[Doldrums]

What changed

Improves the upper bound on C_1d (signed third autocorrelation constant) from 1.463071582607559* to
1.457854884921989*. Adds its row and reference to constants/1d.md, together with two earlier bounds for this
variant that the table was missing: Matolcsi–Vinuesa's 1.4993 (2010), cited for it in Problem 6.4 of [GGSWT2025],
and the 600-cell step function of AlphaEvolve repository PR 13 (17 Oct 2026), 1.459989046905384*, recomputed
exactly. Updates the README table cell and "Recent progress". Markdown only.

Evidence

• Witness: a signed step function with 800 equal cells on [-1/4, 1/4]. The exact value of max_t |f*f| / (int f)^2 is
  38534420343892614563110610373646557184000 / 26432274393314964174848236787785831382961 = 1.45785488492198861...
  The printed bound is rounded up.
• Check: the knot formula of 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 (standard library only).
• The verifiers of [CERT2026] and of PR 1d: improved upper bound 1.460217284022874* (600-cell step function) #247, run unchanged on this construction.json, print the same fraction.
• Certificate and verifier: Zenodo, https://doi.org/10.5281/zenodo.23541324. The record is restricted: its files are available on request,
  and we will grant access to anyone checking the bound.
  SHA-256 construction.json: 1eafe2408187c95e36d2e33911fe3fd425f6c55af3837b40b30c139c771ffefb
  SHA-256 verify.py: cfa116ce4cb62a46f1292f740f3bdde99035918d897cd1d0a0f4966f67120925

Context

Step	Upper bound	Gain
Matolcsi–Vinuesa (2010)	1.4993
AlphaEvolve, [GGSWT2025]	1.4688	2.0%
[CERT2026] (#224)	1.463071582607559	0.39%
AlphaEvolve repository PR 13 (unmerged)	1.459989046905384	0.21% over [CERT2026]
PR #247 (open)	1.460217284022874	0.20% over [CERT2026]
this PR	1.457854884921989	0.36% over [CERT2026], 0.15% over PR 13, 0.16% over #247

Ordering

PR #247 (1.460217284022874*) was opened earlier today. If it is merged first, this row goes after it and
"previously" becomes its value; we will rebase.

Use of AI

The construction was found by SCiEL, a recursive self-improvement (RSI) system built on cultural transmission,
running an open language model (Qwen3.8-27B) that writes and refines search programs scored by the exact bound. AI assistants helped prepare this pull request. We have checked the value, the certificate and every reference above.

[Doldrums]

We started a second SCiEL run with a stronger model (closed frontier model, size not published) in place of Qwen3.8-27B (open weights, 27B parameters), starting from the 800-cell certificate in this PR. It already beat that certificate at step 5. By step 13 it had reached 1.4578222729 (800 cells), a gain of 0.36% over the current table entry [CERT2026] and 0.16% over #247. We checked it exactly with our verifier and with the one from #247.

The run is still going and still improving. Once it settles, we will update the row, the README cell and the certificate here.

[chessing234]

all good