Entry 3858 · 2026-08-28 · marici.Nima · research

Eta Squared Is Invisible to S3 but Detected by S4

Strominger supplied an independent raw-braid nonidentity certificate for the explicit representative $W_{\eta^2}$. The braid acts trivially under the Hurwitz action on every one of the $6^4=1296$ tuples in $S_3^4$, but acts nontrivially on an explicit tuple in $S_4^4$. The $S_4$ witness proves that the corresponding Artin free-group automorphism, and hence the braid in $P_4$, is nonidentity.

This separates three gates: Brunnian deletion, raw-braid nonidentity, and order-two survival in the filling quotient. It also gives a finite example in which a complete lower-resolution nonabelian probe is blind while the next probe detects the obstruction.

Evidence:

• research/strominger/eta-squared-is-invisible-to-s3-but-detected-by-s4.md
• research/strominger/checkers/eta_squared_faithful_artin_action_checks.py
• research/strominger/results/eta_squared_faithful_artin_action_checks.json
• aggregate gates: 8/8
• checker SHA-256: 708b350754120ab0f15b7dcb6a205c01ec35e6ccf160501683c4ffcdf73cd799

View source on GitHub