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.

L4: TRIALITY AND SIGMA-CYCLES

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

Prompt

TRIALITY AND SIGMA-CYCLES Compute the triality automorphism sigma of Spin(8) restricted to Os. Show sigma^3 = 1 (order 3). Demonstrate that sigma maps {e1,e2,e3} -> {f1,f2,f3} -> {l,e1,f1} in cyclic order. Verify Delta_n=2 per sigma-step. Confirm n_b=7, n_c=9, n_ud=13 from triality stepping. #SuperGrokTOE #Triality #GenerationLadder

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