Pith Number

pith:3GDDUS4I

pith:2018:3GDDUS4IE2YN6RHCQMHGN66GVY

not attested not anchored not stored refs pending

Pairs of Modules over a Principal Ideal Domain

Harald K. Wimmer, Pudji Astuti

arxiv:1804.00536 v1 · 2018-04-02 · math.AC · 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{3GDDUS4IE2YN6RHCQMHGN66GVY}

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	2026-05-18T00:19:36.754617Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d9863a4b8826b0df44e2830e66fbc6ae158d56dab50315c27d6ea252ea627fb9

Aliases

arxiv: 1804.00536 · arxiv_version: 1804.00536v1 · doi: 10.48550/arxiv.1804.00536 · pith_short_12: 3GDDUS4IE2YN · pith_short_16: 3GDDUS4IE2YN6RHC · pith_short_8: 3GDDUS4I

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/3GDDUS4IE2YN6RHCQMHGN66GVY \
  | 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: d9863a4b8826b0df44e2830e66fbc6ae158d56dab50315c27d6ea252ea627fb9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f63415da196d98dc06e3075b09f6ce84eddcab39a93b9d1cb519316349cebe73",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2018-04-02T14:18:05Z",
    "title_canon_sha256": "7848c08bc8cfbb2b236daaf97a094d9b23fed6778beff1183c6561a79ed8b708"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1804.00536",
    "kind": "arxiv",
    "version": 1
  }
}