Pith Number

pith:KZ5ZX3WO

pith:2011:KZ5ZX3WOANJ2DI3BN57PQS7LKU

not attested not anchored not stored refs pending

On finite generation and infinite convergence of generalized closures from the theory of cutting planes

Gennadiy Averkov

arxiv:1106.1526 v1 · 2011-06-08 · math.OC · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KZ5ZX3WOANJ2DI3BN57PQS7LKU}

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	2026-05-18T04:20:22.853068Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

567b9beece0353a1a3616f7ef84beb552ef9ad8d37d97036157fda10f82573a8

Aliases

arxiv: 1106.1526 · arxiv_version: 1106.1526v1 · doi: 10.48550/arxiv.1106.1526 · pith_short_12: KZ5ZX3WOANJ2 · pith_short_16: KZ5ZX3WOANJ2DI3B · pith_short_8: KZ5ZX3WO

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/KZ5ZX3WOANJ2DI3BN57PQS7LKU \
  | 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: 567b9beece0353a1a3616f7ef84beb552ef9ad8d37d97036157fda10f82573a8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4583f18632e6bc61bf629baea8a02aac2d1b6cd09bc30871daedf386aad46fcd",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2011-06-08T09:22:17Z",
    "title_canon_sha256": "4341deb3988404aa1f42be9785839cbf8683a90ba1b2b07268b4b604dff4c7d2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.1526",
    "kind": "arxiv",
    "version": 1
  }
}