Pith Number

pith:DOCMTZ2R

pith:2014:DOCMTZ2R6S6FOBATKVPUKWE6ZD

not attested not anchored not stored refs pending

Proper cocycles and weak forms of amenability

Paul Jolissaint

arxiv:1403.0207 v6 · 2014-03-02 · math.GR · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DOCMTZ2R6S6FOBATKVPUKWE6ZD}

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	2026-05-18T02:41:59.548160Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1b84c9e751f4bc570413555f45589ec8d2e3d7503b92556a225c0c5571183873

Aliases

arxiv: 1403.0207 · arxiv_version: 1403.0207v6 · doi: 10.48550/arxiv.1403.0207 · pith_short_12: DOCMTZ2R6S6F · pith_short_16: DOCMTZ2R6S6FOBAT · pith_short_8: DOCMTZ2R

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/DOCMTZ2R6S6FOBATKVPUKWE6ZD \
  | 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: 1b84c9e751f4bc570413555f45589ec8d2e3d7503b92556a225c0c5571183873

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8095dd3b859fab6c07d959ba920f5700c59402e1a0c20b11a0e583610da8677c",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-03-02T13:35:22Z",
    "title_canon_sha256": "1b48afe562d6f2fc7c9c46d346660ce54228fecb364342c844f7e55452c81288"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1403.0207",
    "kind": "arxiv",
    "version": 6
  }
}