Pith Number

pith:QB26IO2W

pith:2019:QB26IO2WMJ5OQ6EDO7LWBIEMND

not attested not anchored not stored refs pending

Some groups with planar boundaries

Genevieve S. Walsh, Sang-hyun Kim

arxiv:1907.06898 v1 · 2019-07-16 · math.GT · 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{QB26IO2WMJ5OQ6EDO7LWBIEMND}

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	2026-05-17T23:40:28.755530Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8075e43b56627ae8788377d760a08c68f821f8024a4f9ce1250ca30fc82a2bb9

Aliases

arxiv: 1907.06898 · arxiv_version: 1907.06898v1 · doi: 10.48550/arxiv.1907.06898 · pith_short_12: QB26IO2WMJ5O · pith_short_16: QB26IO2WMJ5OQ6ED · pith_short_8: QB26IO2W

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/QB26IO2WMJ5OQ6EDO7LWBIEMND \
  | 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: 8075e43b56627ae8788377d760a08c68f821f8024a4f9ce1250ca30fc82a2bb9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "72e02571de819c87449f25efdf8eb0e0c2d38ae768a99ad5ea31d837b094e755",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2019-07-16T09:06:29Z",
    "title_canon_sha256": "ea4ba3f082337321128221ff97b7e0e353b7eddf8e51aaa4d4b60e3f6d5d5fb1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.06898",
    "kind": "arxiv",
    "version": 1
  }
}