Pith Number

pith:4RIPYX6X

pith:2020:4RIPYX6XVDZWHL74HPN2FNKPWC

not attested not anchored not stored refs pending

A regularity criterion for three-dimensional micropolar fluid equations in Besov spaces of negative regular indices

Fan Wu, Maria Alessandra Ragusa

arxiv:2006.00524 v1 · 2020-05-31 · 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{4RIPYX6XVDZWHL74HPN2FNKPWC}

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	2026-07-05T01:07:02.693338Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e450fc5fd7a8f363affc3bdba2b54fb084db709713639f7c3f740b8eed365e16

Aliases

arxiv: 2006.00524 · arxiv_version: 2006.00524v1 · doi: 10.48550/arxiv.2006.00524 · pith_short_12: 4RIPYX6XVDZW · pith_short_16: 4RIPYX6XVDZWHL74 · pith_short_8: 4RIPYX6X

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/4RIPYX6XVDZWHL74HPN2FNKPWC \
  | 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: e450fc5fd7a8f363affc3bdba2b54fb084db709713639f7c3f740b8eed365e16

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c34dd6f145fa1aff3a356f3b355b29a5f456ca1da3355ea2238aa6659e6b4d51",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2020-05-31T13:46:44Z",
    "title_canon_sha256": "344e84d19360b8d0c0bde2c7a02ee6a3890fdb8e09b7ad00ee0024cd9e78c6e8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2006.00524",
    "kind": "arxiv",
    "version": 1
  }
}