Pith Number

pith:VKMHGFRJ

pith:2022:VKMHGFRJZUFFX3F5VESFHU65ZI

not attested not anchored not stored refs pending

Spanning trees in sparse expanders

Donglei Yang, Jie Han

arxiv:2211.04758 v2 · 2022-11-09 · 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{VKMHGFRJZUFFX3F5VESFHU65ZI}

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

Embedding loose trees in $k$-uniform hypergraphs

Receipt and verification

First computed	2026-07-05T05:43:17.238486Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aa98731629cd0a5becbda92453d3ddca3aa40f8a5de8ac9710b5d72e205640fd

Aliases

arxiv: 2211.04758 · arxiv_version: 2211.04758v2 · doi: 10.48550/arxiv.2211.04758 · pith_short_12: VKMHGFRJZUFF · pith_short_16: VKMHGFRJZUFFX3F5 · pith_short_8: VKMHGFRJ

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/VKMHGFRJZUFFX3F5VESFHU65ZI \
  | 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: aa98731629cd0a5becbda92453d3ddca3aa40f8a5de8ac9710b5d72e205640fd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4e7569462b141fa07968d75508640574b2b4687a36d056cbfdff896a31950c70",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2022-11-09T09:22:52Z",
    "title_canon_sha256": "1a45dc633ab75adb865af9be2ceb3bf0794c49bd845dfcd478ee5d17110b3f4d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2211.04758",
    "kind": "arxiv",
    "version": 2
  }
}