Pith Number

pith:JTVZ533P

pith:2006:JTVZ533PGDL676HCHA7L2CFVGE

not attested not anchored not stored refs pending

Regularity of solutions to the Navier-Stokes equations evolving from small data in BMO^{-1}

Gigliola Staffilani, Nata\v{s}a Pavlovi\'c, Pierre Germain

arxiv:math/0609781 v2 · 2006-09-28 · 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{JTVZ533PGDL676HCHA7L2CFVGE}

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	2026-05-18T01:08:49.672356Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4ceb9eef6f30d7eff8e2383ebd08b5310fb786fc1119e3dd73312392c459070e

Aliases

arxiv: math/0609781 · arxiv_version: math/0609781v2 · doi: 10.48550/arxiv.math/0609781 · pith_short_12: JTVZ533PGDL6 · pith_short_16: JTVZ533PGDL676HC · pith_short_8: JTVZ533P

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/JTVZ533PGDL676HCHA7L2CFVGE \
  | 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: 4ceb9eef6f30d7eff8e2383ebd08b5310fb786fc1119e3dd73312392c459070e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1f24977ca3f5bdca7879cac7e2fd463a768bdf0c1f8aef2af0007b4c0dcc4aed",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AP",
    "submitted_at": "2006-09-28T05:44:35Z",
    "title_canon_sha256": "8745726a50bda53fd31eeebb31b88897966d377ddb204636bc1086457feeba71"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0609781",
    "kind": "arxiv",
    "version": 2
  }
}