Chainarong Amornbunchornvej

Some guilt survives everything the person could learn. A mother forced to choose which of two children to save, a soldier who followed an order that killed civilians, a driver who could not have stopped in time: each knows there was no better option, and the guilt stays. Philosophers have read this as evidence that the person really did wrong, or as a mistake that reflection should correct. This paper offers a mechanism instead. Each of a person's commitments keeps its own account of what is owed, and each judges a loss by one question only: could this debt have been paid? When two commitments demand things that cannot both be done, the commitment that loses finds that its debt could have been paid---by giving up the other---and charges the person. It never asks whether both could have been paid, because it carries only one. So the charge is correct on its own books and wrong about the person, and no fact can remove it, because the missing fact has no place in the account. The charge persists because the mind keeps searching for what could have been done, and in an irreversible loss it keeps finding something. The same search can find what the lost person would want now---people run because she ran, keep the garden she kept---and that quiets the charge. What it does not find alone is what she would say about what happened. That release is available, and someone usually has to ask for it.

Groups routinely complete projects that no single member can plan, execute, or verify alone. We propose a formal model of this phenomenon, Collective Counterfactual Planning (CCP), in which the binding limitation on each agent is neither capability, knowledge, nor observability, but representational geometry: each agent perceives the state, conceives moves, consents to actions, and certifies goal requirements only through a projection onto an agent-specific subspace of a common task space. Four gates jointly determine whether a team can reach a conjunctive goal and legitimately recognize that it has done so: the exogenous implementation coalitions required to perform each action, together with three representational gates -- conception, consent, and task-relative verification qualification. We define the Collective Counterfactual Solvability (CCS) problem, separating geometric feasibility, executable attainment, and validated completion. The results expose a positive-negative duality. Iterated cross-agent relay can unlock a solution that no one-shot pooling of individual plans contains, but any goal requirement depending essentially on the subspace dark to the entire team is unverifiable and therefore not validly completable, even when the trajectory accidentally attains it. Memoryless and audited consent further constrain different objects -- action directions versus cumulative trajectory states -- and neither dominates the other. A four-step exhaustive horizon-bounded solvability scheme is sound and complete under exact representation of the relay closure; restricted implementations remain sound on returned plans but need not be complete. The model gives one geometry for sequential mutual enabling, competent execution of steps whose purpose is invisible to the executor, forced sub-teaming at expertise boundaries, and completion that cannot be validly declared.

When two people disagree for years despite understanding each other, the standard diagnosis is representational: they must lack shared resources for representing one another's considerations. The same diagnosis is applied within a single person whose evaluations stay organized around one consideration across situations that should pull them apart. This paper argues that a large class of both cases requires no representational deficit. Given a shared evaluative basis, disagreement and fixation decompose into three separable components that the representational diagnosis conflates: differences in attention profile (what is weighted, relatively), differences in engagement (how much the domain matters at all), and bounded relative plasticity (why neither moves quickly). A minimal formal model makes the decomposition precise. A persistence bound, derived from a single dynamical axiom, then shows that long-lived disagreement and fixation are exactly what bounded plasticity predicts under fully shared representation --- so persistence is not evidence of representational mismatch. Each of the model's structural assumptions is drawn from the formal literature on dimensional attention in category learning, where it has been independently proposed and, in part, fitted; the transfer from stimulus dimensions to evaluative considerations is defended as an explicit, falsifiable hypothesis. The account complements a recent cognitive-geometric theory of interpretation: where that theory locates communication failure in the null space of an interpretation map, this model characterizes the disagreements that survive when nothing is annihilated.

An agent's opportunity to be authorized by a court, congregation, or electorate is modeled as an ontic random closed set. A culture is represented as a generator, namely a probability law over recurrent social realizations. In each realization, audiences evaluate conduct through their own perception maps, and the conducts authorized by a winning coalition form a feasible set in the agent's conduct space. Coverage measures how often a fixed conduct is authorized across realizations, while its superlevel sets define the essential anchor: the conducts robustly authorized by the culture. The value ladder $v_0 \leq v_1(\eta) \leq v_2$ measures the value of adapting conduct to information and classifies ambitions into structural, statesmanship, and fortuna tiers. The capacity threshold defines structural tragedy as the impossibility of reliable attainment at a declared tolerance, even under ideal information and optimal per-world conduct. These quantities measure the depth and fragility of audience authorization, not rightful authority. A cognitive-perception layer further shows how an agent's own representation of the world can eliminate adaptive advantage, while rehearsal certificates state what repeated practice draws can establish about out-of-sample authorization.

