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Bond, A. H. (2025b). “No Escape: Mathematical Containment for Artificial Agents.” Working paper, San José State University.

Bond, A. H. (2025c). “Stratified Quantum Normative Dynamics: A Geometric Framework for Moral Deliberation.” Working paper, San José State University.

Bond, A. H. (2026a). “The Dear Abby Corpus: Thirty-Two Years of Natural Moral Reasoning.” Working paper, San José State University.

Bond, A. H. (2026b). “The Dear Ethicist Game: Engineered Probes for Geometric Ethics.” Working paper, San José State University.

Bond, A. H. (2026c). “ErisML: A Modeling Language for Geometric AI Governance.” Technical specification, San José State University.

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Bond, A. H. (2026e). “The Grand Unified AI Safety Stack (GUASS): A Seven-Layer Architecture for Ethical AI.” Technical specification, San José State University.

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Philosophy: Ethics and Political Theory

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Philosophy: Moral Uncertainty

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Mathematics: Differential Geometry and Topology

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Mathematics: Algebra and Logic

Gödel, Kurt. “On Formally Undecidable Propositions of Principia Mathematica and Related Systems I.” Monatshefte für Mathematik und Physik 38 (1931): 173–198.

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Physics

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Quantum Cognition and Consciousness

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Penrose, Roger. Shadows of the Mind: A Search for the Missing Science of Consciousness. Oxford: Oxford University Press, 1994.

Penrose, Roger, and Stuart Hameroff. “Consciousness in the Universe: A Review of the ‘Orch OR’ Theory.” Physics of Life Reviews 11, no. 1 (2014): 39–78.

Pothos, Emmanuel M., and Jerome R. Busemeyer. “Can Quantum Probability Provide a New Direction for Cognitive Modeling?” Behavioral and Brain Sciences 36, no. 3 (2013): 255–274.

AI Safety and Governance

EU High-Level Expert Group on Artificial Intelligence. Ethics Guidelines for Trustworthy AI. Brussels: European Commission, 2019.

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National Institute of Standards and Technology. Artificial Intelligence Risk Management Framework (AI RMF 1.0). NIST AI 100-1. Gaithersburg, MD: U.S. Department of Commerce, 2023.

Literary and Historical References

Styron, William. Sophie’s Choice. New York: Random House, 1979.

The Bible. New Revised Standard Version. Acts 9:1–19 (the conversion of Saul on the road to Damascus).

Liu An (刘安), ed. Huainanzi (淮南子). c. 139 BCE. The parable of the Old Man at the Border (塞翁失马, Sāi Wēng Shī Mǎ) appears in Chapter 19, “Lessons of the Human World” (人间训).

Robert, Henry M. Robert’s Rules of Order Newly Revised. 12th ed. New York: PublicAffairs, 2020. First published 1876.

Supplementary References in Differential Geometry

Berger, Marcel. A Panoramic View of Riemannian Geometry. Berlin: Springer, 2003.

Chern, Shiing-Shen, Wen-Tsün Wu, and Wei-Liang Chow. “Differential Geometry.” In Handbook of Applicable Mathematics, vol. 5, edited by Walter Ledermann. Chichester: Wiley, 1990.

Milnor, John. Morse Theory. Annals of Mathematics Studies 51. Princeton: Princeton University Press, 1963.

Spivak, Michael. A Comprehensive Introduction to Differential Geometry. 5 vols. 3rd ed. Houston: Publish or Perish, 1999.

Supplementary References in Ethics

Gilligan, Carol. In a Different Voice: Psychological Theory and Women’s Development. Cambridge, MA: Harvard University Press, 1982.

Noddings, Nel. Caring: A Feminine Approach to Ethics and Moral Education. Berkeley: University of California Press, 1984.

Parfit, Derek. Reasons and Persons. Oxford: Clarendon Press, 1984.

Williams, Bernard. “Ethical Consistency.” Proceedings of the Aristotelian Society, Supplementary Volumes 39 (1965): 103–124.

Williams, Bernard. Ethics and the Limits of Philosophy. Cambridge, MA: Harvard University Press, 1985.

Supplementary References in Gauge Theory and Mathematical Physics

Baez, John C., and Javier P. Muniain. Gauge Fields, Knots and Gravity. Series on Knots and Everything 4. Singapore: World Scientific, 1994.

Bleecker, David. Gauge Theory and Variational Principles. Global Analysis Pure and Applied Series A 1. Reading, MA: Addison-Wesley, 1981.

Weinberg, Steven. The Quantum Theory of Fields. 3 vols. Cambridge: Cambridge University Press, 1995–2000.

Supplementary References in Social Choice and Decision Theory

Fishburn, Peter C. The Theory of Social Choice. Princeton: Princeton University Press, 1973.

