Pith Number

pith:GV2ZWNAO

pith:2014:GV2ZWNAOTLUTL3JGPS5WAJC5LX

not attested not anchored not stored refs pending

The primitivity index function for a free group, and untangling closed curves on hyperbolic surfaces. With an appendix by Khalid Bou-Rabee

Ilya Kapovich, Neha Gupta

arxiv:1411.5523 v4 · 2014-11-20 · math.GR · math.DG · 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{GV2ZWNAOTLUTL3JGPS5WAJC5LX}

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	2026-05-18T00:35:52.017067Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

35759b340e9ae935ed267cbb60245d5dc19a514e6e9f3d5c0b20c170425a679c

Aliases

arxiv: 1411.5523 · arxiv_version: 1411.5523v4 · doi: 10.48550/arxiv.1411.5523 · pith_short_12: GV2ZWNAOTLUT · pith_short_16: GV2ZWNAOTLUTL3JG · pith_short_8: GV2ZWNAO

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/GV2ZWNAOTLUTL3JGPS5WAJC5LX \
  | 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: 35759b340e9ae935ed267cbb60245d5dc19a514e6e9f3d5c0b20c170425a679c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d1ae924998600858ca92b7fa73553b408495e55813e9eed6ce87cdba0ca932e8",
    "cross_cats_sorted": [
      "math.DG",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-11-20T12:32:14Z",
    "title_canon_sha256": "eee941c37fa90de9890569a44a62741e149003761a571894d3cc0ffe060548ee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1411.5523",
    "kind": "arxiv",
    "version": 4
  }
}