Pith Number

pith:RGFQA4HT

pith:2010:RGFQA4HTD4IDI7CMJNE332Q6VB

not attested not anchored not stored refs pending

On the Makar-Limanov, Derksen invariants, and finite automorphism groups of algebraic varieties

Vladimir L. Popov

arxiv:1001.1311 v3 · 2010-01-08 · 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{RGFQA4HTD4IDI7CMJNE332Q6VB}

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	2026-05-18T04:10:23.849099Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

898b0070f31f10347c4c4b49bdea1ea851ec0129a5b1d309bab7c16b41580ba5

Aliases

arxiv: 1001.1311 · arxiv_version: 1001.1311v3 · doi: 10.48550/arxiv.1001.1311 · pith_short_12: RGFQA4HTD4ID · pith_short_16: RGFQA4HTD4IDI7CM · pith_short_8: RGFQA4HT

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/RGFQA4HTD4IDI7CMJNE332Q6VB \
  | 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: 898b0070f31f10347c4c4b49bdea1ea851ec0129a5b1d309bab7c16b41580ba5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "727596993809e94c8f7839d4d86146e2ca39daef23b8b6a740b2c8db7f8ecf58",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-01-08T16:31:44Z",
    "title_canon_sha256": "8fd8579e69322a20c3ba03b1ad699be4db4c8c2924281e34354975ea95ac84aa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.1311",
    "kind": "arxiv",
    "version": 3
  }
}