Gibbard, Allan. Wise Choices, Apt Feelings: A Theory of Normative Judgment. Cambridge, MA: Harvard University Press, 1990.

Luce, R. Duncan, and Howard Raiffa. Games and Decisions: Introduction and Critical Survey. New York: Wiley, 1957.

Supplementary References in AI Ethics and Alignment

Amodei, Dario, Chris Olah, Jacob Steinhardt, Paul Christiano, John Schulman, and Dan Mané. “Concrete Problems in AI Safety.” arXiv preprint arXiv:1606.06565, 2016.

Bostrom, Nick. Superintelligence: Paths, Dangers, Strategies. Oxford: Oxford University Press, 2014.

Gabriel, Iason. “Artificial Intelligence, Values, and Alignment.” Minds and Machines 30 (2020): 411–437.

Harris, Sam. The Moral Landscape: How Science Can Determine Human Values. New York: Free Press, 2010.

Russell, Stuart. Human Compatible: Artificial Intelligence and the Problem of Control. New York: Viking, 2019.

Note on citation practice. Many references in this book are to classical works (Aristotle, Kant, Hohfeld) and to named mathematical structures (Riemannian manifolds, Noether’s theorem, Whitney stratification) that are part of the standard inheritance of their respective fields. Where a specific passage is cited — as with Aristotle’s Nicomachean Ethics 1106b21 or Kant’s Groundwork 4:421 — the standard scholarly reference system (Bekker numbers, Akademie pagination) is used. Where a mathematical structure is referenced by its originator’s name, the foundational publication is listed above; the reader seeking textbook treatments is directed to the mathematical preliminaries of Chapter 4 and its bibliographic notes (Section 4.11).

The author’s own prior work, listed at the top of this bibliography, provides the empirical and technical foundations on which the book’s theoretical framework is built. These papers and technical specifications are available through the author’s institutional page at San José State University.

Index

Note: References are to chapter and section numbers (e.g., 5.3 = Chapter 5, Section 5.3). Boldface indicates the primary definition or introduction of a term. “TA” indicates the Technical Appendix of the cited chapter.

A

absorbing strata, 5.6, 8.3, 8.9, 17.2; see also nullifiers - abuse as, 5.6, 8.3, 17.2 - danger as, 5.6, 8.3 - impossibility as, 5.6, 8.3 - retraction property, 8.3 - uniqueness of attractors, 8.TA

action (moral), 12.4; see also Lagrangian (moral)

action functional, 4.9, 12.4

actual duty, 3.4; see also Ross, W. D.

admissible metrics, 9.6, 9.TA; see also moral metric - constraints on, 9.6 - lattice structure, 9.8 - non-uniqueness of, 9.TA - partial order on, 9.8

admissible transformations, 5.5, 5.TA - Type 1 (coordinate redescriptions), 5.5 - Type 2 (perspective shifts), 5.5 - Type 3 (theory shifts), 5.5

affine connection, see connection

agent fiber bundle, 5.4, 5.TA, 6.6, 14.7

aggregation problem, 14.2, 15.2; see also collective moral agency

AI alignment, 1.3.1, 12.9, 18.4, 18.5 - as contraction mismatch, 15.11, 18.5 - as invariance, 18.4 - three sources of misalignment, 18.5 - gap decomposition, 18.5, 18.TA

AI safety, see structural containment; No Escape Theorem; GUASS

alignment gap, 18.5, 18.TA - convergence, 18.TA

Ambrose-Singer theorem, 10.TA, 29.3

anomaly (D), 17.3, 29.5; see also D dihedral group

antisymmetrization, 6.9

Arrow’s impossibility theorem, 15.2

atlas, 4.1

audit completeness (Requirement 3), 18.6

Augustine of Hippo, 13.7

autonomous hospital ward (case study), 19.11

autonomous vehicle dilemma, 8.6

B

basis vectors, capabilities as, 3.6

behavioral rules vs. constitutive constraints, 1.3.1, 18.6

Bianchi identity (contracted), 29.4

BIP, see Bond Invariance Principle

Bond Index, 19.7, 17.4, 19.TA - convergence, 19.TA - rating scale, 19.7

Bond Invariance Principle (BIP), 5.5, 1.8, 3.3, 4.9, 9.6, 12.3, 17.3, 18.4, 29.8 - as gauge symmetry, 12.3, 29.8 - cross-lingual validation, 12.8, 17.3 - experiments, 17.3, 8.4, 9.7, 12.8 - formal statement (Axiom 5.1), 5.5 - invariance violation, 18.4; see also invariance testing

boundary, see stratum boundary

boundary crossing data, 8.8

branch point, 8.6

C

canonicalization, mandatory, 18.6, 29.8 - approximate (-correct), 29.8 - at scale, 29.8

