Pith Number

pith:MJYH34DO

pith:2012:MJYH34DOZNL7XUHIPB5XCJAYFG

not attested not anchored not stored refs pending

Markov chain methods for small-set expansion

David Witmer, Ryan O'Donnell

arxiv:1204.4688 v3 · 2012-04-20 · 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{MJYH34DOZNL7XUHIPB5XCJAYFG}

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.

Cited by

1 paper in Pith

Hardness and Approximation for Coloring Digraphs

Receipt and verification

First computed	2026-05-18T03:08:14.651684Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

62707df06ecb57fbd0e8787b71241829a25601fff73f8124338615658959c48b

Aliases

arxiv: 1204.4688 · arxiv_version: 1204.4688v3 · doi: 10.48550/arxiv.1204.4688 · pith_short_12: MJYH34DOZNL7 · pith_short_16: MJYH34DOZNL7XUHI · pith_short_8: MJYH34DO

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/MJYH34DOZNL7XUHIPB5XCJAYFG \
  | 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: 62707df06ecb57fbd0e8787b71241829a25601fff73f8124338615658959c48b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ce0eb052375d77fb84f1899ff64c039b08c8d185f0074ea2e06df10fb2587f4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2012-04-20T17:52:57Z",
    "title_canon_sha256": "5b468bea5e3f54b0859dd86fdc70f9376e200ba896aea93f88b87db05210a950"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.4688",
    "kind": "arxiv",
    "version": 3
  }
}