Pith Number

pith:5Q76DSTE

pith:2005:5Q76DSTEWHVSWABSGMPV7H3EZ4

not attested not anchored not stored refs pending

Markov solutions for the 3D stochastic Navier--Stokes equations with state dependent noise

Arnaud Debussche (IRMAR), Cyril Odasso (IRMAR)

arxiv:math/0512361 v2 · 2005-12-15 · math.AP · cs.NA · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5Q76DSTEWHVSWABSGMPV7H3EZ4}

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	2026-06-03T22:06:18.512546Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ec3fe1ca64b1eb2b0032331f5f9f64cf3c97fee4616b3140f64320d5839e587c

Aliases

arxiv: math/0512361 · arxiv_version: math/0512361v2 · doi: 10.48550/arxiv.math/0512361 · pith_short_12: 5Q76DSTEWHVS · pith_short_16: 5Q76DSTEWHVSWABS · pith_short_8: 5Q76DSTE

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/5Q76DSTEWHVSWABSGMPV7H3EZ4 \
  | 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: ec3fe1ca64b1eb2b0032331f5f9f64cf3c97fee4616b3140f64320d5839e587c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5f229b0d64f3ab42bbad93345dc2852dd8e75b6577512e0a9badec926f4ceef2",
    "cross_cats_sorted": [
      "cs.NA",
      "math.NA"
    ],
    "license": "",
    "primary_cat": "math.AP",
    "submitted_at": "2005-12-15T13:57:10Z",
    "title_canon_sha256": "0cc7c54e9273bd94aecaf84725630507779d18a45f01eb2c9b1db8c828f2a110"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0512361",
    "kind": "arxiv",
    "version": 2
  }
}