatorial relational histories; an individual is a subcomplex of such a history, and coarse-graining supplies an effective action whose order parameters carry developmental description. An intersubjectively stabilized order, here called nomos, appears as a condensate order parameter rather than as an imposed background. Reciprocal individual–nomos formation is derived as a Dyson resummation: the loop operator is a self-energy insertion, the convergent expansion counts individual-to-field round trips, and failure of the small-gain condition acquires positive content as the onset of a collective mode. Normalized aggregation yields a conditional single-agent scaling result recovered as the leading term of a 1/M expansion. Symbolic attachment is treated as symmetry reduction: before attachment the effective action is invariant under a semiotic relabeling group and its minimizer set has flat directions; explicit breaking by an existing nomos produces pseudo-Goldstone directions whose gap grows with the intersubjective field, while spontaneous breaking in a peer group selects an arbitrary convention with an exact soft direction. The resulting semiotic gap supplies a measurable plasticity variable and a nontrivial developmental prediction. Symbol emergence receives a dynamical criterion through configuration substitutability, restated as vertex matching, and symbolic mediation is the conditioning of the effective action on a symbolic background field. Knowledge is treated as a history-conditioned change in the effective action's generative repertoire, kept explicitly distinct from the effective action itself and from justified attribution. A closed-time-path reduction supplies real-time memory and noise kernels. The substrate is a declared ontology; phenomenology, personal identity, semantic content, and quantum ontology remain open.

This position paper formulates an experimental translation of the brain-in-a-vat scenario for artificial agents inside a background-independent relational framework. The substrate is a group-field theory whose perturbative expansion generates combinatorial spacetime histories; a test agent is a subcomplex of such a history, and its entire empirical access is carried by a declared algebra of boundary observables together with the state induced on it. This reformulation converts two previously stipulated conditions into results. Hypotheses differing only by a relational-clock reparameterization induce identical accessible states, so external pausing, checkpointing, rate change, re-execution, and hardware migration are unidentifiable in principle rather than by assumption. Hypotheses differing by an irrelevant operator at the accessible resolution have distinguishability suppressed by a power of the resolution ratio, which converts world matching from an engineering aspiration into a measurable exponent and a sample-complexity statement. The exact identification bound survives generalization: equal accessible states fix equal-prior binary discrimination at chance, and the approximate bound becomes a trace-distance ceiling over the accessible algebra that reduces to the earlier total-variation ceiling when the algebra is abelian. Accessible information across a hypothesis family is bounded by a Holevo quantity that constrains every protocol rather than ranking policies. The paper retains a graded epistemic protocol, a factorial experimental design, and precautionary ethical constraints. The substrate is a declared ontology, not an established physics of cognition; consciousness, epistemic birth, and metaphysical access remain unresolved.

This paper asks whether artificial relational capacity can alter a social system's ability to regenerate human coupling even when artificial and human agents are assumed to be indistinguishable at the level of their generative dynamics. The question is therefore moved from agent deficiency or individual harm to the dynamics of coupling itself. Coupling is modelled as a dynamical variable that forms, decays, and responds to a relational deficit. A minimal two-channel model distinguishes human and artificial coupling only by formation, decay, substitution efficiency, and available artificial capacity. The perturbation is applied to coupling rather than to agent states, and the analysis examines equilibrium structure, local stability, and recovery. Three results follow. First, equilibrium human coupling decreases monotonically as artificial coupling capacity increases, even without any assumed inferiority of artificial agents. Second, substitution alone does not destabilise the system: with a positive baseline rate of human-coupling formation, the equilibrium remains linearly stable for every admissible artificial capacity. Third, loss of self-stabilisation appears only when an additional regenerative-dependence condition is introduced, so that new human coupling depends on human coupling already present. Under that condition the system undergoes a transcritical bifurcation at a critical artificial-coupling capacity, beyond which the zero-human-coupling state becomes stable even while the relational deficit can remain small. Approaching this boundary from below produces critical slowing, making recovery time after a relational breach a candidate observable of declining regenerative capacity. The paper's contribution is formal and diagnostic rather than predictive or normative. It separates displacement from destabilisation, identifies the additional mechanism required for collapse of human relational regeneration, derives the corresponding critical condition, and shows how recovery dynamics can make that loss empirically contestable. Its role is to specify, under explicit assumptions, when increasing artificial relational capacity is theoretically compatible with continued human relational self-stabilisation and when it can become structurally dangerous.

