Pith Number

pith:I3U72JFU

pith:2017:I3U72JFUPBAHWDF5EPZAKYVM5Z

not attested not anchored not stored refs pending

Critical one component anisotropic regularity for 3-D Navier-Stokes system

Ping Zhang, Yanlin Liu

arxiv:1712.09072 v1 · 2017-12-25 · 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{I3U72JFUPBAHWDF5EPZAKYVM5Z}

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	2026-05-18T00:27:14.507147Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

46e9fd24b478407b0cbd23f20562acee4a0bd84830ee49f61e8eba95de819c5c

Aliases

arxiv: 1712.09072 · arxiv_version: 1712.09072v1 · doi: 10.48550/arxiv.1712.09072 · pith_short_12: I3U72JFUPBAH · pith_short_16: I3U72JFUPBAHWDF5 · pith_short_8: I3U72JFU

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/I3U72JFUPBAHWDF5EPZAKYVM5Z \
  | 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: 46e9fd24b478407b0cbd23f20562acee4a0bd84830ee49f61e8eba95de819c5c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3f7b87d66dc03a3c11d93bac6fc17baea34fe5eb16bfcf661a777989f551f630",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2017-12-25T14:25:20Z",
    "title_canon_sha256": "eec31eb5230019631f9bc3ccdae6099a328c059a01b6ed5163b5604c2fe0faa5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.09072",
    "kind": "arxiv",
    "version": 1
  }
}