Pith Number

pith:HMGDDHA5

pith:2014:HMGDDHA5U4W2FFDSRDBJEULAQ5

not attested not anchored not stored refs pending

Growth of homology torsion in finite coverings and hyperbolic volume

Thang Le

arxiv:1412.7758 v3 · 2014-12-24 · 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{HMGDDHA5U4W2FFDSRDBJEULAQ5}

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	2026-05-18T00:40:19.868717Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3b0c319c1da72da2947288c2925160874a71283c6d53d8bc3f99413e2904af00

Aliases

arxiv: 1412.7758 · arxiv_version: 1412.7758v3 · doi: 10.48550/arxiv.1412.7758 · pith_short_12: HMGDDHA5U4W2 · pith_short_16: HMGDDHA5U4W2FFDS · pith_short_8: HMGDDHA5

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/HMGDDHA5U4W2FFDSRDBJEULAQ5 \
  | 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: 3b0c319c1da72da2947288c2925160874a71283c6d53d8bc3f99413e2904af00

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "177cd046edc518db29762a5f90e825d7ccc93e437548863b2c168f7d68686e12",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2014-12-24T21:01:07Z",
    "title_canon_sha256": "07999dd302196298586a66c36bf55e5ea673eda248c853b8a863d59e7d1a65d7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.7758",
    "kind": "arxiv",
    "version": 3
  }
}