Pith Number

pith:FLANXB2G

pith:2009:FLANXB2GTXVQZJG6OPBESDNFT2

not attested not anchored not stored refs pending

Growing words in the free group on two generators

Bobbe Cooper, Eric Rowland

arxiv:0909.0561 v2 · 2009-09-03 · 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{FLANXB2GTXVQZJG6OPBESDNFT2}

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	2026-05-18T03:29:28.156881Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2ac0db87469deb0ca4de73c2490da59ea7a0241087e6f602397226ab62aabadb

Aliases

arxiv: 0909.0561 · arxiv_version: 0909.0561v2 · doi: 10.48550/arxiv.0909.0561 · pith_short_12: FLANXB2GTXVQ · pith_short_16: FLANXB2GTXVQZJG6 · pith_short_8: FLANXB2G

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/FLANXB2GTXVQZJG6OPBESDNFT2 \
  | 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: 2ac0db87469deb0ca4de73c2490da59ea7a0241087e6f602397226ab62aabadb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9ea2cec08fcc588bf8059c7b1d48bbfa80a7290193cde18f4750020219cf94cf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-09-03T02:16:27Z",
    "title_canon_sha256": "7f27d6bbe2db63d522a872c41c9795d05bd7259001c0be04d50db88f6bb91e67"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.0561",
    "kind": "arxiv",
    "version": 2
  }
}