capabilities approach (Sen and Nussbaum), 1.3.3, 3.6, 5.3 - as basis for moral space, 3.6 - incompleteness thesis, 3.6 - thresholds (Nussbaum), 3.6, 8.3

care ethics, 6.7, 7.3, 8.10, 16.2

categorical imperative (Kant), 3.3 - as invariance condition, 3.3 - Kingdom of Ends as symmetry group, 3.3

character bundle, 6.7; see also virtue ethics

Christoffel symbols, 4.6, 10.3, 17.2

classical limit (quantum normative dynamics), 13.9

cluster expansion (statistical mechanics analogue), 14.TA

cognitive escape, 18.6; see also No Escape Theorem

coherence term, 13.3; see also density matrix

collective agency tensor, 14.3 - decomposition of, 14.3 - emergent component, 14.3

collective holonomy, 14.8

collective moral agency, 14.1–14.13 - collective parallel transport, 14.8 - downward causation, 14.9 - hospital ethics committee (example), 14.12 - upward emergence, 14.9

compilation residue, 19.4, 19.TA

compilation targets (ErisML), 19.4 - multi-agent RL, 19.4 - PDDL, 19.4 - PRISM, 19.4 - safe RL, 19.4

compactness (of moral manifold), 5.8, 29.3

cone point, 8.6

connection (moral), 10.3; see also Levi-Civita connection - covariant derivative, 10.3 - metric-compatible, 4.6, 10.3 - torsion-free, 4.6, 10.3

connectedness (of moral manifold), 5.8

conservation of charge, 12.2

conservation of harm, 12.6, 1.7, 12.7, 15.10, 17.6, 18.8, 29.2 - as Noether charge, 12.5, 12.6 - consequences of, 12.7 - empirical evidence for, 17.6 - euphemism and, 12.7, 17.6 - harm survives contraction, 15.10

conservation laws (physics), 12.2 - angular momentum, 12.2 - charge, 12.2 - energy, 12.2 - momentum, 12.2

constraint surface (Type IV boundary), 8.3, 5.6

constructivism (about the metric), 9.3

contraction (tensor to scalar), 6.4, 2.6, 4.3, 4.4, 15.1–15.13, 29.7 - BIP-compliant, 15.11, 15.TA - by agent / community / institution / algorithm, 15.4 - chain, 15.2 - deferred, 15.8 - information loss in, 15.6 - lexicographic, 15.5 - maximin (Rawlsian), 15.5, 7.4 - mismatch (alignment problem as), 18.5 - necessity of, 15.3 - non-commutativity of, 15.2 - opaque vs. transparent, 15.10 - phenomenology of, 15.9 - probabilistic, 15.5 - satisficing, 15.5 - summative, 15.5 - weighted, 15.5

coordinate chart, 4.1, 5.4, 5.TA

correlative symmetry (Hohfeldian), 3.7, 8.4, 12.8, 17.3 - empirical rates (87%, 82%), 3.7, 8.4, 9.7, 17.3

cost-benefit analysis, 1.3.2

cotangent bundle, 4.3

cotangent space, see dual space

covariance tensor (moral), 6.6, 2.5, 16.3, 29.2 - principal directions of uncertainty, 6.6

covariant derivative, 4.6, 10.3

critical slowing down (moral analogue), 8.7

cross-lingual invariance, 1.6, 12.8, 17.3; see also BIP experiments

curvature (moral), 10.6, 1.8, 29.2, 29.2 - direct measurement (open problem), 29.2 - Ricci tensor (moral), 10.6, 29.4 - scalar curvature (moral), 10.6 - sources of, 10.6 - see also Riemann curvature tensor

cusp singularity, 8.6

D

D dihedral group, 8.4, 1.7, 3.7, 5.9, 12.8, 13.8, 17.3 - anomaly, 17.3, 29.5 - group relations, 8.4 - Hohfeldian transitions as, 8.4

Dear Abby corpus, 17.2, 1.6, 2.5, 5.3, 5.6, 8.3, 8.4, 9.7, 10.9 - context-dependent weighting, 17.2 - nullifier data, 5.6, 8.3, 17.2 - semantic gate data, 8.4, 17.2 - temporal stability, 10.9, 17.2

