Pith Number

pith:VCUETM4U

pith:2015:VCUETM4U5CJFD7UIH43BPKGR5L

not attested not anchored not stored refs pending

Geometric Approach to Subdifferential Calculus

Boris Mordukhovich, Nguyen Mau Nam

arxiv:1504.06004 v4 · 2015-04-22 · 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{VCUETM4U5CJFD7UIH43BPKGR5L}

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	2026-05-18T01:31:11.108742Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8a849b394e89251fe883f3617a8d1eaf2394b297088ab4d28bd794097b77c8e

Aliases

arxiv: 1504.06004 · arxiv_version: 1504.06004v4 · doi: 10.48550/arxiv.1504.06004 · pith_short_12: VCUETM4U5CJF · pith_short_16: VCUETM4U5CJFD7UI · pith_short_8: VCUETM4U

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/VCUETM4U5CJFD7UIH43BPKGR5L \
  | 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: a8a849b394e89251fe883f3617a8d1eaf2394b297088ab4d28bd794097b77c8e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "848a39fec3cc9d7b827d56fdcea87c8bc263893a244ac2e99a46c5bdb008745f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2015-04-22T23:25:12Z",
    "title_canon_sha256": "4edb3d3e75aa23abb1566da9a57e24596002195d62065d04398f00ce4864aa7d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.06004",
    "kind": "arxiv",
    "version": 4
  }
}