Pith Number

pith:HZ5LUQWE

pith:2016:HZ5LUQWE5IPULON5BNICQRG43N

not attested not anchored not stored refs pending

Refined Shapley-Folkman Lemma and Its Application in Duality Gap Estimation

Ao Tang, Yingjie Bi

arxiv:1610.05416 v3 · 2016-10-18 · 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{HZ5LUQWE5IPULON5BNICQRG43N}

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	2026-05-18T00:25:27.148070Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3e7aba42c4ea1f45b9bd0b502844dcdb58b0092ac8665566f74e0c829bda6c17

Aliases

arxiv: 1610.05416 · arxiv_version: 1610.05416v3 · doi: 10.48550/arxiv.1610.05416 · pith_short_12: HZ5LUQWE5IPU · pith_short_16: HZ5LUQWE5IPULON5 · pith_short_8: HZ5LUQWE

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/HZ5LUQWE5IPULON5BNICQRG43N \
  | 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: 3e7aba42c4ea1f45b9bd0b502844dcdb58b0092ac8665566f74e0c829bda6c17

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "51d134f738ff165eb87881a2af22b879e32a7414c152729be4ddb5896720d0ba",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2016-10-18T03:23:09Z",
    "title_canon_sha256": "3d1976f74333bc0ea7c2dfdb90566e685aa5fab9e4297fcd24315e6a1e697145"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.05416",
    "kind": "arxiv",
    "version": 3
  }
}