Pith Number

pith:MKDH74IV

pith:2011:MKDH74IVXI4ONUIXYE7DO4GCTC

not attested not anchored not stored refs pending

On equality of central and class preserving automorphisms of finite p-groups

Deepak Gumber, Hemant Kalra

arxiv:1106.0373 v7 · 2011-06-02 · 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{MKDH74IVXI4ONUIXYE7DO4GCTC}

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	2026-05-18T03:20:45.630460Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

62867ff115ba38e6d117c13e3770c298b710346901d6c29f218f7870ab7d905c

Aliases

arxiv: 1106.0373 · arxiv_version: 1106.0373v7 · doi: 10.48550/arxiv.1106.0373 · pith_short_12: MKDH74IVXI4O · pith_short_16: MKDH74IVXI4ONUIX · pith_short_8: MKDH74IV

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/MKDH74IVXI4ONUIXYE7DO4GCTC \
  | 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: 62867ff115ba38e6d117c13e3770c298b710346901d6c29f218f7870ab7d905c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c22e906f8fdf4dfdf3f35157e696c735e27b278087b5ceda326a910913d217d2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-06-02T06:55:15Z",
    "title_canon_sha256": "09e13ba54c94d4ab28c70b188c9a079c9701e78cad6d364fd756ef319cb3d9fe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.0373",
    "kind": "arxiv",
    "version": 7
  }
}