← Phase 2 / 01 · Phase 2 Route Matrix

Phase 2 · 01 v0.1 · 01 2026-08-12

Phase 2 Route Matrix

Lays out the ruling from document 00 into a complete eight-route comparison table, marking the natural output, global gain, main barrier, and ruling for each route: higher $2$-power descent (STOP as mainline, almost zero gain in the current pipeline, as such curves simply do not exist in the frontier), non-semistable + existing odd-$p$ assembly method (GO as baseline, medium gain, barrier is supersingular/irreducible hypotheses), Fouquet–Wan arbitrary reduction (**PRIMARY GO**, "high" gain, barrier is algorithmising residual hypotheses + $\forall p$), BCS ordinary non-semistable (supporting route, does not cover all reduction types), full rational $2$-torsion and analytic rank 1 (both HOLD, high potential but each lacks a general family theorem or algorithmisation of the (Im) condition), prime conductor (niche), and high rank $2+$ (so independent it belongs to an "entirely different theorem layer", left for a much later Phase). The document condenses the overall ranking into a boxed formula: FW non-semistable compiler > full 2-torsion > rank 1 > higher 2-descent, and specifically notes that this is a ranking of "extensibility for the current Banwait–Huang family theorem", not a ranking of the absolute difficulty of the mathematical conjecture itself—ease of expansion and depth of the problem are two different things, and the document deliberately avoids conflating them.

Main ranking: FW non-semistable compiler > full 2-torsion > rank 1 > higher 2-descent; explicitly stated as an "expandability" ranking, not a "difficulty" ranking. — The phased status self-reported by the documents in the package, reproduced as is.

Connections · Connections

Relationship with other documents, try to use the words from its own document, not my interpretation.

"This is a ranking of 'expandability for the current Banwait–Huang family theorem,' not a ranking of the absolute difficulty of the mathematical conjectures." — Excerpt from the end of this document.

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