Pith Number

pith:4UAA3RDY

pith:2026:4UAA3RDY3A42MVDCGIIET4QVSR

not attested not anchored not stored refs pending

Spanning triangulations in random graphs

M.Zhukovskii, S.Vakhrushev

arxiv:2605.20361 v1 · 2026-05-19 · math.CO · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4UAA3RDY3A42MVDCGIIET4QVSR}

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	2026-05-21T01:04:34.992780Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5000dc478d839a65462321049f2159453e45eec73a0d09b12c47f0c4167a2aa

Aliases

arxiv: 2605.20361 · arxiv_version: 2605.20361v1 · doi: 10.48550/arxiv.2605.20361 · pith_short_12: 4UAA3RDY3A42 · pith_short_16: 4UAA3RDY3A42MVDC · pith_short_8: 4UAA3RDY

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/4UAA3RDY3A42MVDCGIIET4QVSR \
  | 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: e5000dc478d839a65462321049f2159453e45eec73a0d09b12c47f0c4167a2aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9c468d1ed954dc51e6e2ac99e97d6c1ea4b1a8f25d09497d3565e867fceb2bf0",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-19T18:15:26Z",
    "title_canon_sha256": "0f0657efad52667cf12228ce3999ab0c9cee8b36621dffee8df4121dc63d9873"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.20361",
    "kind": "arxiv",
    "version": 1
  }
}