The principle of *correspondence* — that patterns repeat across levels of reality,
so that the heavenly and the earthly, the great and the small, mirror one another.
Its emblem is the Hermetic maxim popularly rendered "as above, so below," drawn from
the *Emerald Tablet* (Tabula Smaragdina). This node deliberately foregrounds a
**provenance correction**: the Emerald Tablet is not an ancient-Egyptian text of
Hermes but an **early-medieval Arabic** Hermetic work, and the exact phrase "as
above, so below" does not appear in that original — a textbook case of a "sacred
mathematics / ancient wisdom" claim that the corpus must record accurately.

The "world axis" — a vertical line imagined at the centre of the cosmos, joining
the underworld, the earth, and the heavens, around which the ordered world is
arranged. It is realised concretely as a world-tree, a cosmic mountain, a pillar, a
ladder, a central temple, or the smoke-hole/pole of a dwelling. The term as a
cross-cultural *category* was popularised by Mircea Eliade in the mid-20th century;
the underlying imagery is genuinely widespread, but Eliade's claim that it is a
single universal archetype is contested and should be held at arm's length.

The cosmic or world-mountain: the most common material form of the `axis mundi` — a
mountain (natural or built) understood as the centre and summit of the world, where
earth meets heaven. It ranges from named sacred peaks (Meru, Zion, Olympus, Kailāsa)
to *artificial* mountains raised precisely to be one: the Mesopotamian ziggurat, the
Buddhist stupa/Borobudur, and — arguably — the Egyptian pyramid as the risen
primeval mound. This node specialises `axis mundi` toward its mountain form and
gathers the built instances in this corpus.

The principle — named independently in many traditions — that the cosmos is fundamentally
*ordered*, and that ritual, ethics, and kingship exist to uphold that order against chaos.
Egyptian *maʿat*, Vedic *ṛta*, Zoroastrian *aša*, Greek *dikē*/*kosmos*, and Chinese *tao*/
*tian* are the great instances. It is the conceptual bedrock beneath "sacred mathematics":
number and geometry are prized precisely because they are seen as the *language* of this
order.

The conception of time as recurring cycles rather than a linear arrow — the wheel of ages
that turns and returns. It structures the Hindu yugas, the Mesoamerican calendar rounds and
world-ages, the Stoic *ekpyrosis*, and the "eternal return," and is emblematised by the
ouroboros. It is the temporal counterpart to the corpus's spatial `axis mundi`: where the
axis centres space, cyclical time centres and renews the ages.

The principle that reality is structured by complementary opposites — light/dark, male/
female, heaven/earth, being/non-being — and that wisdom lies in their pairing or
reconciliation (the *coincidentia oppositorum*). It runs from the Pythagorean table of
opposites and Heraclitus's unity-in-strife to Chinese yin–yang and the interlocking
triangles of the hexagram, and it is the conceptual root of the number 2.

The idea that "nothing" — emptiness, the void, the zero — is not mere absence but a positive,
generative, even sacred principle. It runs from the Buddhist *śūnyatā* (emptiness) and the
Indian *śūnya* (which also names the mathematical zero), through the primeval waters of
creation myths (Egyptian Nun, Genesis *tohu wa-bohu*), to the Daoist "usefulness of what is
not there." It is the conceptual companion to the number 0 and a striking case where a
metaphysical and a mathematical idea share a word.

The Pythagorean–Platonic doctrine that the heavenly bodies, moving at proportional
speeds and distances, produce an inaudible cosmic music — the same whole-number ratios
that govern audible harmony (octave 2:1, fifth 3:2, fourth 4:3) governing the cosmos. It
is the purest expression of "the universe is ordered by number," linking the number and
sound threads of this corpus, and it survived — remarkably — into real science with
Kepler.

The doctrine that the human being is a "little world" (mikros kosmos) that mirrors
the structure of the great world (macrocosm) — so that understanding one illuminates
the other. It is a load-bearing idea in Greek philosophy (Plato's *Timaeus*), the
Hermetic and astrological traditions, and Renaissance natural philosophy (Paracelsus,
Agrippa), and it underwrites much sacred-number and sacred-geometry reasoning: if
body and cosmos share a pattern, then the proportions of one are the proportions of
the other.

The meta-concept of this whole corpus: the attribution of qualitative, sacred, or
cosmological meaning to numbers. It spans the Greek *arithmology* (the "theology of
arithmetic"), Hebrew *gematria* and Greek *isopsephy* (letter-as-number values), and the
number-lore of India and China. This node names the practice the corpus documents — and
carries the standing caution that distinguishes real number *theory* from *numerology*.

The tradition — running from Pythagoras and Plato through Euclid, Vitruvius, and the
Gothic master-masons — that geometric form and numerical proportion express a
cosmic or divine order, so that building and drawing "correctly" participates in
that order. It has a genuine historical spine (the Platonic solids as elements, the
vesica in Gothic setting-out, Vitruvian modular proportion) that must be kept
distinct from the modern esoteric "Sacred Geometry" brand, which retro-projects
universal meanings onto figures like the Flower of Life.

The recurrence of seven as a sacred, structuring number across otherwise
unrelated ancient traditions — Mesopotamian, Hebrew, Vedic, and Pythagorean/
Hellenic. Seven organises cosmology (seven heavens, seven planets), ritual time
(the seven-day week, the sabbatical cycle), and metaphysics (a number that
"neither generates nor is generated"). Whether this convergence reflects
diffusion from a single Mesopotamian source or independent re-discovery of the
same astronomical and arithmetical facts is a genuinely open scholarly question.

The annual journey of the Sun along the horizon — its turning-points at the two solstices
and its balance-points at the two equinoxes — which structures the calendar and orients a
great many of the corpus's sites. It is the single most common organising principle behind
ancient monuments: the "four stations" of the solar year, marked in stone from Newgrange to
Chankillo to Cahokia.

The classic problem of constructing, with compass and straightedge alone, a square equal in
area to a given circle — proven *impossible* in 1882 (Lindemann's proof that π is
transcendental). Long before that verdict, the attempt became a rich symbol: the union of
the circle (heaven, spirit, the infinite) and the square (earth, matter, the measurable),
and hence of the reconciliation of opposites. It sits at the meeting of the corpus's
geometry, π, and mandala threads.

The "Great Year" — the long cycle after which the heavens return to a starting
configuration. In its most concrete modern sense it is the ~25,772-year period of the
precession of the equinoxes; in Plato it is the "perfect year" when all the celestial
motions come back into alignment. It is the astronomical backbone of the corpus's biggest
numbers (432,000; 25,920; 72) and of the contested claim that ancient myth encodes
precession.