Pith Number

pith:HJFAQUEH

pith:2017:HJFAQUEHK5CYLJKEVCLCUY7TAJ

not attested not anchored not stored refs pending

Free subgroups of free products and combinatorial hypermaps

Alexander Kolpakov, Laura Ciobanu

arxiv:1708.03842 v4 · 2017-08-13 · math.CO · math.GR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HJFAQUEHK5CYLJKEVCLCUY7TAJ}

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	2026-05-17T23:54:16.917945Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3a4a085087574585a544a8962a63f30263298969d869016f780da0e13bbcf4cd

Aliases

arxiv: 1708.03842 · arxiv_version: 1708.03842v4 · doi: 10.48550/arxiv.1708.03842 · pith_short_12: HJFAQUEHK5CY · pith_short_16: HJFAQUEHK5CYLJKE · pith_short_8: HJFAQUEH

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/HJFAQUEHK5CYLJKEVCLCUY7TAJ \
  | 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: 3a4a085087574585a544a8962a63f30263298969d869016f780da0e13bbcf4cd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9860965f8424a2b642aec37eb2aa21aa5698a9024749a941af2f4d777a341e7c",
    "cross_cats_sorted": [
      "math.GR",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-08-13T02:55:56Z",
    "title_canon_sha256": "180043918c26fb309429689e8a6f83b09c1387acea6f1c590508a23ed6dc0889"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1708.03842",
    "kind": "arxiv",
    "version": 4
  }
}