Pith Number

pith:ZJYE62JE

pith:2011:ZJYE62JEQABWMLFWEVDYO76V23

not attested not anchored not stored refs pending

Second-order subdifferential calculus with applications to tilt stability in optimization

B.S. Mordukhovich, R.T. Rockafellar

arxiv:1110.4572 v1 · 2011-10-20 · 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{ZJYE62JEQABWMLFWEVDYO76V23}

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	2026-05-18T04:10:36.305143Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ca704f69248003662cb62547877fd5d6fac3ed424965149735888500e9194c36

Aliases

arxiv: 1110.4572 · arxiv_version: 1110.4572v1 · doi: 10.48550/arxiv.1110.4572 · pith_short_12: ZJYE62JEQABW · pith_short_16: ZJYE62JEQABWMLFW · pith_short_8: ZJYE62JE

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/ZJYE62JEQABWMLFWEVDYO76V23 \
  | 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: ca704f69248003662cb62547877fd5d6fac3ed424965149735888500e9194c36

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1f99f4ca928486b9af8c8d8a8622743b48255f7043919ca571e2c2260452c91e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2011-10-20T16:30:09Z",
    "title_canon_sha256": "b0c1176fcea2b726b809683311cfbf74da2d0c52a03d90fdd5cb77b2e86a7ff9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.4572",
    "kind": "arxiv",
    "version": 1
  }
}