Pith Number

pith:L5UNNC54

pith:2015:L5UNNC54AXJYZ2JXHW3LPP7EVB

not attested not anchored not stored refs pending

Decompositions of modules lacking zero sums

Louis Rowen, Manfred Knebusch, Zur Izhakian

arxiv:1511.04041 v2 · 2015-11-12 · math.RA · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{L5UNNC54AXJYZ2JXHW3LPP7EVB}

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	2026-05-18T01:25:17.666548Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5f68d68bbc05d38ce9373db6b7bfe4a8528a0bbe62534dac94ff98126023fdbf

Aliases

arxiv: 1511.04041 · arxiv_version: 1511.04041v2 · doi: 10.48550/arxiv.1511.04041 · pith_short_12: L5UNNC54AXJY · pith_short_16: L5UNNC54AXJYZ2JX · pith_short_8: L5UNNC54

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/L5UNNC54AXJYZ2JXHW3LPP7EVB \
  | 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: 5f68d68bbc05d38ce9373db6b7bfe4a8528a0bbe62534dac94ff98126023fdbf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "69499ab66b79704a7e92a9eaa5944527e42a2661df6484adb345a15f7bccf3ea",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2015-11-12T20:07:55Z",
    "title_canon_sha256": "471e50eb683f221f08c62dc325645a6f8cd6843760630f5f680a62f85213cf85"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.04041",
    "kind": "arxiv",
    "version": 2
  }
}