Pith Number

pith:IXLD4X77

pith:2011:IXLD4X77AZ2LFLIJLFUXKPBMR3

not attested not anchored not stored refs pending

Definable quotients of locally definable groups

Pantelis Eleftheriou, Ya'acov Peterzil

arxiv:1103.4770 v4 · 2011-03-24 · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IXLD4X77AZ2LFLIJLFUXKPBMR3}

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	2026-05-18T04:01:26.351725Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

45d63e5fff0674b2ad095969753c2c8ece2946dc3227ebd184eb0c1f9da44585

Aliases

arxiv: 1103.4770 · arxiv_version: 1103.4770v4 · doi: 10.48550/arxiv.1103.4770 · pith_short_12: IXLD4X77AZ2L · pith_short_16: IXLD4X77AZ2LFLIJ · pith_short_8: IXLD4X77

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/IXLD4X77AZ2LFLIJLFUXKPBMR3 \
  | 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: 45d63e5fff0674b2ad095969753c2c8ece2946dc3227ebd184eb0c1f9da44585

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5bf37f4a5b6f78ceb69d85b8ff6488da77688a4c0215fbdb3508db5a65dd15f5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2011-03-24T14:08:37Z",
    "title_canon_sha256": "3034a78cb59bb84e2e32508feab490d496ab513c2f4cfe673881c37ac24ad050"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.4770",
    "kind": "arxiv",
    "version": 4
  }
}