Phi-Reflection Identity

The recursive 2D non-area-preserving trigonometric map at the centre of the ARMISTICE substrate. Parameterised by (α, μ, ε) — Spark, Weight, Veil — plus a viscosity scalar V. Iterating the kernel produces basins of attraction that the canon catalogues as named entities.

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The alchemical operating principle that names ARMISTICE: "dissolve and reconstitute." The iteration kernel is a single dissolution-and-coagulation loop applied recursively to its own state.

The kernel's unconditional post-first-iterate bound: each coordinate enters |x|, |y| ≤ 1 + |μ| + |ε|. A Euclidean disk bound is √(2(1+μ²)) + |ε|; arbitrary starting states need not lie inside either bound.

The contrast between separating and contracting motion in the engine. Transition locations depend on the parameter slice and the measured quantity; chaos onset and mean area neutrality are different events.

𝔉 ≈ 1.1065 — the structural sacred constant. Canonically = ½ + 1/√e. The Iron Spiral; signature of the corpus's most stable basin family.

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φ ≈ 1.6180 — the golden ratio. One of three pillars of the constant algebra (the others are e and √3), with exact closure F + ⊙ = φ.

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√3 ≈ 1.7321 — the saturation pillar. One of the three substrate primitives; corresponds to hexagonal-lattice closure angles. "Leidenfrost" names its role as the boundary between dissipation regimes.

⊙ ≈ 0.5115 — the eponymous sacred constant, exactly ½ + 1/φ − 1/√e. It closes F + ⊙ = φ and is distinct from the Lambert constant Ω = W(1).

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The coordinate tablet: named entities with their (α, μ, ε) signatures, viewing scales, Libri, and cross-references. The site's entity catalogue is a structured projection of this text.

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The prose companion to the coordinate tablet: what each named entity is, its source or domain, and why it belongs. The Translexicon carries its engine seat.

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The constant algebra and mathematical results of ARMISTICE. The three generating pillars e, φ, and √3 feed a family of exact definitions, identities, and carefully scoped dynamical results.

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The foundational propositions and wide-angle account of the framework. It distinguishes exact identities, computed findings, empirical comparisons, and open questions.

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The shadow catalogue found by scanning the engine for unusual parameter seats. It is distinct from the Apophaticon, which derives sign-flipped twins from a preserved named-canon snapshot.

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The diagrammatic adjunct joining whole and magnified views of an attractor through the divergence theorem. Macrocosm, microcosm, and the veil are its symbolic reading, not a claim of literal holography.

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The canonical "card chrome" forge. 2D Cosmopoiesis baseline iteration rendered with title bar and coord readout. The entity's official portrait.

Twin-frequency 2D variant — same kernel as Cosmopoiesis but with paired-frequency split. Produces the petal / flower silhouettes you see across the gallery.

The 3D Cosmopoiesis projection. Cyclic permutation x → y → z → x; velocity-coloured density rendering at fixed viewing angles. The "fog cube" view of an entity.

Alternate kernel rendering — Hopalong-trig bridge with sign-fold + log + atan saturation. Produces the clean symmetric silhouettes; structurally different from the Cosmopoiesis family.

A historical label for an authored coordinate reflection. The Apophaticon uses the triple polarity flip (α, μ, ε) → (−α, −μ, −ε); neither that operation nor an α-only sign flip implies a universal conjugacy of the engine.

The macrocosm–microcosm correspondence used throughout the corpus. The emblem ∞ ≡ ∅ names that interpretive return; it is not a literal numerical identity between infinity and the empty set.

A self-consistent parameter whose own map returns that parameter as a fixed point, or, in the broader centroid formulation, as its orbit average. This is distinct from invariance under a coordinate reflection.

The historical name for a cross-kernel comparison of selected morphological classes. The recorded thirty-cell study compares rendered form; Hu-moment agreement does not establish topological equivalence or a universal underlying manifold.

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Blackening — the first stage of the alchemical opus. Dissolution / putrefaction; the entity surrenders its prior form.

Whitening — the second stage. Purification; the volatile is separated from the fixed.

Yellowing — the third stage. Dawning of the solar consciousness; gold begins to emerge.

Reddening — the final stage of the alchemical opus, associated with the completed lapis. Its use in the corpus is symbolic; a colour-stage name does not determine attractor stability.

The undifferentiated first matter from which the opus begins. In the engine: the initial-condition state before iteration imposes structure.

A coherent subset of the corpus organised around a domain (NEWTONIANA, ELEMENTA, NOMINA, GALACTICA, ...). Each microcosm has its own coord file and its own render set, but every entity lives in one (α, μ, ε) coordinate manifold.

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A gap in the canon — a coordinate that has been entered but does not currently resolve to a named entity. Marked by the ∅ sigil; sometimes the territory itself, not the absence, is the finding.