Pith Number

pith:VQXXUOJN

pith:2008:VQXXUOJNZW75UAU7S6F2EE2R5O

not attested not anchored not stored refs pending

Automorphic orbits in free groups: words versus subgroups

Pascal Weil (LaBRI), Pedro Silva (CMUP)

arxiv:0809.4386 v3 · 2008-09-25 · 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{VQXXUOJNZW75UAU7S6F2EE2R5O}

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	2026-05-18T00:17:46.780397Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac2f7a392dcdbfda029f978ba21351ebbfbaf5e8d22bcdd21d61fa1317af75ba

Aliases

arxiv: 0809.4386 · arxiv_version: 0809.4386v3 · doi: 10.48550/arxiv.0809.4386 · pith_short_12: VQXXUOJNZW75 · pith_short_16: VQXXUOJNZW75UAU7 · pith_short_8: VQXXUOJN

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/VQXXUOJNZW75UAU7S6F2EE2R5O \
  | 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: ac2f7a392dcdbfda029f978ba21351ebbfbaf5e8d22bcdd21d61fa1317af75ba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b8330360c69573454d056abb35d51934b473625f2324d6f6fef0b34e9222611e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2008-09-25T11:55:52Z",
    "title_canon_sha256": "65d47ece58d42d57ae9bb5aaa6589b4e23842696fa20a1389301dd7778fe3142"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0809.4386",
    "kind": "arxiv",
    "version": 3
  }
}