Pith Number

pith:S7662SP6

pith:2010:S7662SP6WWKQROKFVKWLOBK5OZ

not attested not anchored not stored refs pending

Automorphism towers and automorphism groups of fields without Choice

Itay Kaplan, Saharon Shelah

arxiv:1004.1810 v5 · 2010-04-11 · 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{S7662SP6WWKQROKFVKWLOBK5OZ}

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	2026-05-18T04:08:12.700006Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

97fded49feb59508b945aaacb7055d76664ad77d652a89cdfc7ad898cda12e1a

Aliases

arxiv: 1004.1810 · arxiv_version: 1004.1810v5 · doi: 10.48550/arxiv.1004.1810 · pith_short_12: S7662SP6WWKQ · pith_short_16: S7662SP6WWKQROKF · pith_short_8: S7662SP6

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/S7662SP6WWKQROKFVKWLOBK5OZ \
  | 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: 97fded49feb59508b945aaacb7055d76664ad77d652a89cdfc7ad898cda12e1a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c296ed50da72ae0db0fcaab1c26b855b7ec994f727e46a053e910678fd93766d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2010-04-11T14:14:34Z",
    "title_canon_sha256": "e6644600df32afbfbd0cf52c6099f38d9b0267ead536e83acddb14d085a2173a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.1810",
    "kind": "arxiv",
    "version": 5
  }
}