Pith Number

pith:ADJ243VE

pith:2013:ADJ243VE7OVZXHMQHBCMYBXR3G

not attested not anchored not stored refs pending

Lorentz space estimates for vector fields with divergence and curl in Hardy spaces

Xingfei Xiang, Yoshikazu Giga

arxiv:1312.5823 v1 · 2013-12-20 · 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{ADJ243VE7OVZXHMQHBCMYBXR3G}

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	2026-05-18T03:04:07.761930Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

00d3ae6ea4fbab9b9d903844cc06f1d9b9c51ef2c60023a6df5663476eb89dee

Aliases

arxiv: 1312.5823 · arxiv_version: 1312.5823v1 · doi: 10.48550/arxiv.1312.5823 · pith_short_12: ADJ243VE7OVZ · pith_short_16: ADJ243VE7OVZXHMQ · pith_short_8: ADJ243VE

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/ADJ243VE7OVZXHMQHBCMYBXR3G \
  | 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: 00d3ae6ea4fbab9b9d903844cc06f1d9b9c51ef2c60023a6df5663476eb89dee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "067d71cab118083e86c099ac11f8dd5500250ac38d15bec8eb19c8820b83bd9e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-12-20T06:47:06Z",
    "title_canon_sha256": "7f9eeb3398b7c4f42af3df5b5581122132c5a33d1bed7f47b08c0d542315507a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.5823",
    "kind": "arxiv",
    "version": 1
  }
}