Pith Number

pith:WLG2UIOQ

pith:2025:WLG2UIOQ5Z57VSNNYTPYXPEUAZ

not attested not anchored not stored refs pending

Characterizing hierarchically hyperbolic free by cyclic groups

Eliot Bongiovanni, Funda G\"ultepe, Mark Hagen, Pritam Ghosh

arxiv:2508.15738 v3 · 2025-08-21 · 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{WLG2UIOQ5Z57VSNNYTPYXPEUAZ}

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	2026-05-20T00:02:06.064390Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b2cdaa21d0ee7bfac9adc4df8bbc94064ed6d318d1acc4b61584f3a86227c803

Aliases

arxiv: 2508.15738 · arxiv_version: 2508.15738v3 · doi: 10.48550/arxiv.2508.15738 · pith_short_12: WLG2UIOQ5Z57 · pith_short_16: WLG2UIOQ5Z57VSNN · pith_short_8: WLG2UIOQ

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/WLG2UIOQ5Z57VSNNYTPYXPEUAZ \
  | 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: b2cdaa21d0ee7bfac9adc4df8bbc94064ed6d318d1acc4b61584f3a86227c803

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "01f9ce5b28aa87daf3bf63d4ae292c73038bea2d4fe1ba2107c1b33c91e8d4c7",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2025-08-21T17:28:16Z",
    "title_canon_sha256": "28cd36bdbb317357c858b1f246f72f917e692fe467e48c7fb3f344fc637944f2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.15738",
    "kind": "arxiv",
    "version": 3
  }
}