Pith Number

pith:OFGICGYM

pith:2015:OFGICGYMIJ6CQHOTW7XHBE5MEY

not attested not anchored not stored refs pending

Random Steiner systems and bounded degree coboundary expanders of every dimension

Alexander Lubotzky, Ron Rosenthal, Zur Luria

arxiv:1512.08331 v1 · 2015-12-28 · math.CO · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OFGICGYMIJ6CQHOTW7XHBE5MEY}

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	2026-05-18T01:23:42.595651Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

714c811b0c427c281dd3b7ee7093ac26227068bd656c8c48b17d37da9fbf0a16

Aliases

arxiv: 1512.08331 · arxiv_version: 1512.08331v1 · doi: 10.48550/arxiv.1512.08331 · pith_short_12: OFGICGYMIJ6C · pith_short_16: OFGICGYMIJ6CQHOT · pith_short_8: OFGICGYM

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/OFGICGYMIJ6CQHOTW7XHBE5MEY \
  | 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: 714c811b0c427c281dd3b7ee7093ac26227068bd656c8c48b17d37da9fbf0a16

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f253f3a16250781cc3f152ae0d3be369bb9f68c2d2ea962a55ae25b98840389b",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-12-28T07:25:01Z",
    "title_canon_sha256": "d9a4403c0f817dd6639b7dd6b924ce52fb256bc29827d0fb9c170e001f86a41d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.08331",
    "kind": "arxiv",
    "version": 1
  }
}