Pith Number

pith:END4UPAM

pith:2007:END4UPAMRF6WM5Y6MVBJN7XB63

not attested not anchored not stored refs pending

Heat kernels on metric graphs and a trace formula

Jurgen Potthoff, Robert Schrader, Vadim Kostrykin

arxiv:math-ph/0701009 v1 · 2007-01-04 · math-ph · math.MP · 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{END4UPAMRF6WM5Y6MVBJN7XB63}

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	2026-07-04T15:09:16.411544Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2347ca3c0c897d66771e654296fee1f6c9863d03d58a8e4555ecb7156b1b2e95

Aliases

arxiv: math-ph/0701009 · arxiv_version: math-ph/0701009v1 · doi: 10.48550/arxiv.math-ph/0701009 · pith_short_12: END4UPAMRF6W · pith_short_16: END4UPAMRF6WM5Y6 · pith_short_8: END4UPAM

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/END4UPAMRF6WM5Y6MVBJN7XB63 \
  | 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: 2347ca3c0c897d66771e654296fee1f6c9863d03d58a8e4555ecb7156b1b2e95

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "05a70f769d2daffbdba436daefc9b5b7b258d0103fee545696b91c2c5d824ce8",
    "cross_cats_sorted": [
      "math.MP",
      "math.SP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2007-01-04T12:36:08Z",
    "title_canon_sha256": "16c79177c9dde782b781b0e8e1cc119b74e964a4b0c90171205644d35676556c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0701009",
    "kind": "arxiv",
    "version": 1
  }
}