Pith Number

pith:JOCPRUTO

pith:2016:JOCPRUTOJNVZUFVRKZO33Z4K3Q

not attested not anchored not stored refs pending

Minimizing the Union: Tight Approximations for Small Set Bipartite Vertex Expansion

Eden Chlamt\'a\v{c}, Michael Dinitz, Yury Makarychev

arxiv:1611.07866 v1 · 2016-11-23 · cs.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JOCPRUTOJNVZUFVRKZO33Z4K3Q}

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	2026-05-18T00:56:59.652234Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4b84f8d26e4b6b9a16b1565dbde78adc2c766d3a6057f933265e41f6365920cd

Aliases

arxiv: 1611.07866 · arxiv_version: 1611.07866v1 · doi: 10.48550/arxiv.1611.07866 · pith_short_12: JOCPRUTOJNVZ · pith_short_16: JOCPRUTOJNVZUFVR · pith_short_8: JOCPRUTO

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/JOCPRUTOJNVZUFVRKZO33Z4K3Q \
  | 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: 4b84f8d26e4b6b9a16b1565dbde78adc2c766d3a6057f933265e41f6365920cd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "caa922f6131305c5625b3812ea6a8cd5999e1321a4e2f89de95dd040c2f10331",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2016-11-23T16:24:45Z",
    "title_canon_sha256": "e1f93faaa093e2b13ac289c8ab04e3b684c8c34459bc326c0459bb2de7d41c1c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.07866",
    "kind": "arxiv",
    "version": 1
  }
}