Pith Number

pith:U22S5CG3

pith:2014:U22S5CG3UHZAEFMRQBQGCOPR4F

not attested not anchored not stored refs pending

Second Countable Virtually Free Pro-p Groups whose Torsion Elements have Finite Centralizer

John MacQuarrie, Pavel Zalesskii

arxiv:1408.2235 v1 · 2014-08-10 · 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{U22S5CG3UHZAEFMRQBQGCOPR4F}

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	2026-05-18T02:45:29.958405Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a6b52e88dba1f202159180606139f1e157dabe6e0dc240f42817bd46af8f119e

Aliases

arxiv: 1408.2235 · arxiv_version: 1408.2235v1 · doi: 10.48550/arxiv.1408.2235 · pith_short_12: U22S5CG3UHZA · pith_short_16: U22S5CG3UHZAEFMR · pith_short_8: U22S5CG3

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/U22S5CG3UHZAEFMRQBQGCOPR4F \
  | 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: a6b52e88dba1f202159180606139f1e157dabe6e0dc240f42817bd46af8f119e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7648130eec649a22f2e238213545fb35272f29a5e1684a87ad5d5d10016bbd15",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-08-10T14:52:31Z",
    "title_canon_sha256": "4dc31e178c7ce00397da63629668d1f10e754409d6f639da08915aefcfe31642"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1408.2235",
    "kind": "arxiv",
    "version": 1
  }
}