At N=144 the rational vector 20(c_1,...,c_12)=(20,-20,-20,0,-20,-13,7,6,0,0,0,13) has harmonic balance, coverage through q=5, mass 119/20, and zero positive surplus at every prime power, so the fully saturated paid cost is exactly psi(144).
hunts/paid_surplus_obstruction (Record 98 of 98 in chronological sequence)
Guiding Question
Can balanced rational coefficients supported through 12 and covering q through 5 eliminate paid surplus at N=144?
Method & Verification
Exact rational substitution checked W_d <= 1 at all 47 prime powers through 144, and both interval backends at 35 and 70 digits priced the old endpoint surplus 4.414404 against the new surplus of zero.
Lineage & Relationships
Primary Sources (at pin 8fa46e134)
Editorial Notes
Disposition is qualified because the case log records independent challenge pending. The independent test implementation is by the same producer, not an independent reviewer. This does not supply a scale-dependent family or a uniform bound. Zero of 47 prime powers have positive surplus; eight have strict deficits, including a negative row at d=23 that must be retained in the repair cost.
Date Provenance
commit 8fa46e13440346d27a2e97d653df700f64707416, hunts/paid_surplus_obstruction/RESULTS.md, author 2026-09-14T00:02:06-05:00