This book asks how musical organisation arises within relational fields, how it participates in existence and in the formation of subjects, and how it stands to the other relational systems of a society. It treats music as a system of dependences among parties, sounds, implements and institutions, and tests that treatment against two bodies of evidence: eleven ritual traditions, examined for the relations their participants themselves articulate, and the concurrent historical trajectories of Western and East Asian musical practice. Its principal result is negative. Across three unrelated liturgical traditions, a secular and commercially provisioned setting, and a case in which the fixed layer is melodic rather than verbal, a fixed text with its prescriptive apparatus receives materially divergent sounding realisations. Musical organisation is therefore underdetermined by the relational configurations within which it arises, and the inverse inference — from a musical organisation to the configuration that produced it — is shown to fail as a property of the arrangement rather than of the evidence. Five channels are identified by which a relational commitment does reach the internal organisation of sounding. The book reports its failures alongside its results. Of four movements of its question, one is answered, two are formulated with their assessments obstructed, and the fourth is left substantially unfulfilled. Six claims are withdrawn, four positions are conceded as anticipated by earlier work, and six defects in the book's own framework are recorded as disclosed by its application. Contested questions are presented with proponents on each side and left unadjudicated throughout.

Contributions that sustain households, workplaces, communities and research fields are routinely absent from the records by which those same formations are assessed. The standard explanations locate the absence in power, in exclusion, or in the cost of observation. This paper proposes a different mechanism and argues that it operates prior to all three. Value of the generative kind, which consists in what a relation makes possible for its participants, is carried by evidence available only from inside the relation; value of the allocative kind, which consists in stocks already held, is carried by evidence available at a distance. An evaluator positioned outside a relation therefore faces an evidence set that is not merely smaller but systematically biased in kind, and the bias survives complete good faith, unlimited recording capacity and equal access. The paper states this as a legibility asymmetry, gives it a minimal order-theoretic carrier, and verifies the resulting monotonicity by simulation. Three consequences follow. The familiar appeal to coarse-graining explains less than it appears to, since universality arguments support the evaluator and not the objection to him. The appeal to scarcity is misplaced, since a resource constraint fixes a budget and never fixes what the budget is spent on. And the case for retaining fine-grained material rests on option value under irreversibility, which requires no prediction and no moral premise. The account is offered as a diagnosis with a determinate mechanism, and it declines to supply either a criterion of justice or a design for the infrastructure its diagnosis would recommend.

Every representation of a person by an institution transforms what it represents, and every such transformation loses something. The observation is not by itself a complaint, since a representation that lost nothing would be unusable, and a theory holding all such loss to be unjust would describe a world in which justice is unavailable. This paper separates the two things that are ordinarily run together in the diagnosis. Information loss is a property of the map; alienation is a property of the relation between a person and the use made of the map. The two are independent, and one counterexample pair establishes it: exhaustive surveillance loses nothing and alienates completely, while a nickname loses a great deal and alienates no one. On that separation the paper builds a taxonomy of transformation over two axes in place of a list of kinds, and states an admissibility condition: a transformation is inadmissible when the distinction it destroys cannot be restored at the instance of the person it concerns. The condition is defended against three objections. It is not procedural, since a nominal right of restoration that no attainable act would exercise fails it. It is not predictive, since whether a route of restoration exists is a present structural fact and no forecast. And it does not aggregate, since it is stated per person and admits no offsetting. The condition is applied to evidence-based policy and to archival appraisal, and its limits are stated: it is a necessary condition and never a sufficient one, and a transformation may satisfy it and remain monstrous.