Dear Ethicist game, 17.4

decoherence (moral), 13.6 - channel, 13.6 - Kraus operators, 13.6

degenerate metric, 4.5, 1.3.2, 6.5, 7.5, 8.6, 29.3, 29.4 - as incommensurability, 3.6, 7.5, 29.3, 29.4

deferred contraction, see contraction, deferred

deliberation, as quantum state, 13.3

DEME architecture, 19.6, 1.7, 19.1, 29.4 - audit and monitoring (Layer 4), 19.6 - democratic governance (Layer 3), 19.6 - DEMEProfile, 19.6, 19.9 - EthicalFacts (Layer 1), 19.6 - Ethics Module (Layer 2), 19.6 - four-layer architecture, 19.6

democratic governance, as metric selection, 19.9; see also governance account

density matrix (moral), 13.6, 13.3 - mixed state, 13.6 - pure state, 13.6 - purity, 13.6

deontic structure, 12.8, 17.3 - 100% cross-lingual transfer, 17.3

difference principle (Rawls), 3.5

differential geometry, 1.1, 4.1–4.11

dimensions of moral space, see nine dimensions

directional information, 1.2, 2.2.1, 15.6, 29.7

discount rate, as moral metric choice, 10.9

doctrine of the mean (Aristotle), 3.2 - as context-sensitive calibration, 3.2 - as metric condition, 3.2

dominance relations, 7.3

dual space, 4.3

E

edge modes, 13.TA

Einstein summation convention, 4.2

Einstein’s field equation, 10.6, 29.4 - moral analogue, 10.6, 29.4

electromagnetic field tensor, 12.3

emergence (moral), 14.3, 14.5, 14.10 - criterion for emergent obligation, 14.5 - criterion for emergent moral property, 14.10 - degree of (), 14.3 - structural injustice as, 14.5

entanglement (moral), 13.8 - entropy, 13.TA - EPR states (moral), 13.8 - partial trace, 13.8

epistemic modes (What Matters, Who Decides, What We Know), 5.3

epistemic stance, see pragmatist epistemology

epistemic status tags, Preface, 17.0.2, 17.0.5 - four tags (Definition, Modeling choice, Conjecture, Open question), Preface - as discipline standard, 17.0.2

ErisML, 19.3, 1.9, 19.1 - compilation targets, 19.4 - conflict resolution function, 19.3 - environment specification, 19.3 - formal semantics (NCSG), 19.3 - fragments (Core, Multi, Temporal, Full), 19.4 - norms specification, 19.3 - vector objective, 19.3

ethical scopes (Individual, Relational, Collective), 5.3

EthicalFacts, 19.6

Ethics Module (EM), 19.6

EU AI Act, 19.5, 19.9

Euler-Lagrange equations, 4.9, 12.2, 12.4

evaluation tensor, 6.6 - multi-agent, 6.6

expected utility, 1.1

expressivism (about the metric), 9.4 - agent-indexed metric, 9.4 - Frege-Geach problem, 9.4

external verification, strong (Requirement 4), 18.6

F

falsifiability, 5.3, 17.7, 29.13 - six criteria, 29.13

feasible cone, 8.6

fiber bundle, 4.7, 1.1, 3.2, 12.3, 19.8 - agent fiber bundle, 5.4 - base space, 4.7 - character bundle, 6.7 - frame bundle, 4.7 - local triviality, 4.7 - Mobius strip (example), 4.7, 29.3 - projection, 4.7 - safety stack as, 19.10 - section of, 4.7, 3.2 - separation principle as, 19.8 - total space, 4.7 - typical fiber, 4.7

fidelity classification (faithful/approximate/indicative), 19.5

Fisher-Rao metric, 29.10

forbidden region, see constraint surface

frame bundle, 4.7

Frege-Geach problem, 9.4

Frobenius norm, 29.10

frontier condition, 4.8, 8.2

functionings (Sen), 3.6

fundamental contraction, see contraction; satisfaction

fundamental group (), 5.8, 29.3

fuzz testing (invariance fuzzing), 17.0.4, 17.0.5, 18.4 - as verification methodology, 17.0.4 - scenario generators, 17.0.5 - transformation suites, 18.4; see also invariance testing

G

gauge field (connection 1-form), 4.9

gauge-fixing, 18.6; see also canonicalization

gauge invariance, 4.9, 12.3, 18.4; see also Bond Invariance Principle

gauge symmetry, 4.9, 12.3, 29.8

gauge theory, 4.9, 1.8, 12.3, 18.8

gauge transformation, 4.9, 12.3

Geneva Ethics Module (Geneva EM), 19.6

geodesic (moral), 10.7 - deviation equation, 10.7, 10.TA, 29.2 - equation, 10.7 - moral inertia, 10.7

Godel’s incompleteness theorem, 1.5

Goodhart’s Law, 18.2, 18.7

governance account (of the moral metric), 9.5, 19.9, 29.3 - democratic determination, 9.5 - legal analogy, 9.5 - metric as governance artifact, 9.5 - moral constitutionalism, 9.5 - moral reform as metric revision, 9.5

gradient flow, 10.8 - local maxima (moral complacency), 10.8 - saddle points (moral impasse), 10.8

