Pith Number

pith:6P2NE6XH

pith:2024:6P2NE6XH6X6BZQEDMSDKWFTU2N

not attested not anchored not stored refs pending

Cup and cap products for cohomology and homology groups of ample groupoids

Hiroki Matui, Takehiko Mori

arxiv:2411.14906 v3 · 2024-11-22 · math.OA · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6P2NE6XH6X6BZQEDMSDKWFTU2N}

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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.

Cited by

1 paper in Pith

Cohomology of ample groupoids

Receipt and verification

First computed	2026-07-05T11:26:01.702902Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f3f4d27ae7f5fc1cc0836486ab1674d377e1da815c795b6d62f8546cf6d1d354

Aliases

arxiv: 2411.14906 · arxiv_version: 2411.14906v3 · doi: 10.48550/arxiv.2411.14906 · pith_short_12: 6P2NE6XH6X6B · pith_short_16: 6P2NE6XH6X6BZQED · pith_short_8: 6P2NE6XH

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/6P2NE6XH6X6BZQEDMSDKWFTU2N \
  | 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: f3f4d27ae7f5fc1cc0836486ab1674d377e1da815c795b6d62f8546cf6d1d354

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "59c2977ecc1ab9ba098424b7104c4b8f9253c9d61029340ea08b4155a6a2196d",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2024-11-22T13:03:36Z",
    "title_canon_sha256": "01799de27b3d926477d2f4fbd3cfe45f3c215c88fe097bf1fe83096da3f9d9e8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2411.14906",
    "kind": "arxiv",
    "version": 3
  }
}