Pith Number

pith:4Z6HXIEG

pith:2026:4Z6HXIEGFXYC7W3L36YHMFNNAW

not attested not anchored not stored refs pending

Growth gaps and exponential genericity in acylindrically hyperbolic groups

Lihuang Ding, Wenyuan Yang

arxiv:2607.25578 v1 · 2026-07-28 · math.GR · math.GT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4Z6HXIEGFXYC7W3L36YHMFNNAW}

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	2026-07-29T01:25:47.968097Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e67c7ba0862df02fdb6bdfb07615ad05bbf55c485bd60dd4a2c62f9bf2fd9d7a

Aliases

arxiv: 2607.25578 · arxiv_version: 2607.25578v1 · doi: 10.48550/arxiv.2607.25578 · pith_short_12: 4Z6HXIEGFXYC · pith_short_16: 4Z6HXIEGFXYC7W3L · pith_short_8: 4Z6HXIEG

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/4Z6HXIEGFXYC7W3L36YHMFNNAW \
  | 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: e67c7ba0862df02fdb6bdfb07615ad05bbf55c485bd60dd4a2c62f9bf2fd9d7a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "416e07a0ca21e764df77e0a4c779b05f86a6eda3a8989c2c9ad699effa879bb3",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2026-07-28T11:01:28Z",
    "title_canon_sha256": "b24666d413fb97356a99109c09bbee9ccd05750eadbf74c9412d3143c76e6b6f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.25578",
    "kind": "arxiv",
    "version": 1
  }
}