Record the spare bits in the online storage budget

[jwr404]

Summary

• The prefix bound 2^(8p+18) p^2 is the widest of the 13 published online magnitudes.
• For every precision p >= 101 its bit length leaves at least 56 bits inside G = 8p + 8 ceil(log2(p+2)) + 32, which covers the claimed twelve spare bits.
• All 2,600 bit lengths for precisions 101 through 300 fit in G-56. The selected κ is unchanged.

Test plan

• python3.12 -B research/storage-spare-bits/verify.py
• python3.12 -B research/storage-spare-bits/test_verify.py
• python3.12 scripts/research_package.py --package research/storage-spare-bits
• Maintainer replay from the pinned base commit

Made with Cursor

Made with Cursor