Pith Number

pith:5Q7BJCIO

pith:2021:5Q7BJCIOY4NEBI3JDKGIAE7CFD

not attested not anchored not stored refs pending

Generalized Differentiation and Duality in Infinite Dimensions under Polyhedral Convexity

Boris Mordukhovich, Dang Van Cuong, Nguyen Mau Nam, Sandine Gary

arxiv:2106.15777 v3 · 2021-06-30 · 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{5Q7BJCIOY4NEBI3JDKGIAE7CFD}

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	2026-07-05T03:15:35.026841Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ec3e14890ec71a40a3691a8c8013e228f938a0bf177705e96b709ff43f2813c0

Aliases

arxiv: 2106.15777 · arxiv_version: 2106.15777v3 · doi: 10.48550/arxiv.2106.15777 · pith_short_12: 5Q7BJCIOY4NE · pith_short_16: 5Q7BJCIOY4NEBI3J · pith_short_8: 5Q7BJCIO

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/5Q7BJCIOY4NEBI3JDKGIAE7CFD \
  | 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: ec3e14890ec71a40a3691a8c8013e228f938a0bf177705e96b709ff43f2813c0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "14915e070e8fe9b8b9d998ea5b7247a13a5aa79e6e3cd20bc4a8a56279fd9518",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2021-06-30T02:16:06Z",
    "title_canon_sha256": "a1b4dc75e1bf158ea26d91e0688e098ea09e6ed5912d0ddb986636ab34785ba2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2106.15777",
    "kind": "arxiv",
    "version": 3
  }
}