Pith Number

pith:IACPZY7E

pith:2019:IACPZY7E7XL7FCTTTXYV6H75NH

not attested not anchored not stored refs pending

Bilevel Optimization and Variational Analysis

Boris S. Mordukhovich

arxiv:1907.06140 v1 · 2019-07-13 · 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{IACPZY7E7XL7FCTTTXYV6H75NH}

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	2026-05-17T23:40:38.417133Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4004fce3e4fdd7f28a739df15f1ffd69ccf8552669503b269482b745cd5417d4

Aliases

arxiv: 1907.06140 · arxiv_version: 1907.06140v1 · doi: 10.48550/arxiv.1907.06140 · pith_short_12: IACPZY7E7XL7 · pith_short_16: IACPZY7E7XL7FCTT · pith_short_8: IACPZY7E

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/IACPZY7E7XL7FCTTTXYV6H75NH \
  | 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: 4004fce3e4fdd7f28a739df15f1ffd69ccf8552669503b269482b745cd5417d4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2846ae8c3a4090e22a965608eaee269a4c81efed39e058866a72e55fe734aa5f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2019-07-13T22:37:23Z",
    "title_canon_sha256": "5c48916cd3735955903e0993a3ea7d927a933e636e185acc4b80697bf06d03b8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.06140",
    "kind": "arxiv",
    "version": 1
  }
}