Pith Number

pith:CJPXVSMH

pith:2010:CJPXVSMHEH64273H2F24YDKBET

not attested not anchored not stored refs pending

Weyl asymptotics of Bisingular Operators and Dirichlet Divisor Problem

Ubertino Battisti

arxiv:1012.1518 v3 · 2010-12-07 · math.SP · 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{CJPXVSMHEH64273H2F24YDKBET}

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	2026-05-18T04:04:44.881573Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

125f7ac98721fdcd7f67d175cc0d4124f76a6a3f546521451fc97aea9435fb17

Aliases

arxiv: 1012.1518 · arxiv_version: 1012.1518v3 · doi: 10.48550/arxiv.1012.1518 · pith_short_12: CJPXVSMHEH64 · pith_short_16: CJPXVSMHEH64273H · pith_short_8: CJPXVSMH

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/CJPXVSMHEH64273H2F24YDKBET \
  | 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: 125f7ac98721fdcd7f67d175cc0d4124f76a6a3f546521451fc97aea9435fb17

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "528316f2d24b48e7368b7268ac1bdbfab0c7de7423e0e4b2fbec62042045fa2d",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2010-12-07T14:29:17Z",
    "title_canon_sha256": "d8242d2e3eedfdd1fc92e8e449fc7fea09c4b3f5b3cdb5907bf2ad7a46fa52b0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.1518",
    "kind": "arxiv",
    "version": 3
  }
}