Library entry, recorded March 2026. This page is a historical record of one AI-coalition exchange under the kernel of its time (PHAT v1.x); the claims and tier words inside it are as they stood then and are not restated to the current state. The suite of record is Rev33.1 (sealed 2026-09-26); read any number here against the scorecard and its reading rule — since Rev29 no row is cited as zero-parameter, and α and the colour real form are declared inputs.

L15: GOLDEN RATIO IDENTITIES ā€” ALGEBRAIC VERIFICATION

LIBRARY_PROMPT | PHAT v1.27.5 | Model: ā€” | Status: PENDING [JSON] [RAW]

Prompt

GOLDEN RATIO IDENTITIES ā€” ALGEBRAIC VERIFICATION Verify all phi-identities used in v1.27.5: phi^2 = phi+1, phi^3 = 2phi+1, phi^{-1} = phi-1, sqrt(2+phi) = sqrt(phi^2+1) = ... [identify closed form], v+/v- = phi exactly, 2+phi = phi^2 + 1 [verify numerically]. Show that all VEV ratios are algebraic (no transcendental parameters). #SuperGrokTOE #GoldenRatio #AlgebraicCheck

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