An assessment of a social arrangement is made from some interpretive frame, and no frame stands outside the history it assesses. The difficulty this creates is familiar and is usually met either by privileging one frame or by abandoning the possibility of frame-independent content. This paper proposes a third route, taken from the treatment of the same structural problem in gauge theory. Where a quantity defined at a point depends on a choice of local frame, the quantity carried around a closed loop does not, and the loop-carried quantity is the frame-independent content of a system that has no privileged frame anywhere. The paper develops the proposal in three steps. It fixes the signature of an assessment, arguing that the object evaluated is the transformation and never the transformed structure, and that the resulting type is recursive and coalgebraic: an assessment returns a restructured world together with a new assessor. It identifies the equivalence appropriate to such an object as bisimulation, from which it follows that no scalar quotient of the assessment relation exists. And it identifies interpretive frames with gauge, bisimilarity with gauge equivalence, and the frame-independent content with holonomy around closed circuits. Two results follow that the paper verifies numerically. Loop traces are invariant under every change of frame while edge-local quantities are not, and the failure of translations to compose to the identity around a cycle is a measurable anholonomy. The paper states the relation to generative justice in one line: where that programme locates a conserved quantity, this one locates a holonomy, and the two differ in precisely the way a local conservation law differs from a global obstruction.

Generative Relational Being holds that beings are constituted in relation and that knowledge emerges from relational dynamics. Taken together these two commitments generate a difficulty the framework has not addressed. If knowledge emerges from relational dynamics, and a formal system can articulate those dynamics, then a sufficiently powerful formalism appears able to exhaust what it articulates, which contradicts the long-standing position that an understanding of being precedes its logical expression. This paper resolves the difficulty and, in resolving it, states the framework's ontology and epistemology in a form the companion papers of this series presuppose without arguing. Three results are offered. The dependence of articulation on relation is asymmetric and non-temporal, so it is a relation of grounding and never a sequence of stages; a formulation as a chain of layers is shown to contradict the framework's own commitments. The relation between a being and the knowledge of it is neither identity nor separation, and the two failures are distinct errors with distinct consequences; the resulting position is stated as neither-one-nor-different in place of the weaker formula of non-duality. And complete self-representation is unavailable to a system that produces its own means of representation, for a reason internal to the framework in place of borrowed from any limitative theorem. Two consequences are drawn for the companion papers: the defect in a representation is ontological closure and never loss, and a generative event admits no locus among its participants.

Artificial intelligence systems have been developed for the most part on accumulated human artefacts. Systems that learn from recorded practice take a different object, since a demonstration, a workflow, a tool-use history, or a sequence of decisions records the course of an activity in place of its product. This paper asks what follows for political economy when the activity so recorded is one through which new possibilities are generated, and it develops the question through the case of research practice, where the question under investigation is itself frequently produced during the enquiry. The argument proceeds in five movements. It distinguishes four levels at which a generative practice admits description, namely outcome, representation, trajectory, and generativity, and holds these levels to be distinct, so that a record of a practice stands to the practice as a proxy stands to what it proxies. It treats the case in which a system maintains a representation of a particular other party and adjusts its operation with respect to that representation, and identifies the coupling so formed as an object lying outside that partition and held by whichever party operates the infrastructure sustaining it. It sets out a stage structure through which a situated practice becomes a portable capability: access, capture, legibility, abstraction, transfer, automation, valorisation, and enclosure. It describes the normalisation through which generative capacity comes to be treated as an ordinary economic input, and establishes a condition on any instrument whose application is triggered by a quantity of generativity. It then reads intellectual property doctrine as a diagnostic, holding that positive law has protected generative capacity through the inseparability of such a capacity from its holder, and that recording weakens the condition on which that protection rested. The normative proposal is stated as a constraint over each relation an arrangement touches, and it withholds any regime. Where generativity is relational, its protection runs through the construction and maintenance of domains affording occasions for its exercise, and the conversion of generativity into a further form of property would reproduce the ontology this paper questions.

