Pith Number

pith:TINOCZYR

pith:2013:TINOCZYR4B2SUF65HMTZFMOIGI

not attested not anchored not stored refs pending

Expansion in generalized eigenfunctions for Laplacians on graphs and metric measure spaces

Alexander Teplyaev, Daniel Lenz

arxiv:1310.5650 v3 · 2013-10-21 · 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{TINOCZYR4B2SUF65HMTZFMOIGI}

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	2026-05-18T00:12:11.794642Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9a1ae16711e0752a17dd3b2792b1c8323beb9d22a4394219602e08a6ead1f487

Aliases

arxiv: 1310.5650 · arxiv_version: 1310.5650v3 · doi: 10.48550/arxiv.1310.5650 · pith_short_12: TINOCZYR4B2S · pith_short_16: TINOCZYR4B2SUF65 · pith_short_8: TINOCZYR

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/TINOCZYR4B2SUF65HMTZFMOIGI \
  | 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: 9a1ae16711e0752a17dd3b2792b1c8323beb9d22a4394219602e08a6ead1f487

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7aa19d695f43337004c4220182c6eb3d4d59bb8b72985b1ed2f67b9e106f3e34",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2013-10-21T17:15:02Z",
    "title_canon_sha256": "6c03dbeae9f89e15857f25ee1ae559bef3c1df6ac9f30a925dc575ec09b08600"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.5650",
    "kind": "arxiv",
    "version": 3
  }
}