Pith Number

pith:GV5M6PM4

pith:2016:GV5M6PM4TIFXXBYAKN7JHT7OBQ

not attested not anchored not stored refs pending

Roe C*-algebra for groupoids and generalized Lichnerowicz Vanishing theorem for foliated manifolds

Rufus Willett, Xiang Tang, Yi-Jun Yao

arxiv:1605.07711 v1 · 2016-05-25 · math.OA · math.DG · math.FA · math.KT · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GV5M6PM4TIFXXBYAKN7JHT7OBQ}

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	2026-05-18T01:13:39.327791Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

357acf3d9c9a0b7b8700537e93cfee0c2d402b84c97841bbd93380ac8b5d9a23

Aliases

arxiv: 1605.07711 · arxiv_version: 1605.07711v1 · doi: 10.48550/arxiv.1605.07711 · pith_short_12: GV5M6PM4TIFX · pith_short_16: GV5M6PM4TIFXXBYA · pith_short_8: GV5M6PM4

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/GV5M6PM4TIFXXBYAKN7JHT7OBQ \
  | 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: 357acf3d9c9a0b7b8700537e93cfee0c2d402b84c97841bbd93380ac8b5d9a23

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "79e60c945da07293346a007eaee0aa9562b854e51d31ac6e58d1086642fb2bca",
    "cross_cats_sorted": [
      "math.DG",
      "math.FA",
      "math.KT",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2016-05-25T02:56:01Z",
    "title_canon_sha256": "cf95064dc0a858fd11fd10fb788c2411c278f2e9cdb51ba240a9357c04704a65"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.07711",
    "kind": "arxiv",
    "version": 1
  }
}