Pith Number

pith:GMA2GPMM

pith:2016:GMA2GPMMAQCYAGABSD23CLLISV

not attested not anchored not stored refs pending

Inner amenability, property Gamma, McDuff II_1 factors and stable equivalence relations

Stefaan Vaes, Tobe Deprez

arxiv:1604.02911 v2 · 2016-04-11 · math.OA · math.DS · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GMA2GPMMAQCYAGABSD23CLLISV}

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	2026-05-18T00:05:46.457791Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3301a33d8c040580180190f5b12d6895441459e90627c60d73e3e437e0128d90

Aliases

arxiv: 1604.02911 · arxiv_version: 1604.02911v2 · doi: 10.48550/arxiv.1604.02911 · pith_short_12: GMA2GPMMAQCY · pith_short_16: GMA2GPMMAQCYAGAB · pith_short_8: GMA2GPMM

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/GMA2GPMMAQCYAGABSD23CLLISV \
  | 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: 3301a33d8c040580180190f5b12d6895441459e90627c60d73e3e437e0128d90

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6a4450722545f9d826b1e721bade0b726cfdf39a382378e6a665950775d2bd9f",
    "cross_cats_sorted": [
      "math.DS",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2016-04-11T12:15:35Z",
    "title_canon_sha256": "9d47f9e1c449df9fd149e9eac9d4f66eb0ad7a5c61639e79edd6412bc5a36955"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.02911",
    "kind": "arxiv",
    "version": 2
  }
}