Pith Number

pith:NDQPRDZI

pith:2005:NDQPRDZI2CMO2NUV5PNIEGFVEJ

not attested not anchored not stored refs pending

Exponential mixing for the 3D stochastic Navier--Stokes equations

Cyril Odasso (IRMAR)

arxiv:math/0512056 v2 · 2005-12-02 · 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{NDQPRDZI2CMO2NUV5PNIEGFVEJ}

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	2026-06-03T22:06:18.455144Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

68e0f88f28d098ed3695ebda8218b5226e8aefec0872d464aac686a511ccc1bb

Aliases

arxiv: math/0512056 · arxiv_version: math/0512056v2 · doi: 10.48550/arxiv.math/0512056 · pith_short_12: NDQPRDZI2CMO · pith_short_16: NDQPRDZI2CMO2NUV · pith_short_8: NDQPRDZI

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/NDQPRDZI2CMO2NUV5PNIEGFVEJ \
  | 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: 68e0f88f28d098ed3695ebda8218b5226e8aefec0872d464aac686a511ccc1bb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "76cf86d20c98d2df3e913a9f0227a60502aed281aa252411af8fd34f970db90b",
    "cross_cats_sorted": [
      "cs.NA",
      "math.NA"
    ],
    "license": "",
    "primary_cat": "math.AP",
    "submitted_at": "2005-12-02T14:49:47Z",
    "title_canon_sha256": "b59d4f2b21f9d005335d9a3cd4bbf1127ce7f78a097e7c2248c9d8635f455a05"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0512056",
    "kind": "arxiv",
    "version": 2
  }
}