Pith Number

pith:6GFF6GK4

pith:2016:6GFF6GK4RQQTKN7CAD7BDT6QPI

not attested not anchored not stored refs pending

Uniqueness and Lagrangianity for solutions with lack of integrability of the continuity equation

Gianluca Crippa, Laura Caravenna

arxiv:1608.04324 v2 · 2016-08-15 · 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{6GFF6GK4RQQTKN7CAD7BDT6QPI}

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	2026-05-18T01:02:30.343887Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f18a5f195c8c213537e200fe11cfd07a131cf2d6438492419bf221180ea2bd62

Aliases

arxiv: 1608.04324 · arxiv_version: 1608.04324v2 · doi: 10.48550/arxiv.1608.04324 · pith_short_12: 6GFF6GK4RQQT · pith_short_16: 6GFF6GK4RQQTKN7C · pith_short_8: 6GFF6GK4

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/6GFF6GK4RQQTKN7CAD7BDT6QPI \
  | 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: f18a5f195c8c213537e200fe11cfd07a131cf2d6438492419bf221180ea2bd62

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "49ed58c6e7bd61ced0706cfbe63f5fdb0229e6e18bc0b8f02d931514b3b3ce72",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-08-15T16:54:14Z",
    "title_canon_sha256": "d9152696b4a4f452b367243b3fd5152bbf008f0c07f23cc3dd7a5b29a4d8526a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.04324",
    "kind": "arxiv",
    "version": 2
  }
}