Pith Number

pith:5GQRXWAJ

pith:2013:5GQRXWAJK5EKPKIFUWYIHOGOZM

not attested not anchored not stored refs pending

Extremal functions with vanishing condition

Friedrich Littmann, Mark Spanier

arxiv:1311.1157 v2 · 2013-11-05 · 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{5GQRXWAJK5EKPKIFUWYIHOGOZM}

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	2026-05-18T01:08:29.263771Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e9a11bd8095748a7a905a5b083b8cecb2df48e943e2800b592153d7b2e8f7580

Aliases

arxiv: 1311.1157 · arxiv_version: 1311.1157v2 · doi: 10.48550/arxiv.1311.1157 · pith_short_12: 5GQRXWAJK5EK · pith_short_16: 5GQRXWAJK5EKPKIF · pith_short_8: 5GQRXWAJ

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/5GQRXWAJK5EKPKIFUWYIHOGOZM \
  | 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: e9a11bd8095748a7a905a5b083b8cecb2df48e943e2800b592153d7b2e8f7580

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "69faafb903f7cfee37c656dd00044ad006ca6c6b0364f30f2f45922d4ede50d1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-11-05T18:50:41Z",
    "title_canon_sha256": "a3a3493e5ee46f623e773157a36c178b62fa3e3e0934635d80fb25422201f38e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.1157",
    "kind": "arxiv",
    "version": 2
  }
}