Pith Number

pith:ZKYR5Z5V

pith:2019:ZKYR5Z5V64JNWZ4ERS2CXCGS4Z

not attested not anchored not stored refs pending

Sum-Essential Graphs of Modules

Ali Majidinya, Jerzy Matczuk

arxiv:1908.05921 v1 · 2019-08-16 · math.RA · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZKYR5Z5V64JNWZ4ERS2CXCGS4Z}

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	2026-07-04T23:57:54.443130Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cab11ee7b5f712db67848cb42b88d2e654d2032bb030d2e5b88e9c2c4b2c7c8a

Aliases

arxiv: 1908.05921 · arxiv_version: 1908.05921v1 · doi: 10.48550/arxiv.1908.05921 · pith_short_12: ZKYR5Z5V64JN · pith_short_16: ZKYR5Z5V64JNWZ4E · pith_short_8: ZKYR5Z5V

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/ZKYR5Z5V64JNWZ4ERS2CXCGS4Z \
  | 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: cab11ee7b5f712db67848cb42b88d2e654d2032bb030d2e5b88e9c2c4b2c7c8a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ed5252f7d6edab327a7fd63eed9317644ba7870f90dea87071b89a3546436441",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2019-08-16T10:22:17Z",
    "title_canon_sha256": "7a4e3381c868e1095bb661d9468e8b97b798447bf495aa92fe93601f274d5b5e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.05921",
    "kind": "arxiv",
    "version": 1
  }
}