Pith Number

pith:SPUUTAAH

pith:2016:SPUUTAAHQLG5HR3OLKI6HEZ22A

not attested not anchored not stored refs pending

Intersecting free subgroups in free products of left ordered groups

Sergei V. Ivanov

arxiv:1607.03010 v1 · 2016-07-11 · 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{SPUUTAAHQLG5HR3OLKI6HEZ22A}

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	2026-05-18T01:11:14.189160Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

93e949800782cdd3c76e5a91e3933ad016c7b9566e9cb9f5230f734ca01e5a86

Aliases

arxiv: 1607.03010 · arxiv_version: 1607.03010v1 · doi: 10.48550/arxiv.1607.03010 · pith_short_12: SPUUTAAHQLG5 · pith_short_16: SPUUTAAHQLG5HR3O · pith_short_8: SPUUTAAH

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/SPUUTAAHQLG5HR3OLKI6HEZ22A \
  | 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: 93e949800782cdd3c76e5a91e3933ad016c7b9566e9cb9f5230f734ca01e5a86

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c24e75ccd61758918e7d9a33081c8475eff6e3dc511b3061f4ceabe58328018d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-07-11T16:04:32Z",
    "title_canon_sha256": "bfdb94ab528e93c89ac933e65e6c9315ec58a7b4b52adc7fc0887e337727e14c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.03010",
    "kind": "arxiv",
    "version": 1
  }
}