Pith Number

pith:U7EJZTFB

pith:2010:U7EJZTFBR32PMAGARPX2UC6RF5

not attested not anchored not stored refs pending

Splitting Line Patterns in Free Groups

Christopher H. Cashen

arxiv:1009.2492 v5 · 2010-09-13 · 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{U7EJZTFBR32PMAGARPX2UC6RF5}

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	2026-05-18T01:15:47.389312Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a7c89ccca18ef4f600c08befaa0bd12f5359823cecc2df01abd42636a12f1dfe

Aliases

arxiv: 1009.2492 · arxiv_version: 1009.2492v5 · doi: 10.48550/arxiv.1009.2492 · pith_short_12: U7EJZTFBR32P · pith_short_16: U7EJZTFBR32PMAGA · pith_short_8: U7EJZTFB

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/U7EJZTFBR32PMAGARPX2UC6RF5 \
  | 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: a7c89ccca18ef4f600c08befaa0bd12f5359823cecc2df01abd42636a12f1dfe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "97d942f846c44af1c102b8ca74673219fb842ba226ecdd91e7038417062043ac",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-09-13T19:46:17Z",
    "title_canon_sha256": "7232d99590bd8069bd685eb2191d221beeaedcc0467778e8d2c3ea5d5d388d32"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.2492",
    "kind": "arxiv",
    "version": 5
  }
}