Pith Number

pith:RC66JVHZ

pith:2014:RC66JVHZVBWXB6XAGHSSJCPHGH

not attested not anchored not stored refs pending

Failure of the chain rule for the divergence of bounded vector fields

Emil Wiedemann, Gianluca Crippa, Nikolay Gusev, Stefano Spirito

arxiv:1412.2476 v1 · 2014-12-08 · 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{RC66JVHZVBWXB6XAGHSSJCPHGH}

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	2026-05-18T02:31:57.866460Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

88bde4d4f9a86d70fae031e52489e731e664bac881c9a1bbfc03ecbd65b4f32d

Aliases

arxiv: 1412.2476 · arxiv_version: 1412.2476v1 · doi: 10.48550/arxiv.1412.2476 · pith_short_12: RC66JVHZVBWX · pith_short_16: RC66JVHZVBWXB6XA · pith_short_8: RC66JVHZ

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/RC66JVHZVBWXB6XAGHSSJCPHGH \
  | 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: 88bde4d4f9a86d70fae031e52489e731e664bac881c9a1bbfc03ecbd65b4f32d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6d8498ae6b3a6ead4aa579b7920cb38af55551f8fbbd5d677c7dc8ceaccedb8a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2014-12-08T08:08:55Z",
    "title_canon_sha256": "9d78a656590729feba3244466e92e13ac56b7d112111e890f1ac693b9c63ef86"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.2476",
    "kind": "arxiv",
    "version": 1
  }
}