Pith Number

pith:ZKTP4RZA

pith:1999:ZKTP4RZAQQ2ZXUYXP56NZAXTNQ

not attested not anchored not stored refs pending

A Homology Theory for Etale Groupoids

Ieke Moerdijk, Marius Crainic

arxiv:math/9905011 v1 · 1999-05-03 · math.KT · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZKTP4RZAQQ2ZXUYXP56NZAXTNQ}

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.

Cited by

1 paper in Pith

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

Receipt and verification

First computed	2026-07-04T14:41:08.556917Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

caa6fe472084359bd3177f7cdc82f36c1902404e6ffe0b1b2fa11f5b2977c230

Aliases

arxiv: math/9905011 · arxiv_version: math/9905011v1 · doi: 10.48550/arxiv.math/9905011 · pith_short_12: ZKTP4RZAQQ2Z · pith_short_16: ZKTP4RZAQQ2ZXUYX · pith_short_8: ZKTP4RZA

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/ZKTP4RZAQQ2ZXUYXP56NZAXTNQ \
  | 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: caa6fe472084359bd3177f7cdc82f36c1902404e6ffe0b1b2fa11f5b2977c230

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4b4e5e3bd774f8ecab9565c60ae4ff1d7ae3c5dfff703890ce6ac1004be3e8f5",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "",
    "primary_cat": "math.KT",
    "submitted_at": "1999-05-03T19:24:32Z",
    "title_canon_sha256": "1e8dd9d42fa026ef92673c1e55739febc25c7db156b8619c8b45b0be60455f8b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9905011",
    "kind": "arxiv",
    "version": 1
  }
}