Pith Number

pith:ATYNKIEF

pith:2011:ATYNKIEFPP52ZNN47QADL4QHCR

not attested not anchored not stored refs pending

Self-improving bounds for the Navier-Stokes equations

Fabrice Planchon, Jean-Yves Chemin

arxiv:1111.1356 v2 · 2011-11-05 · 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{ATYNKIEFPP52ZNN47QADL4QHCR}

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	2026-05-18T03:37:19.091935Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

04f0d520857bfbacb5bcfc0035f207144eca8edcb0e496af8dc7d10eaf4a9bfe

Aliases

arxiv: 1111.1356 · arxiv_version: 1111.1356v2 · doi: 10.48550/arxiv.1111.1356 · pith_short_12: ATYNKIEFPP52 · pith_short_16: ATYNKIEFPP52ZNN4 · pith_short_8: ATYNKIEF

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/ATYNKIEFPP52ZNN47QADL4QHCR \
  | 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: 04f0d520857bfbacb5bcfc0035f207144eca8edcb0e496af8dc7d10eaf4a9bfe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "20ce28b72ba0c876c987648bfbb01cab6a0043de2ff46012d3f6d3011c33967a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-11-05T21:55:43Z",
    "title_canon_sha256": "a58dd15a18680f60a6616e9aa1eb1e479df001fae83cca149faee5d89d31630f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.1356",
    "kind": "arxiv",
    "version": 2
  }
}