Pith Number

pith:5CB4XURC

pith:2001:5CB4XURCCCJAPBMSM2VBGSPVTU

not attested not anchored not stored refs pending

Relative completions and the cohomology of linear groups over local rings

Kevin P. Knudson

arxiv:math/0104023 v1 · 2001-04-02 · math.KT · math.AT · 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{5CB4XURCCCJAPBMSM2VBGSPVTU}

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	2026-05-18T01:05:37.848949Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e883cbd222109207859266aa1349f59d3027809faff19519996a9136bff8183c

Aliases

arxiv: math/0104023 · arxiv_version: math/0104023v1 · doi: 10.48550/arxiv.math/0104023 · pith_short_12: 5CB4XURCCCJA · pith_short_16: 5CB4XURCCCJAPBMS · pith_short_8: 5CB4XURC

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/5CB4XURCCCJAPBMSM2VBGSPVTU \
  | 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: e883cbd222109207859266aa1349f59d3027809faff19519996a9136bff8183c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f39c1d61381bf98b8dde4a8a8ada5c81790288d4584e177235a2f1c5796db4cf",
    "cross_cats_sorted": [
      "math.AT",
      "math.GR"
    ],
    "license": "",
    "primary_cat": "math.KT",
    "submitted_at": "2001-04-02T16:59:19Z",
    "title_canon_sha256": "907f7a2b0f08cf5911e3f70216fea69dbc0cd8bd9aae2292ec5f7727a4a77eed"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0104023",
    "kind": "arxiv",
    "version": 1
  }
}