Pith Number

pith:ODO7JDSW

pith:2010:ODO7JDSWTNRFLYTKLYQGNF65TQ

not attested not anchored not stored refs pending

Abstract Wave Equations and Associated Dirac-Type Operators

Fritz Gesztesy, Gerald Teschl, Helge Holden, Jerome A. Goldstein

arxiv:1012.4927 v2 · 2010-12-22 · math.AP · 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{ODO7JDSWTNRFLYTKLYQGNF65TQ}

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	2026-05-18T03:39:29.401235Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

70ddf48e569b6255e26a5e206697dd9c209edfd78b53195055d8789b080645da

Aliases

arxiv: 1012.4927 · arxiv_version: 1012.4927v2 · doi: 10.48550/arxiv.1012.4927 · pith_short_12: ODO7JDSWTNRF · pith_short_16: ODO7JDSWTNRFLYTK · pith_short_8: ODO7JDSW

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/ODO7JDSWTNRFLYTKLYQGNF65TQ \
  | 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: 70ddf48e569b6255e26a5e206697dd9c209edfd78b53195055d8789b080645da

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "66e898858c094713d7891312f419347e21b925399b9e41a8aaf343d3ccac42ee",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-12-22T10:26:20Z",
    "title_canon_sha256": "78a118a2c02561b3f5e956e78f03a224b5b1ac2134e66f641a111dad353bf48e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.4927",
    "kind": "arxiv",
    "version": 2
  }
}