Pith Number

pith:GVK4UEYS

pith:2025:GVK4UEYSZSXRQ7MQZJ2XQ3N3KT

not attested not anchored not stored refs pending

Subgroups of a free group with every growth rate

Daniel T. Wise, Gal Yehuda, Michail Louvaris

arxiv:2505.10650 v1 · 2025-05-15 · 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{GVK4UEYSZSXRQ7MQZJ2XQ3N3KT}

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

On the growth spectrum of hyperbolic groups

Receipt and verification

First computed	2026-07-05T11:04:02.867800Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3555ca1312ccaf187d90ca75786dbb54dc643a8c1bafc0da601ae92f91a9aab6

Aliases

arxiv: 2505.10650 · arxiv_version: 2505.10650v1 · doi: 10.48550/arxiv.2505.10650 · pith_short_12: GVK4UEYSZSXR · pith_short_16: GVK4UEYSZSXRQ7MQ · pith_short_8: GVK4UEYS

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/GVK4UEYSZSXRQ7MQZJ2XQ3N3KT \
  | 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: 3555ca1312ccaf187d90ca75786dbb54dc643a8c1bafc0da601ae92f91a9aab6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "db804befab31226d982589fc6e80e05db3cc4da208d566e7f8c7cf2654c7345c",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2025-05-15T18:46:51Z",
    "title_canon_sha256": "d2cbe1d2909a68c6b44ea95f17800813d76b623658f1a5eacd298cb1c911ae28"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.10650",
    "kind": "arxiv",
    "version": 1
  }
}