Pith Number

pith:WDCXH2CU

pith:2012:WDCXH2CUPGN6IYQZGJHHDFHUX6

not attested not anchored not stored refs pending

A weak Zassenhaus lemma for discrete subgroups of Diff(I)

Azer Akhmedov

arxiv:1211.1086 v2 · 2012-11-06 · math.GR · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WDCXH2CUPGN6IYQZGJHHDFHUX6}

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	2026-05-18T03:11:36.056145Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b0c573e854799be46219324e7194f4bf851d161e1dafbfc84d253faa42f86421

Aliases

arxiv: 1211.1086 · arxiv_version: 1211.1086v2 · doi: 10.48550/arxiv.1211.1086 · pith_short_12: WDCXH2CUPGN6 · pith_short_16: WDCXH2CUPGN6IYQZ · pith_short_8: WDCXH2CU

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/WDCXH2CUPGN6IYQZGJHHDFHUX6 \
  | 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: b0c573e854799be46219324e7194f4bf851d161e1dafbfc84d253faa42f86421

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "af7fd37e97384dd12a84e65269aaddee707db1e4be55d7e6d38bc701b6fd8364",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-11-06T01:41:13Z",
    "title_canon_sha256": "9b893911367ee32df4d613b1f1ee5164ee6cb0e7a4e57186776fde499714cfea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.1086",
    "kind": "arxiv",
    "version": 2
  }
}