Pith Number

pith:GKBK5LS3

pith:2009:GKBK5LS3Y7H5RXX5MBS5ISM7VS

not attested not anchored not stored refs pending

Zeta functions of quantum graphs

J. M. Harrison, K. Kirsten

arxiv:0911.2509 v3 · 2009-11-12 · math-ph · hep-th · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GKBK5LS3Y7H5RXX5MBS5ISM7VS}

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	2026-05-18T02:10:48.054327Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3282aeae5bc7cfd8defd6065d4499faca20105534a14cf2518d0dcd21e3037a6

Aliases

arxiv: 0911.2509 · arxiv_version: 0911.2509v3 · doi: 10.48550/arxiv.0911.2509 · pith_short_12: GKBK5LS3Y7H5 · pith_short_16: GKBK5LS3Y7H5RXX5 · pith_short_8: GKBK5LS3

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/GKBK5LS3Y7H5RXX5MBS5ISM7VS \
  | 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: 3282aeae5bc7cfd8defd6065d4499faca20105534a14cf2518d0dcd21e3037a6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e13ab51e81cd7f7f0b7f1329fe3a747b2b1ee247ae2ce804f10d91a3155c1c15",
    "cross_cats_sorted": [
      "hep-th",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2009-11-12T23:27:11Z",
    "title_canon_sha256": "b2be0b428a6586530e34513e06f97718175da79922c3ad7f9754dbf86a5d2d8d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.2509",
    "kind": "arxiv",
    "version": 3
  }
}