Pith Number

pith:22XIYD4N

pith:2012:22XIYD4NWIFMBJOKF7QIDUY2HP

not attested not anchored not stored refs pending

On the convergence of statistical solutions of the 3D Navier-Stokes-$\alpha$ model as $\alpha$ vanishes

Anne C. Bronzi, Ricardo M. S. Rosa

arxiv:1205.5563 v3 · 2012-05-24 · 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{22XIYD4NWIFMBJOKF7QIDUY2HP}

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	2026-05-18T02:20:47.997071Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d6ae8c0f8db20ac0a5ca2fe081d31a3bd976f44636530e369a846fc160fd6b4d

Aliases

arxiv: 1205.5563 · arxiv_version: 1205.5563v3 · doi: 10.48550/arxiv.1205.5563 · pith_short_12: 22XIYD4NWIFM · pith_short_16: 22XIYD4NWIFMBJOK · pith_short_8: 22XIYD4N

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/22XIYD4NWIFMBJOKF7QIDUY2HP \
  | 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: d6ae8c0f8db20ac0a5ca2fe081d31a3bd976f44636530e369a846fc160fd6b4d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "18d759bfba20234423319b22fdb0c1ca25ec8476e81dfeb9a0e4bb8dfb76ea7c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-05-24T20:38:01Z",
    "title_canon_sha256": "3d7b68a8c39e6a4ecdb54408ae1d73aaa8f47602bc9ebbc0d7db21f0e46311a2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.5563",
    "kind": "arxiv",
    "version": 3
  }
}