Pith Number

pith:J6CJX3HL

pith:2016:J6CJX3HLZ2JQDXP4JD7O4KLTT3

not attested not anchored not stored refs pending

Stable groups and expansions of $(\mathbb{Z},+,0)$

Anand Pillay, Gabriel Conant

arxiv:1601.05692 v3 · 2016-01-21 · 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{J6CJX3HLZ2JQDXP4JD7O4KLTT3}

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

Trace definability I: preservation and characterizations

Receipt and verification

First computed	2026-05-18T00:06:06.589115Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4f849becebce9301ddfc48feee29739ef3de6bc7fb87d1fab47eb1e1f2904810

Aliases

arxiv: 1601.05692 · arxiv_version: 1601.05692v3 · doi: 10.48550/arxiv.1601.05692 · pith_short_12: J6CJX3HLZ2JQ · pith_short_16: J6CJX3HLZ2JQDXP4 · pith_short_8: J6CJX3HL

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/J6CJX3HLZ2JQDXP4JD7O4KLTT3 \
  | 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: 4f849becebce9301ddfc48feee29739ef3de6bc7fb87d1fab47eb1e1f2904810

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c37c7d5474bc32df7ac8e271b981dc53c483e7d4676162c705be09b3cda4d3b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2016-01-21T16:08:01Z",
    "title_canon_sha256": "3a60c6e12684270a1473d5ed7439b80c12d1dacd0f066d80009f3abbda7e2178"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.05692",
    "kind": "arxiv",
    "version": 3
  }
}