Pith Number

pith:3YX7V2V6

pith:2012:3YX7V2V6VSXPEXBOXNSORHZQBT

not attested not anchored not stored refs pending

Existence of densities for the 3D Navier-Stokes equations driven by Gaussian noise

Arnaud Debussche, Marco Romito

arxiv:1203.0417 v1 · 2012-03-02 · math.PR · math-ph · math.AP · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3YX7V2V6VSXPEXBOXNSORHZQBT}

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	2026-05-18T04:01:00.867433Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

de2ffaeabeacaef25c2ebb64e89f300cda752a8031e5009ccd9b321c42391a11

Aliases

arxiv: 1203.0417 · arxiv_version: 1203.0417v1 · doi: 10.48550/arxiv.1203.0417 · pith_short_12: 3YX7V2V6VSXP · pith_short_16: 3YX7V2V6VSXPEXBO · pith_short_8: 3YX7V2V6

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/3YX7V2V6VSXPEXBOXNSORHZQBT \
  | 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: de2ffaeabeacaef25c2ebb64e89f300cda752a8031e5009ccd9b321c42391a11

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c444ef7232491bdf1187054b21a9f8da88305e1bb5cd0abcad05a3a1fcf244eb",
    "cross_cats_sorted": [
      "math-ph",
      "math.AP",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-03-02T11:06:57Z",
    "title_canon_sha256": "9ba8400614a8d6735b5046bcff2165656a0d06efde562e99f7e7a2ac42741e55"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.0417",
    "kind": "arxiv",
    "version": 1
  }
}