Pith Number

pith:OJC36FSH

pith:2016:OJC36FSHFYSVUQ3A2NSGIME2D4

not attested not anchored not stored refs pending

On commensurability of right-angled Artin groups I: RAAGs defined by trees of diameter 4

Alexander Zakharov, Ilya Kazachkov, Montserrat Casals-Ruiz

arxiv:1611.01741 v2 · 2016-11-06 · 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{OJC36FSHFYSVUQ3A2NSGIME2D4}

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	2026-05-18T00:19:59.355129Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7245bf16472e255a4360d36464309a1f2e22e7f4d71ef3ba45abd20135163880

Aliases

arxiv: 1611.01741 · arxiv_version: 1611.01741v2 · doi: 10.48550/arxiv.1611.01741 · pith_short_12: OJC36FSHFYSV · pith_short_16: OJC36FSHFYSVUQ3A · pith_short_8: OJC36FSH

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/OJC36FSHFYSVUQ3A2NSGIME2D4 \
  | 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: 7245bf16472e255a4360d36464309a1f2e22e7f4d71ef3ba45abd20135163880

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ee0290c991c3cbd14cd68df0b58899aa84a30b56a5e1bd08b321f8bfb7b8013c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-11-06T08:25:27Z",
    "title_canon_sha256": "2220a765788b845048ced9e297c1d6cec8a1269ae341582b02e1494a705b8748"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.01741",
    "kind": "arxiv",
    "version": 2
  }
}