Pith Number

pith:Z75NFW57

pith:2013:Z75NFW57VDMZHDZR7JF2X7ORVC

not attested not anchored not stored refs pending

Subgaussian 1-cocycles on discrete groups

Marius Junge, Qiang Zeng

arxiv:1311.5098 v3 · 2013-11-20 · math.PR · math.GR · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Z75NFW57VDMZHDZR7JF2X7ORVC}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T00:44:29.319756Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cffad2dbbfa8d9938f31fa4babfdd1a8a7d1cfc5b716fbde15d012eb4048c780

Aliases

arxiv: 1311.5098 · arxiv_version: 1311.5098v3 · doi: 10.48550/arxiv.1311.5098 · pith_short_12: Z75NFW57VDMZ · pith_short_16: Z75NFW57VDMZHDZR · pith_short_8: Z75NFW57

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/Z75NFW57VDMZHDZR7JF2X7ORVC \
  | 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: cffad2dbbfa8d9938f31fa4babfdd1a8a7d1cfc5b716fbde15d012eb4048c780

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "af5fb9ba354792876aa9f83803436d292ac55de05cb4873efc196c7787daae6e",
    "cross_cats_sorted": [
      "math.GR",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-11-20T15:36:40Z",
    "title_canon_sha256": "623e7da4571bb59b711a8be0b80ced0e8c5c9b1bd010d1d06b6cc8aea88a3f6b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.5098",
    "kind": "arxiv",
    "version": 3
  }
}