Pith Number

pith:G7AERS23

pith:2016:G7AERS23LRNP275EW2YAV2QOIU

not attested not anchored not stored refs pending

The topology and geometry of automorphism groups of free groups

Karen Vogtmann

arxiv:1610.08545 v1 · 2016-10-26 · 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{G7AERS23LRNP275EW2YAV2QOIU}

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	2026-05-18T01:01:07.894893Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

37c048cb5b5c5afd7fa4b6b00aea0e450d1485b82af64858e3713447ad013a71

Aliases

arxiv: 1610.08545 · arxiv_version: 1610.08545v1 · doi: 10.48550/arxiv.1610.08545 · pith_short_12: G7AERS23LRNP · pith_short_16: G7AERS23LRNP275E · pith_short_8: G7AERS23

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/G7AERS23LRNP275EW2YAV2QOIU \
  | 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: 37c048cb5b5c5afd7fa4b6b00aea0e450d1485b82af64858e3713447ad013a71

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e323143a16b652496642e796da995e3b2a3d43df26b07eb544b3071c971ebddf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-10-26T20:44:25Z",
    "title_canon_sha256": "21aa01b307c94ad8cf6967430e29b9fd1685aba47f2f8ea0fe1904b36669da72"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.08545",
    "kind": "arxiv",
    "version": 1
  }
}