Pith Number

pith:BHEKR7IX

pith:2017:BHEKR7IXCF4WTVM6XY7WYWCKGB

not attested not anchored not stored refs pending

A translation of A.A.Vinogradov's "On the free product of ordered groups"

Arnaud Mortier, Victoria Lebed

arxiv:1703.05781 v1 · 2017-03-16 · 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{BHEKR7IXCF4WTVM6XY7WYWCKGB}

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	2026-05-18T00:48:32.120842Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

09c8a8fd17117969d59ebe3f6c584a305813970580bb81bf9e393df074f309b5

Aliases

arxiv: 1703.05781 · arxiv_version: 1703.05781v1 · doi: 10.48550/arxiv.1703.05781 · pith_short_12: BHEKR7IXCF4W · pith_short_16: BHEKR7IXCF4WTVM6 · pith_short_8: BHEKR7IX

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/BHEKR7IXCF4WTVM6XY7WYWCKGB \
  | 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: 09c8a8fd17117969d59ebe3f6c584a305813970580bb81bf9e393df074f309b5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5d7f1252fdb7004be087f2a4b9f92ea99212be7ac75ffceac72c38a4bf03c843",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2017-03-16T18:12:04Z",
    "title_canon_sha256": "29dc2e6af93c504e1c261ae874e9ca595d7e6497a55e1fb7ce7358b4a41fb766"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1703.05781",
    "kind": "arxiv",
    "version": 1
  }
}