[steps-re]

What changed

Improves the upper bound on C_1d (signed third autocorrelation constant) from 1.463071582607559* to 1.460217284022874*. Adds a row to constants/1d.md, a reference, the README table cell, and a "Recent progress" line. Markdown only.

Evidence

• Witness: a signed step function with 600 equal cells on [-1/4, 1/4]. Exact value of max_t |f*f| / (int f)^2 is
  698746209786798359455483373677229695641600 / 478522078482569620433992386249161163190849 = 1.46021728402287398...
  The printed bound is rounded up.
• Check: the same knot formula as the constant page, (f*f)(mh) = h * sum_{i+j=m-1} v_i v_j, in exact rational arithmetic with each stored double read as an exact rational. python -I verify.py construction.json runs in under a second (standard library only).
• Independent numeric check (oversampled direct convolution) gives 1.4602172840228775.
• Same harness reproduces the previous record 1.4630715826075593 from the CERT2026 certificate.
• Certificate, verifier and optimizer, pinned commit: https://github.com/steps-re/c1d-certificate/tree/9a091494facc801eaf6b92b175b63c58b7c3b30b
  SHA-256 of construction.json: 3dd39fae744555179b0356b84e752db724e892bd23dda51403976edfb5b3a28c
• Method: split each cell of the CERT2026 300-cell function in two, then sequential linear programming (trust region, HiGHS) on the max of |f*f|. The descent was still improving slowly when stopped, so finer grids will likely go lower.

The asterisk follows CONTRIBUTING (self-archived, too long to check by hand). Open PRs #234 and #243 touch the same 1d lines, so a small rebase may be needed depending on merge order. Happy to do it.

AI use

An AI agent (Claude Code) wrote and ran the optimizer and both checkers for me, and prepared this PR. The bound does not rest on trusting that work: anyone can rerun verify.py on the archived certificate in a second.

[chessing234]

all good

[maximusrufus]

Replayed from construction.json at steps-re/c1d-certificate@9a09149 (sha256 3dd39fae...b3a28c, matches the PR), reading each stored double as an exact rational:

C(f) = 698746209786798359455483373677229695641600 / 478522078482569620433992386249161163190849 = 1.46021728402287398...

so the stated 1.460217284022874 is a valid upper bound (rounded up by about 1.5e-17). Two computations agree on the same fraction: the knot formula from the constant page (2n max|S_m| / (sum v)^2), and a direct piecewise-linear construction of f*f evaluated exactly at all 2401 knots and midpoints, with each midpoint checked to be the average of its neighbours.