Pith Number

pith:KXCEMGZW

pith:2026:KXCEMGZW3PYZWZPR3HIKYYEU4M

not attested not anchored not stored refs pending

Arithmetic progressions in a random set on a budget

Daniel I\v{l}kovi\v{c}, Jan Hladk\'y, Jared Le\'on, Xichao Shu

arxiv:2607.21565 v1 · 2026-07-23 · math.CO · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KXCEMGZW3PYZWZPR3HIKYYEU4M}

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	2026-07-24T01:24:39.975177Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

55c4461b36dbf19b65f1d9d0ac6094e321f1968c187132e56b9321e9b3fa47ab

Aliases

arxiv: 2607.21565 · arxiv_version: 2607.21565v1 · doi: 10.48550/arxiv.2607.21565 · pith_short_12: KXCEMGZW3PYZ · pith_short_16: KXCEMGZW3PYZWZPR · pith_short_8: KXCEMGZW

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/KXCEMGZW3PYZWZPR3HIKYYEU4M \
  | 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: 55c4461b36dbf19b65f1d9d0ac6094e321f1968c187132e56b9321e9b3fa47ab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fee20fe07a56b5724c8a9e14b2fca643924cae5dfceb4cf0d1ba5a2bebac9acc",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-23T17:49:15Z",
    "title_canon_sha256": "cf3b657a576807b4c65e76b341c96d586129575b3afd3fc1868d914a49a0e0ed"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.21565",
    "kind": "arxiv",
    "version": 1
  }
}