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References

Primary academic sources for the ontologies in this repository.

Relationship to per-ontology citings.md files. Each ontology under crates/domains/src/ now has its own citings.md listing the sources it actually stands on (see issue #57). This file is the workspace-wide cross-reference: it collects the sources that appear in multiple per-ontology bibliographies and provides their full bibliographic entries in one place. When you add a citation to an ontology’s citings.md, check whether the full entry belongs here too — if another ontology already cites it, move the full entry here and replace the per-ontology form with a pointer.

Coverage gap. The sections below were written before the per-ontology rollout and cover only 14 domains (geometry, rotation, time, linear algebra, probability, kinematics, geodesy, sensor fusion, military standards, clock characterization, signal processing, statistics, control theory). The rollout produced ~100 per-ontology citings.md files covering the full formal/natural/applied/social/cognitive tree; many of the sources in those files are not yet represented here. Filling the gap is tracked under issue #57 as a follow-up sweep.

Geometry

  • Hilbert, D. (1899). Grundlagen der Geometrie. Teubner, Leipzig. [The axiomatic foundation of Euclidean geometry — 20 axioms in 5 groups: incidence, order, congruence, parallelism, continuity.]
  • Avigad, J., Dean, E., & Mumma, J. (2009). “A Formal System for Euclid’s Elements.” Review of Symbolic Logic, 2(4):700-768. PDF
  • Coxeter, H.S.M. (1969). Introduction to Geometry (2nd ed.). Wiley.

Rotation (SO(3)) and Rigid Motion (SE(3))

  • Shuster, M.D. (1993). “A Survey of Attitude Representations.” Journal of the Astronautical Sciences, 41(4):439-517. [Comprehensive comparison of rotation representations: quaternion, DCM, Euler, axis-angle, MRP.]
  • Sola, J. (2017). “Quaternion kinematics for the error-state Kalman filter.” arXiv:1711.02508. [Quaternion conventions, composition, perturbation, for sensor fusion.]
  • Murray, R.M., Li, Z., & Sastry, S.S. (1994). A Mathematical Introduction to Robotic Manipulation. CRC Press. [SE(3) Lie group, twists, wrenches, exponential coordinates.]
  • Kumar, V. “Rigid Body Kinematics and the Lie group SE(3).” University of Pennsylvania MEAM 620 lecture notes. PDF
  • Kim, J. “Lie Group Formulation of Articulated Rigid Body Dynamics.” CMU Technical Report. PDF

Time

  • Allen, J.F. (1983). “Maintaining Knowledge about Temporal Intervals.” Communications of the ACM, 26(11):832-843. [The 13 interval relations — foundational temporal reasoning.]
  • Grüninger, M. & Li, Z. (2017). “The Time Ontology of Allen’s Interval Algebra.” TIME 2017, LIPIcs Vol. 90. PDF
  • W3C (2017). “Time Ontology in OWL.” W3C Recommendation. Specification
  • Allan, D.W. (1966). “Statistics of Atomic Frequency Standards.” Proceedings of the IEEE, 54(2):221-230.
  • Riley, W.J. (2008). Handbook of Frequency Stability Analysis. NIST Special Publication 1065. PDF
  • IEEE Std 1139-2008. “Standard Definitions of Physical Quantities for Fundamental Frequency and Time Metrology — Random Instabilities.”

Time Systems

  • IAU 2000 Resolution B1.9: Definition of Terrestrial Time (TT = TAI + 32.184 s).
  • IAU 2006 Resolution B3: Barycentric Coordinate Time (TCB) and related scales.
  • IS-GPS-200 (2022). “Interface Specification: Navstar GPS Space Segment / Navigation User Segment Interfaces.” US Space Force. [GPS time definition: GPS = TAI - 19 s.]
  • ITU-R TF.460 (2002). “Standard-frequency and time-signal emissions.” [UTC definition with leap seconds.]
  • Ashby, N. (2003). “Relativity in the Global Positioning System.” Living Reviews in Relativity, 6(1). PMC
  • ESA Navipedia. “Transformations between Time Systems.” Reference

Linear Algebra

  • Axler, S. (2024). Linear Algebra Done Right (4th ed.). Springer. [Vector space axioms, eigenvalues, spectral theorem.]
  • Strang, G. (2023). Introduction to Linear Algebra (6th ed.). Wellesley-Cambridge Press. [Positive definite matrices, Cholesky, SVD.]
  • Kahan, W. “Axioms for Fields and Vector Spaces.” UC Berkeley Math H110 notes. PDF
  • Horn, R.A. & Johnson, C.R. (2013). Matrix Analysis (2nd ed.). Cambridge University Press. [Determinant properties, matrix inequalities, Schur complement.]

Probability and Estimation Theory

  • Kolmogorov, A.N. (1933). Grundbegriffe der Wahrscheinlichkeitsrechnung. Springer, Berlin. [The axiomatic foundation of probability: 3 axioms.] Archive
  • Tao, T. (2015). “275A, Notes 0: Foundations of probability theory.” Blog
  • Mahalanobis, P.C. (1936). “On the generalized distance in statistics.” Proceedings of the National Institute of Sciences of India, 2(1):49-55.
  • Fisher, R.A. (1925). “Theory of Statistical Estimation.” Mathematical Proceedings of the Cambridge Philosophical Society, 22(5):700-725. [Fisher information, Cramér-Rao bound.]

