Pith Number

pith:TBKRG32O

pith:2013:TBKRG32OA2LFPLIMQTWI4LFRXO

not attested not anchored not stored refs pending

Gap Amplification for Small-Set Expansion via Random Walks

Prasad Raghavendra, Tselil Schramm

arxiv:1310.1493 v3 · 2013-10-05 · cs.CC · 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{TBKRG32OA2LFPLIMQTWI4LFRXO}

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	2026-05-18T02:48:27.264683Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9855136f4e069657ad0c84ec8e2cb1bb8f6eba7635c5436445461d72315e9cef

Aliases

arxiv: 1310.1493 · arxiv_version: 1310.1493v3 · doi: 10.48550/arxiv.1310.1493 · pith_short_12: TBKRG32OA2LF · pith_short_16: TBKRG32OA2LFPLIM · pith_short_8: TBKRG32O

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/TBKRG32OA2LFPLIMQTWI4LFRXO \
  | 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: 9855136f4e069657ad0c84ec8e2cb1bb8f6eba7635c5436445461d72315e9cef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "621db23beea4027a1e57efed995369b9e724d4ef354ad9a28afbbc15a1bc9123",
    "cross_cats_sorted": [
      "cs.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2013-10-05T16:35:35Z",
    "title_canon_sha256": "b6f2fbf877a587c18697bb082c4ec9a1d891d50d8e7295a36bc2064855d494a4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.1493",
    "kind": "arxiv",
    "version": 3
  }
}