Pith Number

pith:2EORTDZT

pith:2016:2EORTDZTD2WJCITZ3IK7DG5VHJ

not attested not anchored not stored refs pending

Harmonic cocycles, von Neumann algebras, and irreducible affine isometric actions

Bachir Bekka

arxiv:1612.08944 v1 · 2016-12-28 · 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{2EORTDZTD2WJCITZ3IK7DG5VHJ}

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	2026-05-18T00:53:46.786006Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d11d198f331eac912279da15f19bb53a5bbd7e909fdc3752d4de369887fb1967

Aliases

arxiv: 1612.08944 · arxiv_version: 1612.08944v1 · doi: 10.48550/arxiv.1612.08944 · pith_short_12: 2EORTDZTD2WJ · pith_short_16: 2EORTDZTD2WJCITZ · pith_short_8: 2EORTDZT

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/2EORTDZTD2WJCITZ3IK7DG5VHJ \
  | 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: d11d198f331eac912279da15f19bb53a5bbd7e909fdc3752d4de369887fb1967

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3bc0b0a1c7ebdb67d2da2bb605d8b1f2fa8d0e6369a754e45cd57c8eb48eff67",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-12-28T18:27:23Z",
    "title_canon_sha256": "038e8d237fd36a7d56126ce778a1898762650a3371d5d5dcc8f3ff02df1dc0dc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.08944",
    "kind": "arxiv",
    "version": 1
  }
}