Pith Number

pith:LGYJ4HBW

pith:2018:LGYJ4HBW4JYBZA54E73WASIRKB

not attested not anchored not stored refs pending

Rational series in the free group and the Connes operator

Aaron Lauve, Christophe Reutenauer

arxiv:1806.03540 v1 · 2018-06-09 · math.CO · 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{LGYJ4HBW4JYBZA54E73WASIRKB}

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	2026-05-18T00:13:43.089112Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

59b09e1c36e2701c83bc27f760491150646a95992fdc712ae0e7dbe87d915c89

Aliases

arxiv: 1806.03540 · arxiv_version: 1806.03540v1 · doi: 10.48550/arxiv.1806.03540 · pith_short_12: LGYJ4HBW4JYB · pith_short_16: LGYJ4HBW4JYBZA54 · pith_short_8: LGYJ4HBW

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/LGYJ4HBW4JYBZA54E73WASIRKB \
  | 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: 59b09e1c36e2701c83bc27f760491150646a95992fdc712ae0e7dbe87d915c89

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1e39261107de1158e3fa95a86289775b867a8fae2219793844560c29b3504d71",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-06-09T20:56:56Z",
    "title_canon_sha256": "9dc001efc21128f122584f1fa15919b57709362679850bf3c8b3f2eeb29a3763"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1806.03540",
    "kind": "arxiv",
    "version": 1
  }
}