SelfSimilarity
plain-language theorem explainer
SelfSimilarity defines a scaling structure on any type X consisting of a positive real factor and a map from X to itself. Researchers deriving the Recognition Science chain from the Meta-Principle would cite this when establishing rescaling invariance as a prerequisite for forcing the golden ratio. The declaration is a bare structure with three fields and no proof obligations or computational content.
Claim. A self-similarity on a type $X$ consists of a positive real number $f > 0$ together with a function $s : X → X$.
background
The Meta-Principle asserts that empty recognition is impossible, so recognition requires a recognizer; this forces a double-entry ledger whose self-similar closure yields the golden ratio. The present structure encodes the scaling invariance needed for that closure step. Upstream, the scale definition in LargeScaleStructureFromRS supplies concrete powers via noncomputable def scale (k : ℕ) : ℝ := phi ^ k, while the map definition in RSNative.Core lifts arbitrary functions across Measurement records while preserving window, protocol, uncertainty and notes.
proof idea
This is a structure definition with no proof body; the three fields are introduced directly as factor : ℝ, factor_pos : 0 < factor and scale : X → X.
why it matters
The definition supplies the scaling object used downstream to derive φ from self-similar closure in the Meta-Principle module. It occupies the slot between the ledger implication of the Meta-Principle and the explicit self_similarity_forces_phi sibling, advancing the MP → Ledger → φ → Constants chain. No open questions are attached in the supplied data.
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