Pith Number

pith:T7HKMPLL

pith:2012:T7HKMPLLMQULJDHV7VWHEHC7NH

not attested not anchored not stored refs pending

Diameter and spectral gap for planar graphs

Juan Souto, Larsen Louder

arxiv:1204.4435 v2 · 2012-04-19 · math.GT · 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{T7HKMPLLMQULJDHV7VWHEHC7NH}

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	2026-05-18T03:56:47.281633Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9fcea63d6b6428b48cf5fd6c721c5f69d2893609b7494e1c7590c83e1b15a8e4

Aliases

arxiv: 1204.4435 · arxiv_version: 1204.4435v2 · doi: 10.48550/arxiv.1204.4435 · pith_short_12: T7HKMPLLMQUL · pith_short_16: T7HKMPLLMQULJDHV · pith_short_8: T7HKMPLL

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/T7HKMPLLMQULJDHV7VWHEHC7NH \
  | 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: 9fcea63d6b6428b48cf5fd6c721c5f69d2893609b7494e1c7590c83e1b15a8e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9f88ac7defb5ca97575ffb03664cac174020f636a6a591ab9d5e6f5b055ceb6a",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-04-19T19:07:13Z",
    "title_canon_sha256": "8f4c4cd7e5526cf60ff2da6aa6bfd881927487accd5c7f3279bae7529f45b6be"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.4435",
    "kind": "arxiv",
    "version": 2
  }
}