Pith Number

pith:4WAQK7HM

pith:2013:4WAQK7HMBMR4ENFQPFXAVQ7SZT

not attested not anchored not stored refs pending

Remarks on functional calculus for perturbed first order Dirac operators

Pascal Auscher (LM-Orsay), Sebastian Stahlhut (LM-Orsay)

arxiv:1303.5047 v1 · 2013-03-20 · math.CA · 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{4WAQK7HMBMR4ENFQPFXAVQ7SZT}

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	2026-05-18T03:30:15.222788Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e581057cec0b23c234b0796e0ac3f2cce62bc5f5e95391cf940deb84f1cf4e42

Aliases

arxiv: 1303.5047 · arxiv_version: 1303.5047v1 · doi: 10.48550/arxiv.1303.5047 · pith_short_12: 4WAQK7HMBMR4 · pith_short_16: 4WAQK7HMBMR4ENFQ · pith_short_8: 4WAQK7HM

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/4WAQK7HMBMR4ENFQPFXAVQ7SZT \
  | 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: e581057cec0b23c234b0796e0ac3f2cce62bc5f5e95391cf940deb84f1cf4e42

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7b4b0c69162f8217f7aa02583fd3788a448ad1e3beb978fc579de14d2f375433",
    "cross_cats_sorted": [
      "math.AP",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-03-20T19:44:28Z",
    "title_canon_sha256": "b1a66cedff34c69da28e64c63008a92c94aea8dc96cd981120343786595429b5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.5047",
    "kind": "arxiv",
    "version": 1
  }
}