Grand Unified AI Safety Stack (GUASS), 19.10 - seven-layer architecture, 19.10

grounded evaluation (Requirement 2), 18.6, 29.8 - domain-specific grounding, 29.8

grounding tensor (Ψ), 17.0.4, 17.0.5, 18.6, 29.8 - adequacy properties, 18.6, 29.8 - as map from observables to moral dimensions, 17.0.4 - construct validity, 17.0.4; see also grounded evaluation

H

Habermas, Jurgen, 9.3

harm, see conservation of harm

harm ledger, 12.6

Hausdorff condition, 4.1

Hilbert space (moral), 13.2

Hohfeld, Wesley Newcomb, 3.7, 8.4 - Fundamental Legal Conceptions, 3.7

Hohfeldian jural positions, 3.7, 1.7, 5.9, 8.4, 12.8, 13.4, 17.3 - Claim, 3.7 - correlatives and opposites, 3.7, 8.4 - D group structure, 8.4 - Duty (Obligation), 3.7 - Immunity-Disability, 3.7 - Liberty, 3.7 - No-claim, 3.7 - operator (quantum), 13.4 - Power-Liability, 3.7

holonomy, 10.5, 2.5, 4.6, 8.8, 14.8, 29.2, 29.2 - collective, 14.8 - detects curvature, 10.TA - group, 10.5 - moral residue as, 10.10, 15.7 - non-abelian, 10.5 - path-dependence and, 10.5 - structural, 14.8

hospital ethics committee (example), 14.12

Huainanzi, 29.1; see also parable of the old man and the horse

human-AI collaboration, 18.12

I

I-EIP (Internal Epistemic Invariance Principle), 18.9, 17.0.6 - I-EIP Monitor, 18.9 - equivariance of internal representations, 18.9 - drift detection, 17.0.6, 18.9; see also invariance testing; structural containment

ideal discourse (Habermas), 9.3

impact vector, 2.2.1

incommensurability, 1.3.2, 3.6, 7.5, 8.6, 29.3 - as degenerate metric, 7.5, 29.3, 29.4 - as metric singularity, 8.6

incompleteness thesis (Sen), 3.6

index raising and lowering, 6.5; see also musical isomorphism

information loss, see contraction, information loss in

institutional manifold, 14.7

interest covector, 6.3, 2.6, 6.4, 29.7 - egalitarian, 6.3 - libertarian, 6.3 - welfarist, 6.3

interference (moral), 13.5 - constructive, 13.5 - destructive, 13.5 - framing alignment (relative phase), 13.5 - mercy vs. justice (example), 13.5

intertheoretic comparison problem, 16.5, 29.10 - meta-metric on theory space, 16.5, 29.10

invariance loss, 18.10

invariance testing, 18.4, 12.9, 17.10, 29.7 - as alignment auditing, 18.4 - transformation suites, 18.4 - violation decomposition, 18.TA

J

Jacobian, 1.7, 4.2

judgment (moral), 1.5, 10.8, 15.9, 29.9 - framework does not replace, 1.5, 9.5, 29.9

junction conditions, 13.7

jural relations, see Hohfeldian jural positions

K

Kant, Immanuel, 3.3 - Groundwork of the Metaphysics of Morals, 3.3

Keats, John, 15.8

kidney allocation (case study), 7.1–7.9, 5.9, 6.8, 15.12, 18.11 - five levels, 7.2–7.6 - revisited (contraction), 15.12 - tensorial (AI), 18.11

Killing vector field, 12.TA

Kingdom of Ends, 3.3

Kraus operators, 13.6

L

LaBSE model, 17.7

Lagrangian (moral), 12.4 - kinetic term, 12.4 - moral potential, 12.4 - stratified, 13.7

Laplace-Beltrami operator, 13.7

lattice (of admissible metrics), 9.8

Levi-Civita connection, 4.6, 10.3, 29.6

lexicographic contraction, see contraction, lexicographic

lexicographic metric, 6.5, 7.5

Lie algebra, 4.9, 12.6

Lie group, see structure group

local triviality, 4.7

Lorentzian signature, 29.3

M

manifold, 4.1; see also moral manifold - smooth, 4.1 - topological, 4.1 - with boundary, 4.1

maximin, see contraction, maximin; Rawls, John

Maximize Expected Choiceworthiness (MEC), 16.4

“maybe” (the geometry of), 29.7 - as deferred contraction, 29.7 - five meanings, 29.7 - see also parable of the old man and the horse

measurement (moral), 13.4 - as decision/collapse, 13.4 - postulate (moral form), 13.4