Kinematics

  • Goldstein, H., Poole, C., & Safko, J. (2002). Classical Mechanics (3rd ed.). Addison-Wesley. [Lagrangian and Hamiltonian formulations, rigid body dynamics.]
  • Shabana, A.A. (2020). Dynamics of Multibody Systems (5th ed.). Cambridge University Press. [Kinematics on manifolds, screw theory.]
  • Bernstein, D.S., Goel, A., & Ansari, A. “Geometry, Kinematics, Statics, and Dynamics.” Cornell University. PDF

Geodesy

  • Torge, W. & Müller, J. (2012). Geodesy (4th ed.). de Gruyter. [WGS84, ellipsoid, coordinate systems.]
  • NIMA (2000). “Department of Defense World Geodetic System 1984.” Technical Report TR8350.2 (3rd ed.). [WGS84 specification: a = 6378137.0 m, f = 1/298.257223563.]
  • Bowring, B.R. (1976). “Transformation from spatial to geographical coordinates.” Survey Review, 23(181):323-327. [Geodetic ↔ ECEF conversion algorithm.]

Sensor Fusion

  • Kalman, R.E. (1960). “A New Approach to Linear Filtering and Prediction Problems.” Journal of Basic Engineering, 82(1):35-45. [The Kalman filter.]
  • Bar-Shalom, Y., Li, X.R., & Kirubarajan, T. (2001). Estimation with Applications to Tracking and Navigation. Wiley. [Multi-target tracking, data association, JPDA, MHT.]
  • Groves, P.D. (2013). Principles of GNSS, Inertial, and Multisensor Integrated Navigation Systems (2nd ed.). Artech House. [INS/GNSS integration, strapdown mechanization, lever arm, boresight.]
  • Maybeck, P.S. (1979). Stochastic Models, Estimation, and Control (Vols. 1-3). Academic Press. [State space models, Kalman filter theory.]
  • Thrun, S., Burgard, W., & Fox, D. (2005). Probabilistic Robotics. MIT Press. [SLAM, particle filters, occupancy grids.]

Military Standards

  • US DoD JDL (1999). “Data Fusion Lexicon.” Joint Directors of Laboratories, Data Fusion Sub-Panel. [JDL fusion model: Levels 0-5.]
  • STANAG 4586 (2012). “Standard Interfaces of UAV Control System for NATO UAV Interoperability.” NATO.
  • MISB ST 0601 (2021). “UAS Datalink Local Set.” Motion Imagery Standards Board. [Sensor metadata for UAS platforms.]
  • MIL-STD-1553B (1978). “Aircraft Internal Time Division Command/Response Multiplex Data Bus.” US DoD.

Clock Characterization

  • IEEE Std 1139-2008. “Standard Definitions of Physical Quantities for Fundamental Frequency and Time Metrology.”
  • ITU-R TF.538-4 (2017). “Measures for random instabilities in frequency and time.” Recommendation
  • Rohde & Schwarz (2019). “Time Domain Oscillator Stability Measurements.” Application Note 1EF69. PDF

Signal Processing

  • Shannon, C.E. (1949). “Communication in the Presence of Noise.” Proceedings of the IRE, 37(1):10-21.
  • Nyquist, H. (1928). “Certain Topics in Telegraph Transmission Theory.” Transactions of the AIEE, 47(2):617-644.
  • Oppenheim, A.V. & Willsky, A.S. (1997). Signals and Systems (2nd ed.). Prentice Hall.
  • Peyré, G. (2019). Mathematical Foundations of Data Sciences. CNRS/DMA. PDF
  • Byrne, C.L. Mathematics of Signal Processing: A First Course. UMass Lowell. PDF

Statistics

  • Fisher, R.A. (1925). “Theory of Statistical Estimation.” Mathematical Proceedings of the Cambridge Philosophical Society, 22(5):700-725.
  • Neyman, J. & Pearson, E.S. (1933). “On the Problem of the Most Efficient Tests of Statistical Hypotheses.” Philosophical Transactions A, 231:289-337.
  • Student (Gosset, W.S.) (1908). “The Probable Error of a Mean.” Biometrika, 6(1):1-25.
  • Cramér, H. (1946). Mathematical Methods of Statistics. Princeton University Press.
  • Rao, C.R. (1945). “Information and the accuracy attainable in the estimation of statistical parameters.” Bulletin of the Calcutta Mathematical Society, 37:81-91.

Control Theory

  • Åström, K.J. & Murray, R.M. (2008). Feedback Systems: An Introduction for Scientists and Engineers. Princeton University Press. PDF
  • Ogata, K. (2010). Modern Control Engineering (5th ed.). Prentice Hall.
  • Lyapunov, A.M. (1892). “The General Problem of the Stability of Motion.” Kharkov Mathematical Society.
  • Ziegler, J.G. & Nichols, N.B. (1942). “Optimum Settings for Automatic Controllers.” Transactions of the ASME, 64:759-768.
  • Doyle, J.C., Francis, B.A. & Tannenbaum, A.R. (1992). Feedback Control Theory. Macmillan.