PR: #17
This work extends the zeta23/ project beyond the paper's Montgomery–Taylor endpoint
(0.672500703679) with fully formal, unconditional improvements of the proportion of
zeta zeros that are simple and on the critical line:
| A |
bound |
certificate |
| 1/80 |
0.672755620655 |
2,969 kernel-replayed modules |
| 51/4000 |
0.6727837118 |
8,953 |
| 257/20000 |
0.6727949489 |
30,153 |
| 129/10000 |
0.6728005676 |
56,924 |
- Method: a positive spectral penalty from six translates of the MT kernel, fed into the
zero-count ledger; the only numerical input per target is a 5D affine inequality
A ≤ E₆(g) + B₆·Σg, proved by decide +kernel replay of an exact rational
branch-and-bound certificate over a Lean-checked envelope of the kernel.
- Also included: the
Union (simple-or-on-line) and LineDecimal (certified decimal
enclosure of the MT constant) comparator topics — 24 new Mathlib-only trusted statements
in total, all in the Palomar template layout.
- Every audited declaration depends only on
propext, Classical.choice, Quot.sound;
no native_decide, floating point, or external oracle. Audits, independent exact
replays and build logs are in zeta23/AUDIT.md and zeta23/certificates/sextuple/.
- The method is near its ceiling: any catalog gives at most ≈ 0.6728111 with this kernel
(analysis in zeta23/certificates/sextuple/a1290/).
Note: the certificate chains are ≈100k kernel modules (≈430 CPU-hours), so CI cannot
rebuild them on a hosted runner; the committed logs are the record of those builds.
PR: #17
This work extends the
zeta23/project beyond the paper's Montgomery–Taylor endpoint(0.672500703679) with fully formal, unconditional improvements of the proportion of
zeta zeros that are simple and on the critical line:
zero-count ledger; the only numerical input per target is a 5D affine inequality
A ≤ E₆(g) + B₆·Σg, proved bydecide +kernelreplay of an exact rationalbranch-and-bound certificate over a Lean-checked envelope of the kernel.
Union(simple-or-on-line) andLineDecimal(certified decimalenclosure of the MT constant) comparator topics — 24 new Mathlib-only trusted statements
in total, all in the Palomar template layout.
propext,Classical.choice,Quot.sound;no
native_decide, floating point, or external oracle. Audits, independent exactreplays and build logs are in
zeta23/AUDIT.mdandzeta23/certificates/sextuple/.(analysis in
zeta23/certificates/sextuple/a1290/).Note: the certificate chains are ≈100k kernel modules (≈430 CPU-hours), so CI cannot
rebuild them on a hosted runner; the committed logs are the record of those builds.