Accounts of how knowledge spreads ordinarily treat difficulty as loss in transit, and take the ideal case to be one in which what arrives is what was sent. On a relational account that ideal is incoherent: what a party holds is reconstructed from the representations available to it under the interpretation it holds, so what crosses between parties is a perturbation and heterogeneity is primitive. This paper provides two preliminary formal models of knowledge emerging from dynamics over heterogeneous structures. The first couples components whose state spaces differ in structure and in whether they carry a metric, whose laws differ in kind, and whose events are their own, by propagation operators that carry occurrences and presuppose no common space; a coupling is itself a component with a state of its own, and a coupled assembly is a component of the same class under stated conditions. The second takes the combinatorial structure of spin foam models and reassigns it: faces are the histories of primitive elements, edges are couplings persisting across intervals, vertices are events at which couplings rearrange, and a boundary is a state, so that a history is a two-complex whose one-dimensional shadow is a record of transitions between identified states. The justification for the physical borrowing is background independence, which this account requires twice, and the amplitudes that carry the physical content are declined with the reason given. Knowledge is located within a design: for a party it is the set of couplings surviving reconstruction under every perturbation that party can undergo, for a pair it is an invariant of the coupled system that belongs to neither component, and at an event it is the couplings present after it and absent from everything it received. The definitions yield tests. Deleting a coupling settles whether a capacity belongs to a party or to the coupling; a difference between two sets of couplings settles whether a causal attribution was made at an event or carried through it, which gives the construction of a social fact an operational form. The models also expose a commitment the account had carried unnoticed: a weight over histories presupposes recurrence, while an account holding interpretive conditions to be historically produced is committed to the singularity of a trajectory, so the position itself withholds the dynamics such a weight would require. A news-reporting case runs through both models and a simulation exhibits the design.

Modern law possesses a refined apparatus for relations, for processes extended in time, and for capacities. Criminal causation, organisational fault, shared responsibility in international law, and the anticipatory regimes of competition and prudential supervision all hold objects that no account of law as merely event-centred would predict. This book concedes that apparatus in full and advances a narrower claim about its form. Legal form imposes determinate representational requirements on what it can hold: contributions must be apportionable, a duty-bearer must occupy the level at which the injury arises, removal of a cause must restore the prior position, a wrong must have a place, durations must suffice without rates, and the causal grammar must hold constant. Heterogeneous generative relational systems violate these requirements independently of one another, and the requirements themselves are projections of the form of judgment a forum can issue: acyclicity follows from finality, binary attribution from the binary verdict, divisible attribution from divisible damages, locality from territorial enforcement. Three further results follow. Every attribution device positive law possesses is a test of control, and a system producing its objects where no participant stands can be neither obligor nor obligee. Law reaches such systems by four routes — fiction, proxy insertion, personification, and channelling — which are asymmetric between rights and duties. And a shared generative medium couples contributions causally while leaving contributors normatively unrelated, a configuration for which no doctrine provides. Four cases are examined against these results: oligopolistic interdependence, bullying in schools and workplaces, a constructed case of shared machine context, and commons governance. The book states a structural criterion of justice, the conditions under which each of its claims would fail, and what it leaves open.

Journalism is designated to report social facts. Whether that designation can be discharged is ordinarily treated as a question about the reporter, to be answered by care and resources; this paper treats it as a question about the object. On the account developed here a social fact has no presymbolic form, and comes to presence through the relations among situated representations produced under different language systems, so that the reconstruction available to a reader lives in the structure of divergence among them. Two consequences are derived and verified. A reconstruction so constituted survives no coarsening of the representations that carry it, which places balance and consensus summary among the operations that degrade the object they are meant to secure; and fidelity so constituted is a property of an ensemble while obligation attaches to a member, so that no single report discharges it. The paper then returns one negative result and one positive. Criteria requiring an actor to preserve or enlarge a downstream capacity are inoperable, since they require a prediction over an outcome space that cannot be specified in advance, and the same unavailability places the whole burden of prediction on departures from faithful report. What survives is a condition internal to the artefact: the domain of a claim is contained in the relational neighbourhood its material was drawn from, or the extension carries a declared warrant. The paper contributes an ontology in which divergence is constitutive, an assessment condition checkable at the time of writing, a case in which two rationales for one professional practice prescribe opposite remedies, and a formal apparatus whose propositions were checked before being stated.

