Pith Number

pith:QZ7LLU4C

pith:2016:QZ7LLU4CM4YVBMIS6DYDXENDGO

not attested not anchored not stored refs pending

Vastness properties of automorphism groups of RAAGs

Andrew Sale, Vincent Guirardel

arxiv:1609.04854 v2 · 2016-09-15 · 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{QZ7LLU4CM4YVBMIS6DYDXENDGO}

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	2026-05-18T00:24:53.234784Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

867eb5d382673150b112f0f03b91a33392a8cddad994c306324856823680c8b8

Aliases

arxiv: 1609.04854 · arxiv_version: 1609.04854v2 · doi: 10.48550/arxiv.1609.04854 · pith_short_12: QZ7LLU4CM4YV · pith_short_16: QZ7LLU4CM4YVBMIS · pith_short_8: QZ7LLU4C

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/QZ7LLU4CM4YVBMIS6DYDXENDGO \
  | 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: 867eb5d382673150b112f0f03b91a33392a8cddad994c306324856823680c8b8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2bd55aaa14d2c2d0ce4cc4735c57cc9b40250534945f2146e060bfb6df222fc4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-09-15T20:40:32Z",
    "title_canon_sha256": "b307d70805b0013dbc46683df67acec89f8859db9209bae6c9b77faca6862261"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.04854",
    "kind": "arxiv",
    "version": 2
  }
}