Pith Number

pith:A46PWVJ2

pith:2026:A46PWVJ225PEGAKQSM5BMXIWV2

not attested not anchored not stored refs pending

Average Distortion of Commensurators of Hyperbolic Groups

Mahan Mj, Nir Lazarovich, Suraj Krishna M S

arxiv:2606.27085 v1 · 2026-06-25 · 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{A46PWVJ225PEGAKQSM5BMXIWV2}

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	2026-06-26T01:16:09.029531Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

073cfb553ad75e430150933a165d16aeb9992d53f25d9269618010a7fb29a174

Aliases

arxiv: 2606.27085 · arxiv_version: 2606.27085v1 · doi: 10.48550/arxiv.2606.27085 · pith_short_12: A46PWVJ225PE · pith_short_16: A46PWVJ225PEGAKQ · pith_short_8: A46PWVJ2

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/A46PWVJ225PEGAKQSM5BMXIWV2 \
  | 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: 073cfb553ad75e430150933a165d16aeb9992d53f25d9269618010a7fb29a174

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "250f5b82097146629da5899e411c6b17cc7525ab2235b6e44dfa042295280d11",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2026-06-25T14:22:34Z",
    "title_canon_sha256": "133b202a32669537de4bd093bced6c371d6c8eae17beb21105bc94a8709efc23"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.27085",
    "kind": "arxiv",
    "version": 1
  }
}