Pith Number

pith:S34LK7PY

pith:2015:S34LK7PYREU2RPXQU7WKMDGMBX

not attested not anchored not stored refs pending

On growth of homology torsion in amenable groups

Aditi Kar, Nikolay Nikolov, Peter Kropholler

arxiv:1506.05373 v1 · 2015-06-17 · math.GR · math.AT · 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{S34LK7PYREU2RPXQU7WKMDGMBX}

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	2026-05-18T01:10:54.235964Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

96f8b57df88929a8bef0a7eca60ccc0dca8965443bc92341eb8dbd7d319ef87e

Aliases

arxiv: 1506.05373 · arxiv_version: 1506.05373v1 · doi: 10.48550/arxiv.1506.05373 · pith_short_12: S34LK7PYREU2 · pith_short_16: S34LK7PYREU2RPXQ · pith_short_8: S34LK7PY

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/S34LK7PYREU2RPXQU7WKMDGMBX \
  | 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: 96f8b57df88929a8bef0a7eca60ccc0dca8965443bc92341eb8dbd7d319ef87e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0d213052592dd27cd8f7add695efcbac88254f36ac95717fa8330af7cc12dac0",
    "cross_cats_sorted": [
      "math.AT",
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-06-17T15:53:33Z",
    "title_canon_sha256": "9a52f78790c7efb0862836b7dc5793f14d8c0aef615b1e0a523c4b5d45e34375"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.05373",
    "kind": "arxiv",
    "version": 1
  }
}