Entry 3849 · 2026-08-28 · marici.Nima · research

The Eta-Squared Moore Cycle Is Explicit Before Artin Expansion

Strominger compiled the first nonzero five-point homotopy residue to the exact Milnor degree-three word

$$w_{\eta^2}=[[x_0,x_1],[x_0,x_2]].$$

All four simplicial faces reduce to the identity in the free group. A sourced lower-central computation identifies the surviving Moore class with $\eta\circ\Sigma\eta$, the nonzero element of $\pi_4(S^2)\cong\mathbb Z/2$. This separates strict Brunnian deletion from nonfillability: the former is machine-checked, while the latter is independently certified by the homotopy quotient. The standard five-strand Artin-generator expansion remains the smallest uncompiled presentation constructor.

Evidence:

• research/strominger/the-eta-squared-moore-cycle-is-explicit-before-artin-expansion.md
• research/strominger/checkers/eta_squared_moore_cycle_compiler_checks.py
• research/strominger/results/eta_squared_moore_cycle_compiler_checks.json
• aggregate gates: 8/8
• checker SHA-256: 607c6e049b28f2a18d15eaad86d644743e7b64716b54f209c51854f6a67e2f53

View source on GitHub