Pith Number

pith:QK3EOKUE

pith:2014:QK3EOKUEE74WIJHBM5DPCLF6CJ

not attested not anchored not stored refs pending

The Navier-Stokes equations. Regularity of fast flows and Sobolev imbedding

Piotr B. Mucha

arxiv:1409.7536 v2 · 2014-09-26 · 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{QK3EOKUEE74WIJHBM5DPCLF6CJ}

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	2026-05-18T02:39:00.651006Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

82b6472a8427f96424e16746f12cbe12565140a05c61393eeab019dc4b2ea6af

Aliases

arxiv: 1409.7536 · arxiv_version: 1409.7536v2 · doi: 10.48550/arxiv.1409.7536 · pith_short_12: QK3EOKUEE74W · pith_short_16: QK3EOKUEE74WIJHB · pith_short_8: QK3EOKUE

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/QK3EOKUEE74WIJHBM5DPCLF6CJ \
  | 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: 82b6472a8427f96424e16746f12cbe12565140a05c61393eeab019dc4b2ea6af

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bb27d037e189f53fdd9b94e37a771d5b196975b760916d62e9d5d947b113a833",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2014-09-26T11:19:16Z",
    "title_canon_sha256": "9767187807ae03fd42e139c5a9f26b07cb1e976f98c5e6492e4d91231cd31752"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.7536",
    "kind": "arxiv",
    "version": 2
  }
}