Pith Number

pith:CJS4T2FY

pith:2010:CJS4T2FYD77EFBSLII5ZJPQXUE

not attested not anchored not stored refs pending

Homology torsion growth and Mahler measure

Thang Le

arxiv:1010.4199 v3 · 2010-10-20 · math.GT · math.DS · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CJS4T2FYD77EFBSLII5ZJPQXUE}

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	2026-05-18T03:40:51.661249Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1265c9e8b81ffe42864b423b94be17a12070b3a03e16a79fb25dd03a430895fb

Aliases

arxiv: 1010.4199 · arxiv_version: 1010.4199v3 · doi: 10.48550/arxiv.1010.4199 · pith_short_12: CJS4T2FYD77E · pith_short_16: CJS4T2FYD77EFBSL · pith_short_8: CJS4T2FY

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/CJS4T2FYD77EFBSLII5ZJPQXUE \
  | 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: 1265c9e8b81ffe42864b423b94be17a12070b3a03e16a79fb25dd03a430895fb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a7d3fd3d92262df97839625d52b2cfd4da9869c5c0bf1d302f9441b7253d0930",
    "cross_cats_sorted": [
      "math.DS",
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2010-10-20T13:39:36Z",
    "title_canon_sha256": "a2dbfb41698318ac516a8b6a32c9bda21ca6e638e79654fe73d30b48dc68fe1d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.4199",
    "kind": "arxiv",
    "version": 3
  }
}