meta-metric, 9.8, 16.5, 29.10 - existence, 20.TA - Fisher-Rao, 29.10

metric, see moral metric; metric tensor

metric tensor, 4.5, 1.3.2 - degenerate, 4.5, 6.5 - musical isomorphism, 4.5 - non-degenerate, 4.5 - pseudo-Riemannian, 4.5 - Riemannian, 4.5 - signature, 29.3 - symmetric, 4.5

metric uncertainty, 16.2, 16.3

minimax regret, 16.TA

Misak, Cheryl, 1.6

Mobius strip, 4.7, 29.3

Model Context Protocol (MCP), 19.10

moral connection, see connection (moral)

moral debt, 12.7, 17.6

moral dynamics, 10.1–10.12; see also parallel transport; holonomy; curvature

moral energy landscape, 12.4

moral field equation (open problem), 29.4, 10.6 - moral stress-energy tensor, 10.6, 29.4

moral Hamiltonian, 13.7

moral Hilbert space, see Hilbert space (moral)

moral inertia, 10.7

moral manifold (), 5.1–5.10, 1.7, 29.3 - compactness, 5.8, 29.3 - connectedness, 5.8 - dimension, 5.3 - formal definition, 5.TA - nine dimensions, 5.3 - points of, 5.2 - stratification of, 5.6 - topology, 5.8, 29.3

moral metric (), 6.5, 2.6, 9.1–9.10, 29.2 - admissible metrics, 9.6 - as governance artifact, 9.5 - as moral infrastructure, 9.9 - as trade-off structure, 2.6, 6.5 - constructivist account, 9.3 - context-dependent weighting, 5.3, 17.2 - diagonal and off-diagonal components, 6.5, 7.5 - expressivist account, 9.4 - governance account, 9.5 - learning from data, 9.7 - not uniquely determined, 29.7 - realist account, 9.2 - signature (open problem), 29.3 - temporal stability, 10.9, 17.2

moral momentum, 12.5

moral observable, 13.4 - non-commuting, 13.4 - satisfaction operator, 13.4 - stratum projector, 13.4

moral phase transition, see phase transition

moral progress, as parallel transport with holonomy, 10.5, 29.4

moral realism, 1.5, 9.2, 29.9

moral residue (), 15.7, 3.4, 6.4, 10.10, 18.3, 29.7 - acknowledgment, 15.7 - as holonomy, 10.10, 15.7 - as information discarded by contraction, 15.7, 29.4 - compensation, 15.7 - inevitability of, 15.7 - memory, 15.7 - regret, 15.7 - residue logging (AI), 18.3

moral risk, 6.6, 16.2, 29.2

moral Schrodinger equation, 13.7

moral singularity, 5.7, 8.6 - Type 1 (metric degeneracy), 8.6 - Type 2 (gradient failure), 8.6 - Type 3 (constraint intersection), 8.6

moral stress-energy tensor, 10.6, 29.4

moral tunneling, 13.7

moral uncertainty, 16.1–16.11, 3.8 - decision under, 16.4 - empirical (Type 1), 16.2 - metric (Type 2), 16.2 - principle, 13.4 - theory (Type 3), 16.2 - three types, 16.2

moral vector, see obligation vector

musical isomorphism, 4.5

My Favorite Theory (MFT), 16.4

N

Norm Kernel (NK), 19.8, 18.9 - as contract automaton, 19.8 - compilation from Semantic Normative Host, 19.8 - integration with I-EIP Monitor, 18.9

NCSG, see Norm-Constrained Stochastic Game

negative capability (Keats), 15.8

nine dimensions (of moral space), 5.3 - Dimension 1: Consequences and Welfare, 5.3 - Dimension 2: Rights and Duties, 5.3 - Dimension 3: Justice and Fairness, 5.3 - Dimension 4: Autonomy and Agency, 5.3 - Dimension 5: Privacy and Data Governance, 5.3 - Dimension 6: Societal and Environmental Impact, 5.3 - Dimension 7: Virtue and Care, 5.3 - Dimension 8: Procedural Legitimacy, 5.3 - Dimension 9: Epistemic Status, 5.3 - necessity and sufficiency arguments, 5.3

NIST AI RMF, 19.9

No Escape Theorem, 18.6, 1.3.1, 1.8, 12.9, 19.10, 29.4, 29.6 - conditional guarantee, 18.TA - four requirements, 18.6 - limitations, 18.7 - proof, 18.6 - scope, 18.7 - see also structural containment

Noether current, 12.5

Noether’s theorem, 12.1–12.11, 1.7, 4.9 - for ethics (Theorem 13.1), 12.5 - moral analogue, 12.5 - physics version, 12.2

