Pith Number

pith:CFJBCZWR

pith:2017:CFJBCZWRGHMPNNROBZGALGLJ53

not attested not anchored not stored refs pending

A Classification of Fundamental Group Elements Representing simple closed curves on the punctured Klein Bottle

Daniel Gomez

arxiv:1704.02601 v1 · 2017-04-09 · 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{CFJBCZWRGHMPNNROBZGALGLJ53}

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	2026-05-18T00:46:45.003259Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

11521166d131d8f6b62e0e4c059969eec15532c725deb923a9500466793c546b

Aliases

arxiv: 1704.02601 · arxiv_version: 1704.02601v1 · doi: 10.48550/arxiv.1704.02601 · pith_short_12: CFJBCZWRGHMP · pith_short_16: CFJBCZWRGHMPNNRO · pith_short_8: CFJBCZWR

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/CFJBCZWRGHMPNNROBZGALGLJ53 \
  | 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: 11521166d131d8f6b62e0e4c059969eec15532c725deb923a9500466793c546b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3a314263c50af98bb464379b18b95597a2a436ae2ea1d28b53cf528b231890c7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2017-04-09T13:28:48Z",
    "title_canon_sha256": "a6532424070de49fb01da4c584abc426e0332eae6a32358c627f76dc20517e68"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1704.02601",
    "kind": "arxiv",
    "version": 1
  }
}