Pith Number

pith:XSPCGAG5

pith:2009:XSPCGAG5Q6MRLDKX63Z6ULNGD5

not attested not anchored not stored refs pending

Vacuum energy, spectral determinant and heat kernel asymptotics of graph Laplacians with general vertex matching conditions

J. M. Harrison, K. Kirsten

arxiv:0912.0036 v2 · 2009-11-30 · 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{XSPCGAG5Q6MRLDKX63Z6ULNGD5}

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	2026-05-18T00:37:38.597661Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bc9e2300dd8799158d57f6f3ea2da61f4bac5270a7e6408e6d0e0865b5c570a7

Aliases

arxiv: 0912.0036 · arxiv_version: 0912.0036v2 · doi: 10.48550/arxiv.0912.0036 · pith_short_12: XSPCGAG5Q6MR · pith_short_16: XSPCGAG5Q6MRLDKX · pith_short_8: XSPCGAG5

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/XSPCGAG5Q6MRLDKX63Z6ULNGD5 \
  | 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: bc9e2300dd8799158d57f6f3ea2da61f4bac5270a7e6408e6d0e0865b5c570a7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d332833834c8e0549bf36c6781211532010de5910856db48e952bcf0ce9c7b25",
    "cross_cats_sorted": [
      "hep-th",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2009-11-30T22:29:21Z",
    "title_canon_sha256": "bfb322b35cc281a8312b45006805b79aa5a55349ebdfde0139a4491500481dd2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.0036",
    "kind": "arxiv",
    "version": 2
  }
}