Pith Number

pith:UMAGHV5P

pith:2016:UMAGHV5PB7MJMS26ESAAMYKF4Y

not attested not anchored not stored refs pending

Critical Multipliers in Variational Systems via Second-order Generalized Differentiation

Boris S. Mordukhovich, M. Ebrahim Sarabi

arxiv:1609.07199 v2 · 2016-09-23 · 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{UMAGHV5PB7MJMS26ESAAMYKF4Y}

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	2026-05-18T00:52:29.299497Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a30063d7af0fd8964b5e2480066145e61aaf2b28250de5feed9d94b1743d3f06

Aliases

arxiv: 1609.07199 · arxiv_version: 1609.07199v2 · doi: 10.48550/arxiv.1609.07199 · pith_short_12: UMAGHV5PB7MJ · pith_short_16: UMAGHV5PB7MJMS26 · pith_short_8: UMAGHV5P

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/UMAGHV5PB7MJMS26ESAAMYKF4Y \
  | 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: a30063d7af0fd8964b5e2480066145e61aaf2b28250de5feed9d94b1743d3f06

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "daa3b8ce067b7e8de12a98bf8cdbac62faf8691e63346b9248ad0a389f79c19d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2016-09-23T00:59:34Z",
    "title_canon_sha256": "e89053ddad52a0330bfe13c7d8c15e2063c124574f1e543596c591be4f9d2df0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.07199",
    "kind": "arxiv",
    "version": 2
  }
}