SUPPLEMENTARY RESULT (post-submission): verified frontier extended to n=10
=========================================================================
Method identical to paper Section 4 (exact integer DP over ideals, anchored
pair-count identity), plus a machine-soundness-tested accelerator:
Olson-Sagan twin argument - a clean inversion guarantees an exactly half-
balanced pair (delta>=1/2). Soundness verified exhaustively against exact
computation at n=5 (zero violations).

Enumeration: all sum-indecomposable permutations of size 10:
  total                = 2,829,325
  clean-inversion skip = 1,680,243  (delta >= 1/2 guaranteed)
  exactly computed     = 1,149,082

RESULT: minimum delta over indecomposable non-chain instances = 37/106
  approx 0.34906  >  1/3
  witnesses: 1350279468, 3041728596 (central-dip family)
  counterexamples found: NONE
  witnesses re-verified with independent brute-force engine (exact agree);
  indecomposability re-confirmed.

Deficit delta_n - 1/3 (indec. class): n=6: 0.02381, n=7: 0.02564,
n=8: 0.02222, n=9: 0.01961, n=10: 0.01573  (~c/n decay, c ~ 0.16-0.18).
This supports Conjecture 1 (tightness of the constant 1/3) and extends the
exhaustive frontier for the dimension-two class from n<=9 to n<=10.