Pith Number

pith:P7LQGKMC

pith:2009:P7LQGKMC3F5UPRLN3AZC4MFH7X

not attested not anchored not stored refs pending

Algebraic groups over the field with one element

Oliver Lorscheid

arxiv:0907.3824 v1 · 2009-07-22 · math.AG · 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{P7LQGKMC3F5UPRLN3AZC4MFH7X}

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

Groupoid Cardinality and Random Permutations

Receipt and verification

First computed	2026-07-04T15:46:41.440370Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7fd7032982d97b47c56dd8322e30a7fdee2cfef458706cec5145e19dd8dbab82

Aliases

arxiv: 0907.3824 · arxiv_version: 0907.3824v1 · doi: 10.48550/arxiv.0907.3824 · pith_short_12: P7LQGKMC3F5U · pith_short_16: P7LQGKMC3F5UPRLN · pith_short_8: P7LQGKMC

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/P7LQGKMC3F5UPRLN3AZC4MFH7X \
  | 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: 7fd7032982d97b47c56dd8322e30a7fdee2cfef458706cec5145e19dd8dbab82

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ed89274cc056b4d105ac05fc2ab56baa2c5e18815a2d928327c9c969f1d719a0",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2009-07-22T12:02:36Z",
    "title_canon_sha256": "bd5b21ef36f374c19cf67c7c70544b3109ab9e55ab9c448147c96e849e973274"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.3824",
    "kind": "arxiv",
    "version": 1
  }
}