Pith Number

pith:U6KWTDTZ

pith:2011:U6KWTDTZBHGHIO7ITS5I5LCWVC

not attested not anchored not stored refs pending

The surjectivity of the combinatorial Laplacian on infinite graphs

Jozef Dodziuk, Michel Coornaert, Tullio Ceccherini-Silberstein

arxiv:1103.4901 v1 · 2011-03-25 · math.AP · 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{U6KWTDTZBHGHIO7ITS5I5LCWVC}

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	2026-05-18T03:45:01.180432Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a795698e7909cc743be89cba8eac56a8ad879a96ad2a545112af399d007fe056

Aliases

arxiv: 1103.4901 · arxiv_version: 1103.4901v1 · doi: 10.48550/arxiv.1103.4901 · pith_short_12: U6KWTDTZBHGH · pith_short_16: U6KWTDTZBHGHIO7I · pith_short_8: U6KWTDTZ

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/U6KWTDTZBHGHIO7ITS5I5LCWVC \
  | 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: a795698e7909cc743be89cba8eac56a8ad879a96ad2a545112af399d007fe056

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3347a5723541fae3e5a82b1648dbfaa187ad14300e8fe188070075b652241b78",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-03-25T04:05:10Z",
    "title_canon_sha256": "c79fd91de96b5e8be38c9b14b4b65ee324289c907a762e534d3021595e356e48"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.4901",
    "kind": "arxiv",
    "version": 1
  }
}