Pith Number

pith:OLDKSLQO

pith:2018:OLDKSLQO5NXZGBRHBO7HYJWW5B

not attested not anchored not stored refs pending

Canonical Duality Theory and Algorithm for Solving Bilevel Knapsack Problems with Applications

David Yang Gao

arxiv:1811.10130 v1 · 2018-11-26 · math.OC · cs.DM

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OLDKSLQO5NXZGBRHBO7HYJWW5B}

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	2026-05-17T23:59:57.197995Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

72c6a92e0eeb6f9306270bbe7c26d6e8686c857bce9c35473b48c5c64a203858

Aliases

arxiv: 1811.10130 · arxiv_version: 1811.10130v1 · doi: 10.48550/arxiv.1811.10130 · pith_short_12: OLDKSLQO5NXZ · pith_short_16: OLDKSLQO5NXZGBRH · pith_short_8: OLDKSLQO

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/OLDKSLQO5NXZGBRHBO7HYJWW5B \
  | 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: 72c6a92e0eeb6f9306270bbe7c26d6e8686c857bce9c35473b48c5c64a203858

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a734e1cbf2874b674be92f193f6058be145d678deacb0c91e80cc2e66446faea",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2018-11-26T00:48:37Z",
    "title_canon_sha256": "21c672f8bbe78f3fa3cca8e03bc17a79b429a4b8920a3b90d533658af3ab9bbd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.10130",
    "kind": "arxiv",
    "version": 1
  }
}