Pith Number

pith:CZATPQPB

pith:2019:CZATPQPBDWTLF6ZRZTZL5T4WV6

not attested not anchored not stored refs pending

An integral formula for a pair of singular distributions

Paul Popescu, Vladimir Rovenski

arxiv:1908.07261 v3 · 2019-08-20 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CZATPQPBDWTLF6ZRZTZL5T4WV6}

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	2026-07-05T00:20:18.785017Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

164137c1e11da6b2fb31ccf2becf96af89926a82204211b574ca6ec2a26fbe30

Aliases

arxiv: 1908.07261 · arxiv_version: 1908.07261v3 · doi: 10.48550/arxiv.1908.07261 · pith_short_12: CZATPQPBDWTL · pith_short_16: CZATPQPBDWTLF6ZR · pith_short_8: CZATPQPB

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/CZATPQPBDWTLF6ZRZTZL5T4WV6 \
  | 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: 164137c1e11da6b2fb31ccf2becf96af89926a82204211b574ca6ec2a26fbe30

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6409a165019ccbea1a13b67462bf47e184eb3c0c3fcb319dea1ec035379ced73",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2019-08-20T10:19:45Z",
    "title_canon_sha256": "eece2662c66c80a1a47debc6176b544d0d66744ce350dd509eef39e717310c51"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.07261",
    "kind": "arxiv",
    "version": 3
  }
}