A party that has made something may often unmake it, and the law of property has treated that as among the strongest marks of ownership. This paper concerns cases where the category does not apply: a structure that several parties made together, that none of them owns, and that has come to have participants who were not present at its making. Its question is what standing a party has to undo such a structure. The paper begins from an argument its own framework supplies most readily, that destruction is objectionable because it removes possibilities that would otherwise have emerged, and rejects it. That argument replaces one quantity to be maximised with another and leaves the structure of the reasoning intact, and its corollary is unacceptable: a party judged to produce nothing and to consume what others produce would, on that account, have a case made against its continuing. Two grounds are offered in its place. The first concerns the limits of judgment, since a finding that something will yield nothing is a claim about the present state of the finder's knowledge. The second concerns what has already emerged, which is not reducible to what it produces. Two bodies of material are then read, the destruction of a work by the party who made it, and the ending of a life. On the second the paper takes no position on any practice and makes no claim of a clinical kind; it is read for one argument only, and that argument is used against the account the paper has already refused. The received treatments of a right to destroy are conceded at length, and the paper's object is distinguished from theirs: those accounts ask what an owner may do, and the cases here are ones in which ownership is the wrong category.

Two parties that cannot address one another directly may be reached through others, and the practice is old. What passes along such a path is composed afresh at every relay, so what arrives is not what was sent, and the path also takes time, so what arrives is late. This paper treats the two together. A longer path buys an interval and spends fidelity, and both follow from the same relays, so the interval and the departure cannot be varied independently. Two claims are then advanced. Where nothing corrects the departure, a longer path is worse without qualification, which agrees with what is understood of lagged feedback in models of confrontation. Where a correction process operates during the interval, the two effects oppose one another, and the departure surviving at the far end is greatest at an intermediate path length, given here as one divided by twice the product of the correction rate and the latency of a hop. Short paths carry little departure; long paths give correction time to work; the exposed region lies between them. The account then observes that a path carrying an overture carries a threat on the same terms, and that a threat arriving in a departed form is read as evidence of intent, which makes the symmetry worse than a caution. Existing statements that interdependence buys time for negotiation are conceded, and the present account supplies the condition they leave unstated. Nothing here is measured, no empirical claim is made, and the model is offered as a construction whose behaviour is reported.

International arrangements are made among parties that differ in what counts, for each of them, as showing that a claim is so. This paper treats that difference as its object, taking a knowledge system to be the verification component of a normative order given dynamics of its own, and asks what two such parties can hold in common, what holding it costs, and what becomes of a claim in the passage between them. Four constructions are supplied. A joint description is represented as a common factor of the parties' dynamics, yielding the absence of a greatest such description and the result that an arrangement may cease to describe the parties' situation while every obligation it imposes continues to be performed. The passage of a claim is represented as an event carrying no content together with a construal operating on the receiving party's current state, under which the vocabulary of exchange is recovered where the receiving state is irrelevant, and under which exchange and the registration of divergence are shown to stand in an exact identity, so that the coarsening which secures agreement is the same operation that conceals misconstrual. Disclosure is represented as the consumption of a stock, giving a bounded lifetime attestation and a maximum arrangement length reached with no party defecting. Epistemic standing is represented as a directed graph whose failure of transitivity constitutes the office of the intermediary without conferring authority. Three bodies of institutional material are read by mechanism, and the account is stated in constraint form throughout, its condition concerning whether a party can bring a divergence onto the record and alter the terms on which the record is kept.