Norm-Constrained Stochastic Game (NCSG), 19.3, 19.TA - well-posedness, 19.TA

normal bundle, 8.5

null directions, 29.3

nullifiers, 5.6, 8.3, 17.2 - abuse, 5.6, 8.3, 17.2 - danger, 5.6, 8.3 - impossibility, 5.6, 8.3 - universality of, 17.2

Nussbaum, Martha, 3.6, 8.3 - capability thresholds, 3.6, 8.3

O

obligation stratum (), 5.9, 8.9

obligation vector (), 6.2, 2.6, 29.2 - as vector field, 1.7, 6.2 - nine components, 6.2 - parallel transport of, 10.4 - zero vector, 6.2

observational chaos, 19.2

old man and the horse, see parable of the old man and the horse

open problems, 29.1–29.14 - curvature measurement, 29.2 - institutional design, 29.11 - intertheoretic comparison, 29.10 - metaphysics of moral geometry, 29.9 - metric signature and topology, 29.3 - moral field equation, 29.4 - scalability of containment, 29.8 - symmetries and conservation, 29.5 - tensorial interpretability, 29.7 - torsion, 29.6

Orch-OR hypothesis (Penrose and Hameroff), 1.5, 1.8, 13.1

order effects, 13.5, 17.5

original position (Rawls), 3.5 - as symmetry condition, 3.5

orthogonal values, 2.6, 6.5

“ought implies can,” 5.6, 8.3

P

parable of the old man and the horse (Sai Weng Shi Ma), 1.2, 2.1, 29.1, 29.2, 29.7 - geometric interpretation, 2.1–2.8, 29.2

parallel transport, 4.6, 10.4, 10.5, 14.8, 29.2 - collective, 14.8 - faithful maintenance, 10.4 - of obligations across contexts, 10.4 - preserves satisfaction, 10.TA

partial order on metrics, 9.8

path-dependence, 2.2.3, 10.5, 17.4, 29.7; see also holonomy

Penrose formula (), 1.8, 13.1

penumbral zone, 8.5

perspective shifts, see admissible transformations, Type 2

phase transition (moral), 8.7, 2.5, 8.3 - emergency, 8.3, 7.6 - first-order, 8.3 - higher-order, 8.3 - second-order, 8.3 - wartime, 8.3

phronesis (practical wisdom), 15.9

policy DAG, 19.5

power tensor (), 6.9, 14.4 - antisymmetric part (structural inequity), 6.9, 14.4

pragmatist epistemology, 1.6, Preface, 9.5

Price, Huw, 1.6

prima facie duties (Ross), 3.4, 1.3.3 - as vector components, 3.4

prioritarian metric, 3.5, 6.7

promise landscape (worked example), 8.9, 5.9

Q

quantum cognition, 13.5, 17.5 - conjunction/disjunction errors, 13.5 - order effects, 13.5, 17.5 - violation of law of total probability, 13.5

quantum normative dynamics, 13.1–13.11, 1.8

R

rank (of a tensor), 4.4, 6.1

Rawls, John, 3.5, 1.3.3, 7.4, 9.3, 15.5 - A Theory of Justice, 3.5 - difference principle, 3.5 - maximin criterion, 3.5, 7.4, 15.5 - original position, 3.5 - supremum metric (), 3.5 - veil of ignorance, 3.5, 9.3

re-description invariance, see Bond Invariance Principle

realist account (of the metric), 9.2

reflective equilibrium, 9.3

regime-dependent evaluation, 1.2, 2.2.3, 29.7; see also stratification

relabeling attack, 18.9

responsibility tensor, 14.6 - causal contribution, 14.6 - collective responsibility remainder, 14.6 - complicity gradient, 14.6 - epistemic position, 14.6 - responsibility gap/surplus, 14.6 - role authority, 14.6

reward hacking, 1.3.1, 15.11, 18.2, 18.9

Ricci tensor, 4.6, 10.6, 29.4

Riemann curvature tensor, 4.6, 10.6, 29.2 - moral interpretation, 10.6 - vanishes iff flat, 4.6

Riemannian manifold, 4.5

Riemannian metric, see metric tensor, Riemannian

robust core (), 16.6, 18.10, 19.6 - as convex cone, 16.6 - Geneva EM as implementation of, 19.6 - stability under perturbation, 16.6

robust obligation, 16.6

Robert’s Rules, 13.6

Ross, W. D., 3.4, 1.3.3 - The Right and the Good, 3.4

S

Sai Weng Shi Ma, see parable of the old man and the horse

Safety Reduction, 18.9.5, 17.0.6 - three tractable categories (governance, engineering, security), 18.9.5; see also structural containment

satisfaction (), 6.4, 2.6, 12.4, 29.3 - fundamental formula, 6.4 - operator, 13.4

