Pith Number

pith:DHFIK23C

pith:2012:DHFIK23CRCU5RLJJW324GQ67IS

not attested not anchored not stored refs pending

Effective embedding of residually hyperbolic groups into direct products of extensions of centralizers

Jeremy Macdonald, Olga Kharlampovich

arxiv:1202.3835 v2 · 2012-02-17 · 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{DHFIK23CRCU5RLJJW324GQ67IS}

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	2026-05-18T03:34:03.376784Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

19ca856b6288a9d8ad29b6f5c343df44a7a995b1fbd54db1b82cdb37fbc11ebd

Aliases

arxiv: 1202.3835 · arxiv_version: 1202.3835v2 · doi: 10.48550/arxiv.1202.3835 · pith_short_12: DHFIK23CRCU5 · pith_short_16: DHFIK23CRCU5RLJJ · pith_short_8: DHFIK23C

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/DHFIK23CRCU5RLJJW324GQ67IS \
  | 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: 19ca856b6288a9d8ad29b6f5c343df44a7a995b1fbd54db1b82cdb37fbc11ebd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "105e9bcef06f8a59c71aea68b82709eee789f521ca141ede7170275349c0da16",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-02-17T03:40:17Z",
    "title_canon_sha256": "7f761dbbbc0346cb0916a299bf54ce0cb89d47d4712f74bf871bd2047ac750ed"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.3835",
    "kind": "arxiv",
    "version": 2
  }
}