Pith Number

pith:GTDYYYAE

pith:2015:GTDYYYAEOI5KKLDLVJAQFSP7OG

not attested not anchored not stored refs pending

Cusp and $b_1$ growth for ball quotients and maps onto $\mathbb{Z}$ with finitely generated kernel

Matthew Stover

arxiv:1506.06126 v3 · 2015-06-19 · math.GT · math.AG · math.GR · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GTDYYYAEOI5KKLDLVJAQFSP7OG}

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	2026-05-18T00:08:36.890167Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

34c78c6004723aa52c6baa4102c9ff71bb6308ca4dc82389693e307e791461fd

Aliases

arxiv: 1506.06126 · arxiv_version: 1506.06126v3 · doi: 10.48550/arxiv.1506.06126 · pith_short_12: GTDYYYAEOI5K · pith_short_16: GTDYYYAEOI5KKLDL · pith_short_8: GTDYYYAE

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/GTDYYYAEOI5KKLDLVJAQFSP7OG \
  | 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: 34c78c6004723aa52c6baa4102c9ff71bb6308ca4dc82389693e307e791461fd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9d18ff551e4d1be2dbabbd875268de690b4de1e4982c24b7cda91e73c0cf101c",
    "cross_cats_sorted": [
      "math.AG",
      "math.GR",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2015-06-19T19:55:30Z",
    "title_canon_sha256": "6e6d481e18559317cf64c921e8ba8a1ef7e8779674fdf7e0845d0c3ef0c27c39"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.06126",
    "kind": "arxiv",
    "version": 3
  }
}