Pith Number

pith:US25KBI4

pith:2024:US25KBI4KCQ4TZYTZGI7QTSWUA

not attested not anchored not stored refs pending

Fourier optimization, the least quadratic non-residue, and the least prime in an arithmetic progression

Antonio Pedro Ramos, Emanuel Carneiro, Emily Quesada-Herrera, Micah B. Milinovich

arxiv:2404.08380 v2 · 2024-04-12 · math.NT · math.CA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{US25KBI4KCQ4TZYTZGI7QTSWUA}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-07-05T11:52:12.857060Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a4b5d5051c50a1c9e713c991f84e56a0349381cbcf7435ffa054fbfe70380277

Aliases

arxiv: 2404.08380 · arxiv_version: 2404.08380v2 · doi: 10.48550/arxiv.2404.08380 · pith_short_12: US25KBI4KCQ4 · pith_short_16: US25KBI4KCQ4TZYT · pith_short_8: US25KBI4

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/US25KBI4KCQ4TZYTZGI7QTSWUA \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: a4b5d5051c50a1c9e713c991f84e56a0349381cbcf7435ffa054fbfe70380277

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c213070d92e61c4c8d8d52976bad7e1343f8227cc80f3ca3f1cfb80c482de8a4",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2024-04-12T10:31:19Z",
    "title_canon_sha256": "4c91977451949d84aefebb67db6a25478cc753231e3dff9db9d9fd8731b44452"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2404.08380",
    "kind": "arxiv",
    "version": 2
  }
}