Pith Number

pith:LX3WOD5H

pith:2001:LX3WOD5HGYED6BWD6CWS4DVFM5

not attested not anchored not stored refs pending

On sets of integers not containing long arithmetic progressions

Izabella Laba, Michael T. Lacey

arxiv:math/0108155 v1 · 2001-08-22 · 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{LX3WOD5HGYED6BWD6CWS4DVFM5}

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	2026-07-04T14:35:29.330503Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5df7670fa736083f06c3f0ad2e0ea56774cf64c7138171db4fe342f63526b584

Aliases

arxiv: math/0108155 · arxiv_version: math/0108155v1 · doi: 10.48550/arxiv.math/0108155 · pith_short_12: LX3WOD5HGYED · pith_short_16: LX3WOD5HGYED6BWD · pith_short_8: LX3WOD5H

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/LX3WOD5HGYED6BWD6CWS4DVFM5 \
  | 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: 5df7670fa736083f06c3f0ad2e0ea56774cf64c7138171db4fe342f63526b584

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7f6558bee6cc3eded99b5ac510db17b87291e0aa5e035dffa60e591269a3f357",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2001-08-22T23:31:13Z",
    "title_canon_sha256": "ea59109fbc6e81fbef9478533a0db9b6a449d869e991d110e9333e7ad25fa124"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0108155",
    "kind": "arxiv",
    "version": 1
  }
}