An agent must act on the situation before it, learn what it cannot yet represent, and model other agents well enough to coordinate. These faculties are usually realized by separate mechanisms, yet they share a failure mode: the situation can exceed what the agent can currently represent, and the honest response is then a principled refusal that says what was missing. We develop a small cognitive architecture in which these limits arise from a single quantity. An Interpretation-Decision Unit (IDU) interprets a content vector through a family of regimes, local representational frames with private bases, and decides which actions the interpretation licenses. A scalar residual of the content against the active regimes' representational scope drives the unit. Low residual with a clean licensing emits an action. Otherwise, the unit re-interprets, attempts a description-length-justified expansion of its representation, or halts with a typed, witnessed terminal. We prove the unit is total and deterministic: for any content and fixed configuration, it halts in finitely many bounded-cost steps with a unique terminal witness, so abstention carries its cause by construction. We then show, by binding the architecture's open parameters without changing its mechanics, that the same residual-against-scope constraint recovers three independently documented phenomena at three scopes: the typology of not-knowing (typed abstention), a misunderstanding between agents that is forced, localized to one shared concept, and structurally invisible to the agent committing it (bounded empathy), and prerequisite dependence in learning derived from a bounded focus window rather than posited (developmental prerequisites). Each instantiation is worked for both a natural and an artificial agent and states a falsifiable prediction, showing that the same constraint can model limits in both human and machine cognition. The account contributes a unification: three faculties as one constraint, and a notion of accountable abstention that is typed and witnessed by construction.

Generative AI enables value co-creation by scaling ideation and analysis, but risks value co-destruction when fluent yet insufficiently warranted claims enter commitment pipelines. The binding constraint is therefore not output generation but verification scarcity: AI-generated claims are produced faster than an organization can determine whether they warrant commitment. Organizational AI governance has been theorized at the level of the model and the ethical principle—how AI systems should be designed and overseen—but not at the level of the individual claim those systems emit, where commitment is incurred. This paper develops epistemic governance as the capability that closes this claim-level gap: the admissibility layer, operating claim by claim and gate by gate, that model-level governance presupposes but leaves unspecified. It comprises three complementary components—admissibility infrastructure, institutionalized challenge architecture, and epistemic maintenance—specified counterfactually. Two results follow. First, the components are complementary, not additive: partial implementation can yield worse decision quality than no formal governance. Second, admissibility without protected challenge produces procedurally concealed overreliance—documented compliance rises while substantive verification falls, so confidence inverts from its actual basis. Because this failure is the ceremonial enactment of formally present structures, it is invisible to model-level governance, which audits whether structures exist rather than whether challenge is substantive. Nor is it accidental: compliance demands satisfiable by documentation, throughput pressure, and steep authority gradients jointly select firms into it. Epistemic governance is thus a redistribution of epistemic authority, determining when generative abundance becomes advantage rather than a threat to decision quality.

Contemporary social epistemology faces a critical challenge in explaining "deep disagreements" that defy resolution through evidence-sharing. While recent scholarship has turned to Wittgensteinian hinge epistemology and social ontology to address this, a unified framework connecting individual belief structure to macro-level social conflict is lacking. This paper proposes a three-dimensional geometric model of moral cognition defined by Negotiability (d), Target Scope (τ), and Actionability (α). We argue that deep disagreements are not merely epistemic failures but instances of structural incompatibility between "Normative Selves." Crucially, we demonstrate that this framework is scale-invariant: the Legitimacy Trilemma applies isomorphically to individual cognition, reframing cognitive dissonance as an internal boundary defense. We establish a limit result demonstrating that a normative system -- whether a community or a single mind -- cannot simultaneously maintain Universal Invariant Norms, acknowledge Internal Violations, and practice Quiet Tolerance. We conclude by reinterpreting epistemic injustice not as a vice, but as a structural "repair move" necessary to preserve identity in the face of deep disagreement.

