Pith Number

pith:B5JJY7QF

pith:2016:B5JJY7QF4CU74XQTRT6GAVBLY2

not attested not anchored not stored refs pending

Higher order fractional Leibniz rule

Kazumasa Fujiwara, Tohru Ozawa, Vladimir Georgiev

arxiv:1609.05739 v1 · 2016-09-19 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{B5JJY7QF4CU74XQTRT6GAVBLY2}

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	2026-05-17T23:57:15.973966Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0f529c7e05e0a9fe5e138cfc60542bc6ad5f54234dc46e2362d49c5d7ddb8043

Aliases

arxiv: 1609.05739 · arxiv_version: 1609.05739v1 · doi: 10.48550/arxiv.1609.05739 · pith_short_12: B5JJY7QF4CU7 · pith_short_16: B5JJY7QF4CU74XQT · pith_short_8: B5JJY7QF

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/B5JJY7QF4CU74XQTRT6GAVBLY2 \
  | 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: 0f529c7e05e0a9fe5e138cfc60542bc6ad5f54234dc46e2362d49c5d7ddb8043

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ad2e5b97531c58f4a6513e21863426a74cce6c2ebee04e634468f636df03887c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-09-19T14:18:52Z",
    "title_canon_sha256": "660db39abf3fae490811555a44361018a2f374299cdc42b474289f997c60730d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.05739",
    "kind": "arxiv",
    "version": 1
  }
}