Pith Number

pith:OP4DFRPO

pith:2014:OP4DFRPOTENZVMFKF5ALWX5PRW

not attested not anchored not stored refs pending

Local spectral expansion approach to high dimensional expanders

Izhar Oppenheim

arxiv:1407.8517 v4 · 2014-07-31 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OP4DFRPOTENZVMFKF5ALWX5PRW}

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	2026-05-18T02:20:28.788496Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

73f832c5ee991b9ab0aa2f40bb5faf8d84a7b871000475480d357bb33409d854

Aliases

arxiv: 1407.8517 · arxiv_version: 1407.8517v4 · doi: 10.48550/arxiv.1407.8517 · pith_short_12: OP4DFRPOTENZ · pith_short_16: OP4DFRPOTENZVMFK · pith_short_8: OP4DFRPO

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/OP4DFRPOTENZVMFKF5ALWX5PRW \
  | 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: 73f832c5ee991b9ab0aa2f40bb5faf8d84a7b871000475480d357bb33409d854

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4674acc04ac7b783d3882442e68db03efb03d491d0ad0af1474a734b23b011c2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-07-31T18:35:24Z",
    "title_canon_sha256": "d9df67e33042cfdb65c75bfea3cf6527fe1d39dedf7d3d42d02fce8ec9a175b9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1407.8517",
    "kind": "arxiv",
    "version": 4
  }
}