PiFalsifier
plain-language theorem explainer
A structure encodes the conditions under which the Recognition Science derivation of π from 8-tick geometry would be falsified. Foundational researchers in the framework would reference these conditions to test the eight-tick model. The definition consists of three failure-mode propositions together with a statement that two of them cannot hold simultaneously.
Claim. A falsifier consists of propositions asserting no connection between π and the 8-tick structure, that φ-π relations fail, that the discrete 8-tick does not converge to the circle, and that the first two propositions imply a contradiction.
background
The module derives π from 8-tick geometry in Recognition Science, where the 8-tick circle comprises 8 discrete phases and π arises in the continuous limit of this discreteness. The eight-tick octave (period 2^3) from the forcing chain constrains the geometry. This structure lists the ways the derivation could fail according to the supplied conditions.
proof idea
The declaration is a bare structure definition introducing four fields, each a proposition, with the final field encoding an inconsistency between the first two.
why it matters
This supplies the falsifiability interface for the MATH-002 target of deriving π from RS 8-tick geometry. It directly addresses the 8-tick connection, φ-π relationships, and convergence to the circle limit. It touches the open question of whether the eight-tick octave forces the observed value of π in the framework.
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