Pith Number

pith:ISMDXIFM

pith:2011:ISMDXIFMOJ4ABC73PYHYRNSB2G

not attested not anchored not stored refs pending

Volume Growth, Spectrum and Stochastic Completeness of Infinite Graphs

Daniel Lenz, Matthias Keller, Radoslaw K. Wojciechowski

arxiv:1105.0395 v2 · 2011-05-02 · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ISMDXIFMOJ4ABC73PYHYRNSB2G}

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	2026-05-18T03:44:34.047976Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

44983ba0ac7278008bfb7e0f88b641d1b3af7ae1f6adc0b40bc91ac49cf92bdb

Aliases

arxiv: 1105.0395 · arxiv_version: 1105.0395v2 · doi: 10.48550/arxiv.1105.0395 · pith_short_12: ISMDXIFMOJ4A · pith_short_16: ISMDXIFMOJ4ABC73 · pith_short_8: ISMDXIFM

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/ISMDXIFMOJ4ABC73PYHYRNSB2G \
  | 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: 44983ba0ac7278008bfb7e0f88b641d1b3af7ae1f6adc0b40bc91ac49cf92bdb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "73e08a262f838b8ef3ebb9cc0063af632a8f5726c826da7be4e106891c47a019",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2011-05-02T18:16:39Z",
    "title_canon_sha256": "3ba2254bc0696c7ddf76adfa91bf040ec1ef262a5e084f7c102cac6a6c1d8658"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.0395",
    "kind": "arxiv",
    "version": 2
  }
}