Pith Number

pith:QLPHKLEW

pith:2012:QLPHKLEWVFA2FKVUEY7346AV3V

not attested not anchored not stored refs pending

Analysis of the Hodge Laplacian on the Heisenberg group

Detlef M\"uller, Fulvio Ricci, Marco M. Peloso

arxiv:1206.4540 v1 · 2012-06-20 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QLPHKLEWVFA2FKVUEY7346AV3V}

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	2026-05-18T03:53:05.476624Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

82de752c96a941a2aab4263fbe7815dd4c1cf579d7b0975d6cdb064d8d473dea

Aliases

arxiv: 1206.4540 · arxiv_version: 1206.4540v1 · doi: 10.48550/arxiv.1206.4540 · pith_short_12: QLPHKLEWVFA2 · pith_short_16: QLPHKLEWVFA2FKVU · pith_short_8: QLPHKLEW

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/QLPHKLEWVFA2FKVUEY7346AV3V \
  | 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: 82de752c96a941a2aab4263fbe7815dd4c1cf579d7b0975d6cdb064d8d473dea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c28f2f7bd4a53bc911f28bba034b4d6a8e5615bb8ca2a53586c28062c0769880",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-06-20T15:37:23Z",
    "title_canon_sha256": "af3264b8bbe60652a85c0478d32e6227b1f5b7004b4fc8e50a7bd2a296a2bc97"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.4540",
    "kind": "arxiv",
    "version": 1
  }
}