The n-point pressure family saturates: lim Phi_n = H = 0.6725007036794116 and sup_n Phi_n <= 0.675142509660254, more than 0.0066 short of the configuration ceiling 0.6818286874638, which is 71.7% of the H-to-ceiling distance.
hunts/family_wall (Record 62 of 98 in chronological sequence)
Guiding Question
Does the n-point pressure family converge to a limit strictly below the configuration ceiling 0.6818286874638, and to what value?
Method & Verification
The bound was reduced to Phi_n <= H(1+W) by cancelling the pressure term against a witness of length (n-1)/H, then an independent audit repaired two invalid chain steps and supplied a period-37 word that covers every n, verified here against famlib.
Lineage & Relationships
Primary Sources (at pin 8fa46e134)
Editorial Notes
Case-log status is probe, complete. BARRIER. Disposition maps to completed because the barrier is the recorded outcome. The audit broke two inequality steps as written and did not break the claim. inf F_7,3000 still has no global certificate. Nothing here is machine-checked.
Date Provenance
commit 0f51b208543d6ee693eb4b0e25cb2d66749e8044, hunts/family_wall/RESULTS.md, author 2026-08-23T21:39:09-05:00