Pith Number

pith:D3JBGRAG

pith:2017:D3JBGRAGCEV7HRVC6VX5O5AIYT

not attested not anchored not stored refs pending

On the residual and profinite closures of commensurated subgroups

Colin D. Reid, Peter H. Kropholler, Phillip Wesolek, Pierre-Emmanuel Caprace

arxiv:1706.06853 v3 · 2017-06-21 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{D3JBGRAGCEV7HRVC6VX5O5AIYT}

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	2026-05-17T23:41:37.384342Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1ed2134406112bf3c6a2f56fd77408c4d87165095831a8a3bc0abe0c512360da

Aliases

arxiv: 1706.06853 · arxiv_version: 1706.06853v3 · doi: 10.48550/arxiv.1706.06853 · pith_short_12: D3JBGRAGCEV7 · pith_short_16: D3JBGRAGCEV7HRVC · pith_short_8: D3JBGRAG

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/D3JBGRAGCEV7HRVC6VX5O5AIYT \
  | 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: 1ed2134406112bf3c6a2f56fd77408c4d87165095831a8a3bc0abe0c512360da

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "061fea12b6a36adf7af081bf5e142e30da82c2f9e3dd231ddc9d82b09f0bd57e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2017-06-21T12:20:32Z",
    "title_canon_sha256": "d822f3487735aafaf44d14949f4724f5a78dcff41d9068959f245698e7ec32e9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1706.06853",
    "kind": "arxiv",
    "version": 3
  }
}