Pith Number

pith:S76VG246

pith:2015:S76VG2467S3RIBNW5X4FMAXGCM

not attested not anchored not stored refs pending

A nonautonomous chain rule in $W^{1,p}$ and $BV$

Graziano Crasta, Guido De Philippis, Luigi Ambrosio, Virginia De Cicco

arxiv:1512.02839 v1 · 2015-12-09 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{S76VG2467S3RIBNW5X4FMAXGCM}

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	2026-05-18T01:24:39.539700Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

97fd536b9efcb71405b6edf85602e61311ee7e4354f795f87d13c723786e8d20

Aliases

arxiv: 1512.02839 · arxiv_version: 1512.02839v1 · doi: 10.48550/arxiv.1512.02839 · pith_short_12: S76VG2467S3R · pith_short_16: S76VG2467S3RIBNW · pith_short_8: S76VG246

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/S76VG2467S3RIBNW5X4FMAXGCM \
  | 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: 97fd536b9efcb71405b6edf85602e61311ee7e4354f795f87d13c723786e8d20

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3bb17a2dcfcdb1a177ebc8631da9700aded98a7629caa9eeb261c84103e49a46",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-12-09T12:55:07Z",
    "title_canon_sha256": "24c0dadcd0ec1d372ceef6b7b7b9658232ad23ea282e8bd1e4750ec2966b5c40"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.02839",
    "kind": "arxiv",
    "version": 1
  }
}