Pith Number

pith:USAOHLKA

pith:2013:USAOHLKA76AHKWW4KV5MTYBZS5

not attested not anchored not stored refs pending

Ultracompanions of subsets of a group

I. Protasov, S. Slobodianiuk

arxiv:1308.1499 v1 · 2013-08-07 · math.GR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{USAOHLKA76AHKWW4KV5MTYBZS5}

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	2026-05-18T03:16:37.883953Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a480e3ad40ff80755adc557ac9e03997548f9731d0c035ff5ae3cb0cb469ca32

Aliases

arxiv: 1308.1499 · arxiv_version: 1308.1499v1 · doi: 10.48550/arxiv.1308.1499 · pith_short_12: USAOHLKA76AH · pith_short_16: USAOHLKA76AHKWW4 · pith_short_8: USAOHLKA

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/USAOHLKA76AHKWW4KV5MTYBZS5 \
  | 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: a480e3ad40ff80755adc557ac9e03997548f9731d0c035ff5ae3cb0cb469ca32

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d2db055ed5ad3be5616d500c614f2129427429dbe7c08744c5f57887899c4640",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-08-07T08:20:23Z",
    "title_canon_sha256": "9943391c235e2a297b3bdbb0adaf75712c6cdbdd99018038b7a8816ebc26c20a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.1499",
    "kind": "arxiv",
    "version": 1
  }
}