Pith Number

pith:R57DVF6N

pith:2010:R57DVF6NM43WBORBLLZ7IXVDBY

not attested not anchored not stored refs pending

Group covers, o-minimality, and categoricity

Alessandro Berarducci, Anand Pillay, Ya'acov Peterzil

arxiv:1009.5097 v1 · 2010-09-26 · math.LO · 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{R57DVF6NM43WBORBLLZ7IXVDBY}

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	2026-05-18T04:40:19.192670Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8f7e3a97cd673760ba215af3f45ea30e219064ac9ba994041414d3822a7a2887

Aliases

arxiv: 1009.5097 · arxiv_version: 1009.5097v1 · doi: 10.48550/arxiv.1009.5097 · pith_short_12: R57DVF6NM43W · pith_short_16: R57DVF6NM43WBORB · pith_short_8: R57DVF6N

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/R57DVF6NM43WBORBLLZ7IXVDBY \
  | 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: 8f7e3a97cd673760ba215af3f45ea30e219064ac9ba994041414d3822a7a2887

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "31076ad443b6c757d017385964b3be35706bcbaf5459d8085f3a3f6e034c5f7d",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2010-09-26T14:26:33Z",
    "title_canon_sha256": "63195f86e494543063287f2f281aafc9615156359a43a3c7d6d8eb103590bdbd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.5097",
    "kind": "arxiv",
    "version": 1
  }
}