Pith Number

pith:ZL5EFPNH

pith:2007:ZL5EFPNHHMCU6FVURUJVS6WVBW

not attested not anchored not stored refs pending

Blow-up criterion of strong solutions to the Navier-Stokes equations in Besov spaces with negative indices

Baoquan Yuan, BoZhang

arxiv:math/0703883 v1 · 2007-03-29 · 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{ZL5EFPNHHMCU6FVURUJVS6WVBW}

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	2026-05-18T01:26:03.399071Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cafa42bda73b054f16b48d13597ad50d96ae9fd6da7c4982196051e3bd93e5d9

Aliases

arxiv: math/0703883 · arxiv_version: math/0703883v1 · doi: 10.48550/arxiv.math/0703883 · pith_short_12: ZL5EFPNHHMCU · pith_short_16: ZL5EFPNHHMCU6FVU · pith_short_8: ZL5EFPNH

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/ZL5EFPNHHMCU6FVURUJVS6WVBW \
  | 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: cafa42bda73b054f16b48d13597ad50d96ae9fd6da7c4982196051e3bd93e5d9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c2feba7f0f868fbb15bb0f31bd09d5d4ac00dddb7d35ed794bf0c7741c5d981c",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AP",
    "submitted_at": "2007-03-29T14:27:03Z",
    "title_canon_sha256": "bf028e9aa1fbb82fdc1169cd77cc4d0cf265ce9a564137c8a4cc5e90f5c2ac70"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0703883",
    "kind": "arxiv",
    "version": 1
  }
}