Sources
Where all of this comes from
Laegna is a private mathematics made public. This page names its own documents and the classical work each concept stands next to — so that any claim here can be checked against something older and better tested.
Primary
The repositories
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laGEOsis
Master geometry; laGEOsis18 is the ball document of this site.
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LaegnaPDFSources
The long-form written corpus of Laegna in PDF form.
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LaegnaPhysics
c ≡ 2, octave shells, relativity and quantum readings.
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SpiritualReasoningLogecs
Spiritual reasoning as the inner channel of Logecs.
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LaegnaioTaeEvolution
Evolution, goal-directed growth, and time as constraint.
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LaegnaBaseAlphabet
The base alphabet in images; text source on laegna.notaku.site.
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Laegna18
The 1..8 digit range and slice notation.
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SimplyAboutInfinities
Base theory of infinities, with the SimulationMode data.
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LaeLane
The linearizer; LaneDatums holds the coordinate tables.
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LaeLogecsLogex
Laegna logic automation.
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Landscopes
Voyages; infinitecircle.md and exterior.md are essential.
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FuzzyLogecs
Why Laegna Logecs already is fuzzy logecs.
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LaeSpiEssentialTheorems
The theorems in classical mathematical language.
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LaeMath
Reinterpretation of classical mathematics through Laegna.
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SpiReason Playground
Number-system visualizations, generators and databases.
Traditional
Classical mathematics, physics and spirituality
Octahedral / HEALPix sphere mapping
Górski et al., equal-area sphere pixelisation
The ball's quilt is a same-family construction: equal solid angle per cell, hierarchical refinement.
Loop subdivision & geodesic polyhedra
Buckminster Fuller; Charles Loop
The refinement operator R and its commutation with projection.
Conformal & inversive geometry
Möbius, Steiner; r ↦ 1/r
Interior/exterior duality and the fixed membrane.
Projective compactification
Real projective line, Riemann sphere, ∞ as a point
Laegna's ∞ ≡ 2 is a compactification with an octave index attached.
Renormalisation group
Wilson, Kadanoff
Scale as a coordinate; behaviour that repeats across octaves.
Fuzzy sets & many-valued logic
Zadeh; Łukasiewicz; Belnap's four-valued logic
Belnap's four values are the nearest classical relative of I, E, O, A.
Non-standard analysis
Robinson; infinitesimals
The Z-regime: structure below the continuum.
Tao Te Ching / Zen circle (ensō)
Laozi; Zen calligraphic tradition
The lane as way; the whole drawn in one unclosed gesture.
Runic and northern cosmology
Elder Futhark; world-tree levels
Mark-making as structure; thresholds and levels as octaves.
Holographic principle
't Hooft, Susskind
Finite boundary addressing an interior — the quilt as hologram.
Interactive
One last look at the multi-scale field
The infinite circle, again — now as a reading instrument
Push the magnitude outward and you are in Y-space, where the classical references above about compactification and renormalisation apply. Push it inward and you are in Z-space, the territory of non-standard analysis and of the pre-continuum logic graph.
Homes