Background: Classical computability and complexity theory analyze how costly a computation is in time or space, assuming inputs are already encoded as finite strings. The knowledge-representation tradition recognizes that representation choices constrain inference—most notably through the expressiveness–tractability tradeoff—but focuses on the complexity of querying a fixed representation, not on whether certain representational resources are necessary for a task to be expressible at all. Meanwhile, deep learning systems exhibit systematic failures on compositional and multi-object reasoning, symbolic systems face the classical symbol-grounding problem, and neuro-symbolic architectures lack a formal account of which representational resources are required for which tasks. Objectives: I aim to develop a computability-theoretic framework that classifies computational tasks by their minimal representational requirements—an axis orthogonal to time–space complexity—thereby providing formal criteria for determining when connectionist, symbolic, or neuro-symbolic architectures are representationally adequate, or provably inadequate, for a given task. Methods: I introduce the Hierarchical Representational Machine (HRM), which stratifies representational resources into four layers: Structured Input Space (L1), grounded in Type-2 Theory of Effectivity; Equivalence and Measurement (L2), formalized via computable quotient spaces and representational measurement theory; Formal Symbolic Representation (L3), providing compositional syntax with effective derivation; and Admissibility Constraints (L4), supplying decidable meta-level filters for safety, legality, and verification. For each layer, I define necessity schemas that identify structural conditions on tasks—invariance, unbounded compositionality, and hard admissibility—under which that layer is provably required. I establish separation results via diagonal and undecidability arguments, and introduce the meta-problem HRM-Classify with the minimal requirement operator Req(T). Results: The main results are: (i) three necessity schemas identifying when specific layers are unavoidable; (ii) separation theorems establishing strict gaps between layer-restricted solvability classes—{L1} ⊊ {L1,L2}, {L3} ⊊ {L1,L2,L3}, and {L1,L2,L3} ⊊ {L1,L2,L3,L4} under external-standard semantics—demonstrating that these layers correspond to genuine computability-theoretic distinctions even for constant-output tasks; and (iii) a solvability classification via Req(T) with worked examples spanning object recognition, program verification, and autonomous driving that illustrate the full layer hierarchy. Conclusions: HRM provides a formal vocabulary for diagnosing representational insufficiency in AI systems: distribution-shift brittleness is identified as missing invariance structure, systematic compositional failures as insufficient symbolic resources, and constraint violations as absent admissibility gates. The framework serves as a principled pre-architectural analysis tool that determines minimal representational commitments before algorithm selection. Because HRM addresses representational feasibility rather than computational efficiency, it complements existing frameworks such as PAC/VC theory, knowledge compilation, and category-theoretic approaches, and is applicable wherever the question "what must be representable?" precedes "how hard is inference?"

This paper develops a geometric framework for modeling concepts, motivation, and influence across cognitively heterogeneous agents. Each agent is represented by a personalized value space, a vector space encoding the internal dimensions through which the agent interprets and evaluates meaning. Evaluative concepts are formalized as structured vectors -- abstract beings -- whose transmission is mediated by linear interpretation maps. An abstract being survives communication only if it avoids the null spaces of these maps, yielding a structural criterion for intelligibility, miscommunication, and concept death. Within this framework, I show how conceptual distortion, motivational drift, and the limits of mutual understanding arise from purely algebraic constraints. A central result -- the No-Null-Space Leadership Condition -- characterizes leadership as a property of representational reachability rather than persuasion or authority. More broadly, the model explains how abstract beings can propagate, mutate, or disappear as they traverse diverse cognitive geometries. The account unifies insights from conceptual spaces, social epistemology, and AI value alignment by grounding meaning preservation in structural compatibility rather than shared information or rationality. I argue that this cognitive-geometric perspective clarifies the epistemic boundaries of influence in both human and artificial systems, and offers a general foundation for analyzing conceptual dynamics across heterogeneous agents.

Concept learning becomes possible only when existing representations fail to account for experience. Most models of learning and inference, however, presuppose a fixed representational basis within which belief updating occurs. In this paper, I address a prior question: under what structural conditions can the representational basis itself expand in a principled and selective way? I propose a geometric framework in which conceptual growth is modeled as admissible basis extension evaluated under a Minimum Description Length (MDL) criterion. Experience, whether externally observed or internally simulated, is represented as vectors relative to a current conceptual subspace. Residual components capture systematic representational failure, and candidate conceptual extensions are restricted to low-rank, admissible transformations. I show that any MDL-accepted extension can be chosen so that its novel directions lie entirely within the residual span induced by experience, while extensions orthogonal to this span strictly increase description length and are therefore rejected. This yields a conservative account of imagination and conceptual innovation. Internally generated counterfactual representations contribute to learning only insofar as they expose or amplify structured residual error, and cannot introduce arbitrary novelty. I further distinguish representational counterfactuals--counterfactuals over an agent's conceptual basis--from causal or value-level counterfactuals, and show how MDL provides a normative selection principle governing representational change. Overall, the framework characterizes conceptual development as an error-driven, geometry-constrained process of basis extension, clarifying both the role and the limits of imagination in learning and theory change.