Pith Number

pith:DERB4DUZ

pith:2012:DERB4DUZZGC4W3BVNLYPXEKOE4

not attested not anchored not stored refs pending

Heat kernel fluctuations for a resistance form with non-uniform volume growth

David A. Croydon

arxiv:1210.5860 v1 · 2012-10-22 · 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{DERB4DUZZGC4W3BVNLYPXEKOE4}

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	2026-05-18T03:42:34.891806Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

19221e0e99c985cb6c356af0fb914e271a151240a3f82cecfc366136d40259c5

Aliases

arxiv: 1210.5860 · arxiv_version: 1210.5860v1 · doi: 10.48550/arxiv.1210.5860 · pith_short_12: DERB4DUZZGC4 · pith_short_16: DERB4DUZZGC4W3BV · pith_short_8: DERB4DUZ

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/DERB4DUZZGC4W3BVNLYPXEKOE4 \
  | 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: 19221e0e99c985cb6c356af0fb914e271a151240a3f82cecfc366136d40259c5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4f302a8ce3abf82dd4f46e13e842d4256d6226b7295e5e436a38ad281e75fc8a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-10-22T10:40:41Z",
    "title_canon_sha256": "1e43ff34860a1be68e7f7b3b6c994dc6cbc64ea7b0d0a974d070aa6c3679cefe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.5860",
    "kind": "arxiv",
    "version": 1
  }
}