Pith Number

pith:NUYDR6NP

pith:2023:NUYDR6NPL2QCF2YVOS66U2EJ65

not attested not anchored not stored refs pending

Uniform exponential growth for groups with proper product actions on hyperbolic spaces

Renxing Wan, Wenyuan Yang

arxiv:2307.08400 v3 · 2023-07-17 · 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{NUYDR6NPL2QCF2YVOS66U2EJ65}

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.

Cited by

1 paper in Pith

Short positive loxodromics in graph products

Receipt and verification

First computed	2026-07-05T08:46:51.137373Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6d3038f9af5ea022eb1574bdea6889f75f7be8f73ed7499ad48e5227ed4c7a2b

Aliases

arxiv: 2307.08400 · arxiv_version: 2307.08400v3 · doi: 10.48550/arxiv.2307.08400 · pith_short_12: NUYDR6NPL2QC · pith_short_16: NUYDR6NPL2QCF2YV · pith_short_8: NUYDR6NP

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/NUYDR6NPL2QCF2YVOS66U2EJ65 \
  | 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: 6d3038f9af5ea022eb1574bdea6889f75f7be8f73ed7499ad48e5227ed4c7a2b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a65b421dea81cb2034d005905cf1e1a4a734b78d4c40966dda03cfde7b46a422",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2023-07-17T11:33:52Z",
    "title_canon_sha256": "931eff5feac84f015ce628a1103be93317d01c9659e7b36a5539d0ddfb17d42f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2307.08400",
    "kind": "arxiv",
    "version": 3
  }
}