[maximusrufus]

What changed

Adds constants/1d.md and the matching README table row and "Recent progress" line. The page records the signed third autocorrelation constant:

C_1d is the largest C such that max_t |(f*f)(t)| >= C (int_{-1/4}^{1/4} f)^2 for all real f supported on [-1/4, 1/4].

The best published upper bound I could find is 1.4688 (Problem 6.4 of arXiv:2511.02864, signed variant). The new row is a signed step function with 300 equal cells on [-1/4, 1/4] whose ratio max|f*f| / (int f)^2 equals 1.463071582607559 (exact rational: 2039224160683882663565441886346340189798400 / 1393796574908163689489385839036226787118881).

I found no existing page for this variant (searching constants/ for 1.4688, "third" and "autocorrelation" hits only 1a and 1b), so this is a new page. Per CONTRIBUTING it takes the first unclaimed letter in family 1; 1c is claimed by open PR #207, hence 1d. The number is provisional and can be renamed.

Evidence

• Variant: this is max_t |ff| for signed f, not |max_t ff|. The latter's reported record is 1.4523 (arXiv:2606.10402, Appendix A.5) and is a different, smaller quantity; the two are sometimes conflated.
• Certificate: construction.json (300 signed cell values) and verify.py, given in full below because CONTRIBUTING asks that this repository hold Markdown only. SHA-256: 44f3f2b63b0d698dd5f279661d4be7077ca6703d62ea7ae6e2b2945e0f001e1c (construction.json), 3e75c4ab0cdb40387765cbd086a572e46605f0c9fd8b8252783ed01aada80258 (verify.py).
• Verification: for a step function on a uniform grid, f*f is piecewise linear with knots at multiples of the cell width, so the maximum is attained at a knot and the ratio is computed exactly in rational arithmetic. python -I verify.py construction.json uses only the Python standard library, runs in under a second, and prints C(f) = 1.4630715826075593.
• Literature check: searched through 2026-10-12; no equal or better value for the signed max|f*f| variant found.
• Asterisk: used per the README convention (self-archived artifact, 300 values too many to check by hand). Please drop it if you consider the exact verifier sufficient.

Evidence standard: a bound is listed only with a certificate that a reader can recompute exactly. I can adjust the number, the page layout, or fold this into an existing page if you prefer.

Certificate (copy both into files and run: python -I verify.py construction.json)

construction.json:

{
 "problem": "Third autocorrelation inequality, signed variant: largest C with max_{t} |(f*f)(t)| >= C (int_{-1/4}^{1/4} f)^2 for all f: R->R supported on [-1/4,1/4]",
 "domain": "[-1/4, 1/4]",
 "cells": 300,
 "cell_width": "(1/2)/300",
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 ],
 "claimed_upper_bound": 1.463071582607559,
 "previous_best_published": 1.4688
}

verify.py:

"""Exact verification of the step-function upper bound (stdlib only).
Usage: python -I verify.py construction.json
f is a step function on [-1/4, 1/4] with n equal cells of width h = (1/2)/n and the listed (signed) cell values.
(f*f)(t) = int f(t-x) f(x) dx is piecewise linear with knots at integer multiples of h, so max_t |f*f| is attained
at a knot, where (f*f)(m h) = h * sum_{i+j=m-1} v_i v_j. The ratio below is therefore the exact value of
max|f*f| / (int f)^2 for this f, computed in rational arithmetic, and it is an upper bound for the constant C.
"""
import json, sys
from fractions import Fraction as F
d = json.load(open(sys.argv[1]))
v = [F(x) for x in d["values"]]; n = len(v); h = F(1, 2) / n
conv = [F(0)] * (2 * n - 1)
for i in range(n):
    if v[i] == 0: continue
    for j in range(n): conv[i + j] += v[i] * v[j]
max_abs = h * max(abs(c) for c in conv)
integral = h * sum(v)
C = max_abs / (integral ** 2)
print("n =", n, " int f =", float(integral), " max|f*f| =", float(max_abs))
print("C(f) =", float(C), " (exact rational:", C.numerator, "/", C.denominator, ")")
print("upper bound C <=", float(C), "; previous best published 1.4688; improvement:", float(C) < 1.4688)