Pith Number

pith:JM4G4VV5

pith:2013:JM4G4VV5NQ4SILXOB645WCKXL2

not attested not anchored not stored refs pending

On the growth of torsion in the cohomology of arithmetic groups

Jonathan Pfaff, Werner Mueller

arxiv:1302.0742 v1 · 2013-02-04 · 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{JM4G4VV5NQ4SILXOB645WCKXL2}

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	2026-05-18T03:34:36.455862Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4b386e56bd6c39242eee0fb9db09575e9589fa57c70c1b501f02c4d73b73cd6a

Aliases

arxiv: 1302.0742 · arxiv_version: 1302.0742v1 · doi: 10.48550/arxiv.1302.0742 · pith_short_12: JM4G4VV5NQ4S · pith_short_16: JM4G4VV5NQ4SILXO · pith_short_8: JM4G4VV5

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/JM4G4VV5NQ4SILXOB645WCKXL2 \
  | 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: 4b386e56bd6c39242eee0fb9db09575e9589fa57c70c1b501f02c4d73b73cd6a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "33c98c92964f7bd59ce6fc5bb0ff52e8670ccb7019c5a9516975956efc833bac",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-02-04T16:13:42Z",
    "title_canon_sha256": "19cb6961b4bf86a6cce28ce3fbad7b62edd113e60c5ef98f73cd8d7bd3c01673"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.0742",
    "kind": "arxiv",
    "version": 1
  }
}