Pith Number

pith:OKB7OHDY

pith:2013:OKB7OHDYYJ6SJFCHBKPL2UDIHF

not attested not anchored not stored refs pending

A variant of H\"ormander's $L^2$ theorem for Dirac operator in Clifford analysis

Yang Liu, Yifei Pan, Zhihua Chen

arxiv:1304.4653 v1 · 2013-04-17 · 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{OKB7OHDYYJ6SJFCHBKPL2UDIHF}

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	2026-05-18T03:27:44.062672Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7283f71c78c27d2494470a9ebd506839794b117ab96ab3e259f55224d987106e

Aliases

arxiv: 1304.4653 · arxiv_version: 1304.4653v1 · doi: 10.48550/arxiv.1304.4653 · pith_short_12: OKB7OHDYYJ6S · pith_short_16: OKB7OHDYYJ6SJFCH · pith_short_8: OKB7OHDY

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/OKB7OHDYYJ6SJFCHBKPL2UDIHF \
  | 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: 7283f71c78c27d2494470a9ebd506839794b117ab96ab3e259f55224d987106e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "277eb7170a6b1d76be3ea4155ed55747cf560d8970f3c127a55348d78a455a42",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-04-17T00:39:58Z",
    "title_canon_sha256": "cf4244306ef2dd25c27c8d5abb42e288ff29a2768afce69ccf9597d2dbec3f18"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.4653",
    "kind": "arxiv",
    "version": 1
  }
}