Pith Number

pith:3AGPPOIQ

pith:2019:3AGPPOIQUQD3KGF5E2L2EUAIXG

not attested not anchored not stored refs pending

Some extremal results on K_{s,t}-free graphs

Gennian Ge, Tao Zhang

arxiv:1903.03233 v2 · 2019-03-08 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3AGPPOIQUQD3KGF5E2L2EUAIXG}

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	2026-05-17T23:49:49.864763Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d80cf7b910a407b518bd2697a25008b984015f37c36e2a15905022ba53574a67

Aliases

arxiv: 1903.03233 · arxiv_version: 1903.03233v2 · doi: 10.48550/arxiv.1903.03233 · pith_short_12: 3AGPPOIQUQD3 · pith_short_16: 3AGPPOIQUQD3KGF5 · pith_short_8: 3AGPPOIQ

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/3AGPPOIQUQD3KGF5E2L2EUAIXG \
  | 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: d80cf7b910a407b518bd2697a25008b984015f37c36e2a15905022ba53574a67

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ab8984d9fe026e9417ab4161b30e88d69bcdaf9196c7a002750a6bb4c3b48ec2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-03-08T00:54:00Z",
    "title_canon_sha256": "cae1e953930ba07e6fce6d17ecdeef94713d585fd218b08bc7554acd151e6c17"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1903.03233",
    "kind": "arxiv",
    "version": 2
  }
}