Skip to content
ƒxyz

Grounding

The literature behind the canon. None of this is original to ƒxyz; the synthesis is.

The graph

K_N is the absolute. E8 is its geometric substrate. Petrie projection is the canonical render.

  • Moxness, J. G.·2023
    E8 → H4 × H4 folding and the 600-cell signature
    — Geometric substrate for the Petrie projection
  • Coxeter, H. S. M.·1973
    Regular Polytopes
    Dover, 3rd ed.
    — Petrie projection, Coxeter number h=30
  • Conway, J. H.; Sloane, N. J. A.·1999
    Sphere Packings, Lattices and Groups
    Springer-Verlag, 3rd ed.
    — E8 root system, 240 roots in ℝ⁸

Realm / domain / territory

Three-deep ontic containment. Bourdieu nested fields, Smith-Varzi fiat boundary, Padgett-Ansell multiplex sociology — predates physics-style multilayer-network theory by 21 years.

  • Bourdieu, P.; Wacquant, L.·1992
    An Invitation to Reflexive Sociology
    University of Chicago Press
    — Nested fields: field of power ⊃ field ⊃ sub-field
  • Bourdieu, P.·1986
    The Forms of Capital
    in Richardson (ed.), Handbook of Theory and Research for the Sociology of Education
  • Sack, R. D.·1986
    Human Territoriality: Its Theory and History
    Cambridge University Press
  • Smith, B.; Varzi, A. C.·1997
    Fiat and Bona Fide Boundaries
    Philosophy and Phenomenological Research 60(2)
  • Padgett, J. F.; Ansell, C. K.·1993
    Robust Action and the Rise of the Medici, 1400–1434
    American Journal of Sociology 98(6)
    — Multiplex with 9 tie types over 92 families — 21 years before Kivelä
  • Mitchell, J. C. (ed.)·1969
    Social Networks in Urban Situations
    Manchester University Press
    — Manchester School multi-stranded ties
  • Floridi, L.·2008
    The Method of Levels of Abstraction
    Minds and Machines 18(3)
    — Method-relative LoA — anchor for canon §0 apophatic frame
  • List, C.·2019
    Levels: Descriptive, Explanatory, and Ontological
    Noûs 53(4)
    — Mixed-register chain defense

Layer / dimension / perspective + aspect

Three orthogonal axes inside any territory, plus aspect as the meta-axis. Kivelä parallel axis-of-variation; Wittgenstein seeing-as; Tinbergen four questions; Wimsatt perspective.

  • Kivelä, M.; Arenas, A.; Barthélemy, M.; Gleeson, J.; Moreno, Y.; Porter, M.·2014
    Multilayer Networks
    Journal of Complex Networks 2(3)
    — Aspect = parallel axis-of-variation indexing elementary layers
  • Tinbergen, N.·1963
    On Aims and Methods of Ethology
    Zeitschrift für Tierpsychologie 20
    — Four independent explanatory questions = aspect-as-meta
  • Wittgenstein, L.·1953
    Philosophical Investigations II.xi
    — Aspect-seeing (seeing-as)
  • Wimsatt, W. C.·1994
    The Ontology of Complex Systems: Levels of Organization, Perspectives, and Causal Thickets
    Canadian Journal of Philosophy Suppl. Vol. 20
    — Perspective when part-whole becomes too intricate for clean levels
  • Mac Lane, S.; Moerdijk, I.·1992
    Sheaves in Geometry and Logic
    Springer-Verlag
    — Sheaf section formalism for perspective
  • Dennett, D. C.·1987
    The Intentional Stance
    MIT Press
  • Lefebvre, H.·1974
    La production de l'espace
    (Eng. The Production of Space, 1991)
    — Perceived/conceived/lived (vécu) — non-hierarchical triad
  • Buckingham, E.·1914
    On Physically Similar Systems; Illustrations of the Use of Dimensional Equations
    Physical Review 4(4)
  • Slater, P. J.·1975
    Leaves of trees
    Proc. 6th Southeastern Conf. on Combinatorics, Graph Theory and Computing
    — Metric dimension
  • Aristotle·ca. 350 BCE
    Categories
    — Parallel highest-kinds — categorial test for the chain

What we do not claim

ƒxyz canon is mixed-register (Christian List 2019). It engages with anti-stratal positions — DeLanda, Latour, Kim — rather than dismissing them.

  • DeLanda, M.·2006
    A New Philosophy of Society: Assemblage Theory and Social Complexity
    Continuum
    — Flat ontology
  • Latour, B.·2005
    Reassembling the Social: An Introduction to Actor-Network-Theory
    Oxford University Press
    — How to keep the social flat
  • Kim, J.·1998
    Mind in a Physical World
    MIT Press
    — Non-reductive physicalism collapse argument
  • Merleau-Ponty, M.·1964
    Le visible et l'invisible
    — Trans-stratal flesh — medium, not level
  • Harman, G.·2011
    The Quadruple Object
    Zero Books
    — OOO — co-equal poles, no fundamental

Eight-domain synthesis

The 2026-04-28 deep-grounding pass: ~270 KB across 8 reports, ~125 primary citations. Synthesis lives in canon.

  • ƒxyz canon·2026-04-28
    Layer + Aspect Deep Grounding — 8-Domain Synthesis
    thoughts/grounding-rewrite-2026-04-27/SYNTHESIS-DEEP-2026-04-28.md
    — ~270 KB across 8 reports, ~125 primary citations
  • ƒxyz canon·2026-04-28
    Multiplex Ontology — Canonical Reference v3.1
    docs/canon/multiplex-ontology.md
    — 3+3 tree: realm⊃domain⊃territory + axes (layer/dimension/perspective) + aspect meta
  • ƒxyz canon·2026-04-28
    Multiplex Terminology v3.0
    .claude/rules/multiplex-terminology.md
    — Locked vocabulary; aspect-as-Kivelä-axis vs AOP-aspect vs Comrie-aspect resolved

Mixed-register chain per Christian List 2019: realm / domain / territory are ontic; layer / dimension are analytical; perspective is hermeneutic; aspect is formal-categorial.