Pith Number

pith:D7A2KXMT

pith:2026:D7A2KXMTWYRQDPGYFGC44PNG47

not attested not anchored not stored refs pending

Asymptotics of the number of labelled connected sparse multitype graphs

Luisa Andreis, Mario Veshaj

arxiv:2606.17912 v1 · 2026-06-16 · 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{D7A2KXMTWYRQDPGYFGC44PNG47}

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	2026-06-19T16:10:43.425948Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1fc1a55d93b62301bcd82985ce3da6e7feb58d36641a899d728db675e21dc3d6

Aliases

arxiv: 2606.17912 · arxiv_version: 2606.17912v1 · doi: 10.48550/arxiv.2606.17912 · pith_short_12: D7A2KXMTWYRQ · pith_short_16: D7A2KXMTWYRQDPGY · pith_short_8: D7A2KXMT

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/D7A2KXMTWYRQDPGYFGC44PNG47 \
  | 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: 1fc1a55d93b62301bcd82985ce3da6e7feb58d36641a899d728db675e21dc3d6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4ff3bf5b9b6a877d4e2e3e437b81cd4b181774405e2789e2d32335bfb4bbe102",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-16T13:34:03Z",
    "title_canon_sha256": "3fa081ec3200332cf268eaf75d8d9de59f439e13ef814a107b1bfa8b4ed3645c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.17912",
    "kind": "arxiv",
    "version": 1
  }
}