Saul on the road to Damascus, 13.7

scalar curvature (moral), 10.6

scalar evaluation, 1.1, 2.2, 18.2, 29.8 - inadequacy of, 2.2 - three limitations, 2.2

Scanlon, T. M., 9.3

Schrodinger equation, see moral Schrodinger equation

semantic gate, 8.4, 2.5, 5.6, 17.2 - “life-threatening” (emergency), 7.6 - “only if convenient,” 5.6, 8.4 - “you promised,” 5.6, 8.4 - as D group element, 8.4 - compositional structure, 8.4 - cross-linguistic evidence, 8.4, 17.3 - detection results, 8.4 - discreteness, 8.4, 17.2

Sen, Amartya, 3.6, 1.3.3 - capabilities approach, 3.6 - incompleteness thesis, 3.6

separation principle, 19.8 - as fiber-bundle structure, 19.8 - composability, 19.8

signature, see metric tensor, signature

singularity, see moral singularity

smooth manifold, see manifold, smooth

Sophie’s Choice, 5.7, 8.6, 12.4

specification gaming, 1.3.1, 15.11, 18.2, 18.9

spontaneous symmetry breaking, 29.5

stratification, 5.6, 8.1–8.11, 2.5, 29.2, 29.3 - as patchwork structure, 8.1 - moral theories and, 8.10 - Whitney, 4.8, 8.2

Stratified Quantum Normative Dynamics (SQND), 1.7, Preface

stratum boundary, 8.3, 5.6, 29.2, 29.4 - Type I (threshold), 8.3 - Type II (phase transition), 8.3 - Type III (absorbing / nullifier), 8.3 - Type IV (constraint surface), 8.3

structural containment, 18.6, 1.3.1, 29.4 - architecture, 18.6 - four requirements, 18.6 - scalability (open problem), 29.8 - see also No Escape Theorem

structural injustice, 14.5

structure group (Lie group), 4.9

structure tensor (), 14.4 - antisymmetric part (power differential), 14.4 - symmetric part, 14.4

structured pluralism, 9.8, 16.7

structured uncertainty, 1.2, 2.2.2; see also covariance tensor

superposition (moral), 13.3, 3.8 - vs. mixture, 13.3

supremum metric, see Rawls, John, supremum metric

symmetrization, 6.9

symmetry, see gauge symmetry; Noether’s theorem; D dihedral group - additional (open problem), 29.5

T

tangent bundle, 4.2

tangent space (), 4.2

tangent vector, 4.2, 2.2.1

temporal discounting, 10.9

temporal stability (moral structure), 10.9, 17.2

tensor, 4.4 - contraction of, 4.4; see also contraction - field, 4.4 - rank, 4.4 - transformation law, 4.4 - type (r,s), 4.4

tensor hierarchy, 6.1–6.10, 29.3

tensor product, 6.9, 13.8, 14.2

tensor-valued objectives (AI), 18.3 - vector-valued reward, 18.3 - vector value function, 18.3

tensorial interpretability (open problem), 29.7 - contraction identification, 29.7 - mechanistic interpretability, 29.7 - probe extraction, 29.7

theory covariance tensor, 16.3

theory uncertainty, see moral uncertainty, theory (Type 3)

tidal forces (moral analogue), 10.6

topology (of moral manifold), see moral manifold, topology

torsion, 10.3, 29.6 - closure failure, 29.6 - detection criterion, 20.TA - tensor (), 29.6

tragic dilemma, 8.6

trajectory-dependence, see path-dependence

transition function, 4.1, 8.8

transition map, 8.8

translation layer, 19.5 - fidelity classification, 19.5 - loss documentation, 19.5 - policy DAGs, 19.5

transparency, of contraction, 15.10, 18.3

trolley problem, 12.4

tubular neighborhood, 8.2

tunneling, see moral tunneling

U

uncertainty, see moral uncertainty; covariance tensor

uncertainty principle (moral), 13.4

utilitarianism - as contraction, 6.7, 15.5 - as Euclidean metric, 2.6, 3.5 - as scalar ethics, 1.1, 2.2 - metric (), 3.5

V

value collapse, 18.2

vector field, 4.2

veil of ignorance, see Rawls, John, veil of ignorance

virtue, as non-gradient agency, 10.8

virtue ethics, 6.7, 8.10, 16.2 - as fiber-bundle section, 1.5, 3.2, 6.7

W

welfare function, 1.1

whistleblower’s dilemma (worked example), 13.10

Whitney, Hassler, 4.8, 8.2 - condition (A), 4.8, 8.2 - condition (B), 4.8, 8.2 - stratification, 4.8, 8.2, 5.6, 13.TA

Y

Yang-Mills gauge theory, 3.1

Young, Iris Marion, 14.5

Notation Index

Page references omitted; notation is listed with the section where it is introduced.