Pith Number

pith:SNZDRZO3

pith:2016:SNZDRZO3QJXINAM7WYUSMSPQII

not attested not anchored not stored refs pending

On the growth of torsion in the cohomology of arithmetic groups

Avner Ash, Dan Yasaki, Mark McConnell, Paul E. Gunnells

arxiv:1608.05858 v1 · 2016-08-20 · 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{SNZDRZO3QJXINAM7WYUSMSPQII}

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	2026-05-18T01:08:22.958860Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

937238e5db826e86819fb6292649f0421e57d77e347b90c5cc92a5926510724b

Aliases

arxiv: 1608.05858 · arxiv_version: 1608.05858v1 · doi: 10.48550/arxiv.1608.05858 · pith_short_12: SNZDRZO3QJXI · pith_short_16: SNZDRZO3QJXINAM7 · pith_short_8: SNZDRZO3

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/SNZDRZO3QJXINAM7WYUSMSPQII \
  | 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: 937238e5db826e86819fb6292649f0421e57d77e347b90c5cc92a5926510724b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "815236c7fa74c89970de4bb1ed8f26fd1bd043c39ede8bfcd9bd1676d97e8869",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-08-20T18:31:09Z",
    "title_canon_sha256": "19cb6961b4bf86a6cce28ce3fbad7b62edd113e60c5ef98f73cd8d7bd3c01673"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.05858",
    "kind": "arxiv",
    "version": 1
  }
}