Pith Number

pith:QJJDMLH2

pith:2018:QJJDMLH2D6QLTC4C57WHH36VVF

not attested not anchored not stored refs pending

Subdifferential stability and subdifferential sum rules

Marc Lassonde

arxiv:1812.11464 v1 · 2018-12-30 · 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{QJJDMLH2D6QLTC4C57WHH36VVF}

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	2026-05-17T23:57:11.882585Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8252362cfa1fa0b98b82efec73efd5a955319b0fae5289518c6c2c512b1f387f

Aliases

arxiv: 1812.11464 · arxiv_version: 1812.11464v1 · doi: 10.48550/arxiv.1812.11464 · pith_short_12: QJJDMLH2D6QL · pith_short_16: QJJDMLH2D6QLTC4C · pith_short_8: QJJDMLH2

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/QJJDMLH2D6QLTC4C57WHH36VVF \
  | 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: 8252362cfa1fa0b98b82efec73efd5a955319b0fae5289518c6c2c512b1f387f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7474c9ac3ff2cfa6e347588d70714288d47a04886b50028843b74275654d56ca",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2018-12-30T03:47:07Z",
    "title_canon_sha256": "82de5d5c3b3e25dee67e11913c46ed0c0417cf982f486cff27771f63e90bacef"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.11464",
    "kind": "arxiv",
    "version": 1
  }
}