Pith Number

pith:MG7RNZKE

pith:2023:MG7RNZKEC2BMDX3ND2GFUCMLU4

not attested not anchored not stored refs pending

$K_r$-saturated Graphs and the Two Families Theorem

Asier Calbet

arxiv:2302.13389 v1 · 2023-02-26 · 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{MG7RNZKEC2BMDX3ND2GFUCMLU4}

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.

Cited by

1 paper in Pith

Twin-free $K_r$-saturated Graphs and Maximally Independent Sets in $K_3$-free Graphs

Receipt and verification

First computed	2026-07-05T05:45:46.401815Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

61bf16e5441682c1df6d1e8c5a098ba73929210ee902484f813bc78478bd8a31

Aliases

arxiv: 2302.13389 · arxiv_version: 2302.13389v1 · doi: 10.48550/arxiv.2302.13389 · pith_short_12: MG7RNZKEC2BM · pith_short_16: MG7RNZKEC2BMDX3N · pith_short_8: MG7RNZKE

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/MG7RNZKEC2BMDX3ND2GFUCMLU4 \
  | 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: 61bf16e5441682c1df6d1e8c5a098ba73929210ee902484f813bc78478bd8a31

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e4fd61bf75bbefbce5bca4a459d7fecfc8a16c56912d6632fdeaa65f70beae1a",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2023-02-26T19:16:02Z",
    "title_canon_sha256": "5cce70669f2078b9b7d3d2aef5bd74a05acb70fb2c830b3c8f9104cf0856b7d7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2302.13389",
    "kind": "arxiv",
    "version": 1
  }
}