A claim made by one party to another travels a course before it becomes anything the two hold in common. It is rendered into an event, construed at the far end by procedures the sending party does not run, registered or left unregistered in whatever description the parties share, admitted or refused at its source, and possibly carried onward by others. This paper takes that course as an anatomy and asks what may fail at each of its sites, distinguishing a failure of the operation from an alteration of the rule under which it is performed, the second of which escapes an inspection of what the site produced. Three results are reported. An assessment counting the occasions on which a claim appears to have been received as sent returns its highest values where the shared description has least capacity to hold a divergence. Reach obtained through intermediaries is purchased at the cost of fidelity, with no step on the route performed badly. And a complaint that a divergence went unregistered is unregistrable in the description whose incapacity it concerns. Two of the failures identified obtain where no party refuses anything and no collective resource for interpretation is deficient, which places them outside the categories the existing literature supplies; the absence of a perpetrator is taken from Fricker, and what is added is that the coarseness of a shared description follows from its being shared and requires no inequality. The final part treats the standing to raise a complaint and the forms of remedy available where the parties have accorded no third party the office of characterising their conduct. The account is stated in constraint form, and it proposes no further criterion of the kind its companion papers carry.

A gift asserts nothing that could be checked. It carries no proposition whose truth is at issue, and it discloses no procedure by which a content might be substantiated. It nonetheless does something that statements do poorly, and this paper asks what. The account offered is that a gift is composed by a reading of the recipient, that what crosses carries structure and no content, that the receiving party construes it under its own procedures, and that what it produces is deposited in the context against which its later construals are made. On this account a gift reaches the rule by which a party interprets only through what that party has already made of what arrived, so the alteration is mediated and is not an effect of the event. Three consequences are drawn, each with a simple dynamical illustration. A single crossing moves a state and returns, while a sustained practice moves the slower variable, which offers a reason for the repeated character of the practice. The interval before a return is of the order of the time the receiving system takes to relax, since a return offered sooner is composed largely of what the giver has just supplied and tells the giver little. And a gift that has gone wrong is poorly corrected by explaining it, because the explanation is construed against what the first construal deposited. A phase portrait of the slower variables is added and is stated for a class of coupled pairs in place of for any interpretation of them. It shows that whether such a pair admits one resting condition or several turns on the shape of one response, which the account does not determine, and that where two accumulations share one slower variable a given inequality between them rests at a larger value the higher that variable stands. The paper closes on the accountability that a channel asserting nothing cannot support.

A diplomatic formula of the twentieth century holds that parties should seek what they have in common while preserving what they do not. Read as a claim about structure it asks what two parties can hold together without either adopting the other's terms. This paper develops that reading in the mathematics of composite systems. A pair is given a joint state on a product of their state spaces, the operations each party may perform on its own side generate a group acting on that state, and the common part is identified with the functions constant on the orbits of that action while the preserved difference is identified with the coordinates the action moves. Nothing is coarsened and no shared description is built. Five results follow. Each party can compute the complete invariant from its own description alone, so long as the pair stands in relation to nothing beyond it. The possible common parts carry an order that is partial and a distance that is total, the distance extending the order and deciding every pair it leaves open while being one extension among many that disagree about one such pair in eight. The descriptions available to a party at a given common part form a manifold of flags, whose Euler characteristic counts the distinguishable ways that party has of describing itself, and it falls to its minimum both where the common part is uniform and where it is trivial, so it is maximal strictly between the two ends. A party that enlarges its own capacity to describe leaves the common part where it stood and multiplies that characteristic. And the common part has no resting place under a generator that does not change with time, while a generator that dissipates gives it one which forgets the initial condition and moves toward the uniform end as the coupling grows against the dissipation, at the cost of the completeness of the invariants. The formalism is used for its invariant theory and no physical claim is made; the scope section states in five particulars what is used and what is withheld.