Pith Number

pith:HO2WOOJL

pith:2017:HO2WOOJLAFEEZVXFOK7UNV7L7B

not attested not anchored not stored refs pending

High Dimensional Expanders

Alexander Lubotzky

arxiv:1712.02526 v1 · 2017-12-07 · math.GR · math.CO · math.GT · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HO2WOOJLAFEEZVXFOK7UNV7L7B}

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

A Spectral Gap for Spinors on Hyperbolic Surfaces

Receipt and verification

First computed	2026-05-18T00:28:33.744971Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3bb567392b01484cd6e572bf46d7ebf86ce1379a434a841da1d4ae0d7834b3b9

Aliases

arxiv: 1712.02526 · arxiv_version: 1712.02526v1 · doi: 10.48550/arxiv.1712.02526 · pith_short_12: HO2WOOJLAFEE · pith_short_16: HO2WOOJLAFEEZVXF · pith_short_8: HO2WOOJL

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/HO2WOOJLAFEEZVXFOK7UNV7L7B \
  | 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: 3bb567392b01484cd6e572bf46d7ebf86ce1379a434a841da1d4ae0d7834b3b9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0d058469edf2dd629e1c42eaffe11a6f10a73e2a50447468a03075871699b057",
    "cross_cats_sorted": [
      "math.CO",
      "math.GT",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2017-12-07T07:59:00Z",
    "title_canon_sha256": "6a8a85e0ee758b6fc93a552d79e0e1573ca59e57bdbb343018a12fd55d02aea8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.02526",
    "kind": "arxiv",
    "version": 1
  }
}