Pith Number

pith:2T5OCLVO

pith:2021:2T5OCLVOF576XPISKINBXJ47C6

not attested not anchored not stored refs pending

Tur\'an Number of Subdivisions of Multipartite Graphs

Danni Peng, Xiao-Chuan Liu, Xu Yang

arxiv:2112.13119 v3 · 2021-12-24 · 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{2T5OCLVOF576XPISKINBXJ47C6}

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	2026-07-05T11:18:56.197347Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d4fae12eae2f7febbd12521a1ba79f17a978f08642d1c251a1fa40dd5f7dc255

Aliases

arxiv: 2112.13119 · arxiv_version: 2112.13119v3 · doi: 10.48550/arxiv.2112.13119 · pith_short_12: 2T5OCLVOF576 · pith_short_16: 2T5OCLVOF576XPIS · pith_short_8: 2T5OCLVO

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/2T5OCLVOF576XPISKINBXJ47C6 \
  | 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: d4fae12eae2f7febbd12521a1ba79f17a978f08642d1c251a1fa40dd5f7dc255

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5cd1dde37894c94057d2e165d09dc80ff28cfa68d0f990767d580533566e225f",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2021-12-24T18:30:21Z",
    "title_canon_sha256": "be939127e970edbb1890e8abc69cd8ae1233d6c5e39ca8d5d228ff0c1a49c532"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2112.13119",
    "kind": "arxiv",
    "version": 3
  }
}