Pith Number

pith:CQER6FQT

pith:2015:CQER6FQTG5CEVSLQLOIR454VIO

not attested not anchored not stored refs pending

Fattening up Warning's Second Theorem

Pete L. Clark

arxiv:1506.06743 v1 · 2015-06-20 · math.CO · math.AC · 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{CQER6FQTG5CEVSLQLOIR454VIO}

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	2026-05-18T01:40:57.760387Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

14091f161337444ac9705b911e77954391e235f3572bd34d14a156319303e4c6

Aliases

arxiv: 1506.06743 · arxiv_version: 1506.06743v1 · doi: 10.48550/arxiv.1506.06743 · pith_short_12: CQER6FQTG5CE · pith_short_16: CQER6FQTG5CEVSLQ · pith_short_8: CQER6FQT

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/CQER6FQTG5CEVSLQLOIR454VIO \
  | 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: 14091f161337444ac9705b911e77954391e235f3572bd34d14a156319303e4c6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "59b52101c52aa6917f1fb88088b8e3dcfc1878af9991aa7c86927855eab987e4",
    "cross_cats_sorted": [
      "math.AC",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-06-20T20:11:11Z",
    "title_canon_sha256": "3580309bd0dc363df1d35830049f3d3912be1e91c5ae98690adb4ae7d3b7b727"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.06743",
    "kind": "arxiv",
    "version": 1
  }
}