Pith Number

pith:56JNWM5L

pith:2022:56JNWM5L6HAXXJEUZWSAVQAER6

not attested not anchored not stored refs pending

Spectral conditions for $k$-extendability and $k$-factors of bipartite graphs

Dandan Fan, Huiqiu Lin

arxiv:2211.09304 v1 · 2022-11-17 · math.CO

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{56JNWM5L6HAXXJEUZWSAVQAER6}

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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

Spectral conditions for graphs to contain $k$-factors

Receipt and verification

First computed	2026-07-05T05:16:54.467942Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ef92db33abf1c17ba494cda40ac0048fb0cad70b02313de7bd07189e858bf74a

Aliases

arxiv: 2211.09304 · arxiv_version: 2211.09304v1 · doi: 10.48550/arxiv.2211.09304 · pith_short_12: 56JNWM5L6HAX · pith_short_16: 56JNWM5L6HAXXJEU · pith_short_8: 56JNWM5L

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/56JNWM5L6HAXXJEUZWSAVQAER6 \
  | 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: ef92db33abf1c17ba494cda40ac0048fb0cad70b02313de7bd07189e858bf74a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c4001030c42a8c0c20d005d57bf96eece6e4703ed7896755307a64ea68897c94",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2022-11-17T02:45:09Z",
    "title_canon_sha256": "1922adc436cac5e71005b7b9419ea86045e88bc81417213f20b4024ab4d5cca2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2211.09304",
    "kind": "arxiv",
    "version": 1
  }
}