dm³ 103 · Week 13 · Synthesis

τ = 2 — The Fixed Point, Reached at G⁵

Correcting a naming error: it’s G⁵, not G⁹, and here’s the source that says so
dm³ 103 · Week 13 · Synthesis
τ = 2 — The Fixed Point, Reached at G⁵
Course: dm³ 103  ·  Synthesis  ·  Source: Book 5, chV-g6.html

An earlier draft of this course described the destination as “\(G^9=G^\infty\)” and “Vol IX of Principia Orthogona.” The actual source material says otherwise, directly: “O limiar \(\tau=2\) é alcançado em \(G^5\)” — “the threshold \(\tau=2\) is reached at \(G^5\)” — and Volume V of the series is explicitly subtitled “\(G^5\) · Complete Completeness.” Five applications of the operator chain, across five published volumes, is where this course’s destination is actually reached — not nine.

Where the G⁵ framing sits: an explicitly open conjecture
The source material does discuss a sixth iteration — but names it precisely as open, not reached: “Conjectura G⁶ (Aberta · AXLE Issue 6)”, proposing \(\chi(H^*(X^6))=33\) for all \(n\), motivated by numerical convergences (\(g_{{33}}=33\), \(666=6\times111\)) rather than derived. There is no \(G^9\) claim in the source material at all — that framing appears to have been invented rather than sourced, and is removed here.

Corrected picture: \(\tau=2\) as fixed point, \(G(\Gamma^*)=\Gamma^*\), is reached at \(G^5\) — matching Theorem Ω.1’s ladder limit and the canonical triple from Week 7. \(G^6\) is a separate, explicitly open, numerically-motivated conjecture about cohomology, not a further stage of the same proved arc.

This week’s content is grounded directly in the AXLE/Book 3/5 sources cited above — no material in this page depends on the external, unverified source removed from dm³ 102.
-- dm³ 103 · Week 13 · Correction: G⁵, not G⁹

-- Source (chV-g6.html, book5): "O limiar τ=2 é alcançado em G⁵"
-- Volume V subtitle: "G⁵ · Complete Completeness"
-- No G⁹ claim exists in the source material — that framing is
-- removed from this course as unsourced.

-- G⁶ IS discussed, but explicitly as OPEN:
--   "Conjectura G⁶ (Aberta · AXLE Issue 6)"
--   χ(H*(X⁶)) = 33 ∀n — motivated numerically (g₃₃=33, 666=6×111),
--   NOT derived. A real, honestly-labelled open conjecture.
example : True := trivial
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