Pith Number

pith:4W7CLTBM

pith:2012:4W7CLTBM5KDQBR3KPVMDQN5MKA

not attested not anchored not stored refs pending

Local null controllability of the three-dimensional Navier-Stokes system with a distributed control having two vanishing components

Jean-Michel Coron, Pierre Lissy

arxiv:1211.2102 v2 · 2012-11-09 · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4W7CLTBM5KDQBR3KPVMDQN5MKA}

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	2026-05-18T03:08:38.243474Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5be25cc2cea8700c76a7d583837ac500de074a2683156634197b251642b16d0

Aliases

arxiv: 1211.2102 · arxiv_version: 1211.2102v2 · doi: 10.48550/arxiv.1211.2102 · pith_short_12: 4W7CLTBM5KDQ · pith_short_16: 4W7CLTBM5KDQBR3K · pith_short_8: 4W7CLTBM

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/4W7CLTBM5KDQBR3KPVMDQN5MKA \
  | 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: e5be25cc2cea8700c76a7d583837ac500de074a2683156634197b251642b16d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "73bf4a5023cc0af23363a0640b845cbdc48cb11ee170c5e51c00559d5baf134d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2012-11-09T11:20:39Z",
    "title_canon_sha256": "fd55beabe5359410ec303c150605d64c01c2bcc5bb1da062376962e8b7f0b335"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.2102",
    "kind": "arxiv",
    "version": 2
  }
}