Pith Number

pith:R236AITS

pith:2021:R236AITS3G4D3WSWGYGRV4ATHI

not attested not anchored not stored refs pending

Banach Zuk's criterion for partite complexes with application to random groups

Izhar Oppenheim

arxiv:2112.02929 v2 · 2021-12-06 · math.GR · math.CO · math.FA · 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{R236AITS3G4D3WSWGYGRV4ATHI}

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

Sequential Sweeps and High Dimensional Expansion

Receipt and verification

First computed	2026-07-05T03:41:04.920178Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8eb7e02272d9b83dda56360d1af0133a2f14f7b557c96af9ad71c788e637b0d1

Aliases

arxiv: 2112.02929 · arxiv_version: 2112.02929v2 · doi: 10.48550/arxiv.2112.02929 · pith_short_12: R236AITS3G4D · pith_short_16: R236AITS3G4D3WSW · pith_short_8: R236AITS

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/R236AITS3G4D3WSWGYGRV4ATHI \
  | 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: 8eb7e02272d9b83dda56360d1af0133a2f14f7b557c96af9ad71c788e637b0d1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c2ea96a3f0f0790336f1217363f7a01973153237e3a242984d1b8892b677eb9d",
    "cross_cats_sorted": [
      "math.CO",
      "math.FA",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2021-12-06T11:02:42Z",
    "title_canon_sha256": "75ddd2df7e82b613dc3298143b5ee43fe1bcc3b862925ac4f2dfcc3b1e37454a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2112.02929",
    "kind": "arxiv",
    "version": 2
  }
}