Pith Number

pith:SX3JJCPB

pith:2009:SX3JJCPB2FRSESEFJSXRQNAKRF

not attested not anchored not stored refs pending

Multiple operator integrals and spectral shift

Anna Skripka

arxiv:0907.0432 v2 · 2009-07-02 · math.SP · math-ph · math.MP · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SX3JJCPB2FRSESEFJSXRQNAKRF}

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	2026-05-18T04:27:25.685794Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

95f69489e1d1632248854caf18340a894b0a768b1fd277b0c2acade978cd13c0

Aliases

arxiv: 0907.0432 · arxiv_version: 0907.0432v2 · doi: 10.48550/arxiv.0907.0432 · pith_short_12: SX3JJCPB2FRS · pith_short_16: SX3JJCPB2FRSESEF · pith_short_8: SX3JJCPB

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/SX3JJCPB2FRSESEFJSXRQNAKRF \
  | 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: 95f69489e1d1632248854caf18340a894b0a768b1fd277b0c2acade978cd13c0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "61619f9d78361f724b60021bcefca939bf86e9b5f961b032c837be2992ae851b",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2009-07-02T16:35:06Z",
    "title_canon_sha256": "4be17fa4f69221ccabd633020303ed2b1d80bf4977f2235fba44c695b1e5943b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.0432",
    "kind": "arxiv",
    "version": 2
  }
}