AGENTS.md

Verification Instructions for FSO

1. Mathematical Integrity

• Ensure all theorems, lemmas, and definitions from the whitepaper are present in the whitepaper and verified in verify_fso.py.
• Verify the $H^2$ parity obstruction (even $m$, odd $k$).
• Verify the canonical $r$-triple: $(1, m-2, 1)$.

2. LaTeX Syntax

• The document fso_whitepaper.tex must be valid LaTeX.
• All environments (theorem, lemma, proof, definition) must be closed.

3. Computational Proofs

• Run python3 verify_fso.py to confirm the algebraic density and parity obstruction theorems.
• Run python3 fso_simulator.py to verify the Hamiltonian Spike routing for $m=3$.

4. Routing Dynamics

• Ensure ROUTING_DYNAMICS.md correctly explains how the Spike breaks the $m^2$ subgroup constraint.
• The Spike parameters for $m=3$ (x1=0, s!=1, swap_dims(0,2)) are the only verified Hamiltonian configuration for higher-dimensional linkage.