Pith Number

pith:X3B2KWDY

pith:2016:X3B2KWDYXSHPWT25TBSL3I2DSV

not attested not anchored not stored refs pending

On the flatness and the projectivity over Hopf subalgebras of Hopf algebras over discrete valuation rings

Nguyen Dai Duong, Nguyen Huy Hung, Phung Ho Hai

arxiv:1601.00748 v3 · 2016-01-05 · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{X3B2KWDYXSHPWT25TBSL3I2DSV}

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	2026-05-18T00:43:21.232498Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bec3a55878bc8efb4f5d9864bda343957d4a998e5d6359d3a2186411b280b11d

Aliases

arxiv: 1601.00748 · arxiv_version: 1601.00748v3 · doi: 10.48550/arxiv.1601.00748 · pith_short_12: X3B2KWDYXSHP · pith_short_16: X3B2KWDYXSHPWT25 · pith_short_8: X3B2KWDY

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/X3B2KWDYXSHPWT25TBSL3I2DSV \
  | 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: bec3a55878bc8efb4f5d9864bda343957d4a998e5d6359d3a2186411b280b11d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e375b25073f510844b1d368fc393d306d5b21764ae3200bacad74470bcdc4a7c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2016-01-05T06:52:06Z",
    "title_canon_sha256": "90a9d63114bbfe99e64b0e58853402ba6455520f76a71deb778b06bb69f2ccfc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.00748",
    "kind": "arxiv",
    "version": 3
  }
}