Pith Number

pith:UQEY5BBF

pith:2011:UQEY5BBF5DONQVYDLCYQYOO2TE

not attested not anchored not stored refs pending

Distributions of sparse spanning subgraphs in random graphs

Pu Gao

arxiv:1105.5913 v2 · 2011-05-30 · 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{UQEY5BBF5DONQVYDLCYQYOO2TE}

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	2026-05-18T02:29:23.806295Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a4098e8425e8dcd8570358b10c39da99211d857c825416d3527e52c771749b85

Aliases

arxiv: 1105.5913 · arxiv_version: 1105.5913v2 · doi: 10.48550/arxiv.1105.5913 · pith_short_12: UQEY5BBF5DON · pith_short_16: UQEY5BBF5DONQVYD · pith_short_8: UQEY5BBF

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/UQEY5BBF5DONQVYDLCYQYOO2TE \
  | 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: a4098e8425e8dcd8570358b10c39da99211d857c825416d3527e52c771749b85

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "77a59902547c9a6273d275568a087fcbe288f524c4557894b386f8ed3725e897",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-05-30T09:23:46Z",
    "title_canon_sha256": "f3166883a8f945fbbdf4fb41afe320e0463db817be52a41ee8f78c2932204751"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.5913",
    "kind": "arxiv",
    "version": 2
  }
}