Pith Number

pith:F5PKAODX

pith:2011:F5PKAODX6R5Z2EGUI2GAWAEASH

not attested not anchored not stored refs pending

Strict Gr-categories and applications on classification of extensions of groups of the type of a crossed module

Nguyen Thu Thuy, Nguyen Tien Quang, Pham Thi Cuc

arxiv:1112.2440 v1 · 2011-12-12 · math.CT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{F5PKAODX6R5Z2EGUI2GAWAEASH}

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	2026-05-18T04:06:34.393148Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f5ea03877f47b9d10d4468c0b008091eaaf01c496400c23afca63e402b5df27

Aliases

arxiv: 1112.2440 · arxiv_version: 1112.2440v1 · doi: 10.48550/arxiv.1112.2440 · pith_short_12: F5PKAODX6R5Z · pith_short_16: F5PKAODX6R5Z2EGU · pith_short_8: F5PKAODX

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/F5PKAODX6R5Z2EGUI2GAWAEASH \
  | 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: 2f5ea03877f47b9d10d4468c0b008091eaaf01c496400c23afca63e402b5df27

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "89abf3608100ab1b602288d7db868dcfd03c2fc895f93c96eb7de32470901e15",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2011-12-12T04:49:37Z",
    "title_canon_sha256": "8472401f04bf6834d46e4a45c40879b31cda08e1f716495b690990278ee9a2a5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.2440",
    "kind": "arxiv",
    "version": 1
  }
}