Pith Number

pith:MTPXUWK3

pith:2015:MTPXUWK3NRIE7IP6RW273OQU7L

not attested not anchored not stored refs pending

Graded-irreducible modules are irreducible

Justin Chen, Youngsu Kim

arxiv:1508.07518 v2 · 2015-08-30 · 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{MTPXUWK3NRIE7IP6RW273OQU7L}

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	2026-05-18T01:03:36.849177Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

64df7a595b6c504fa1fe8db5fdba14fadef894715e2be296dea89612c36c2e86

Aliases

arxiv: 1508.07518 · arxiv_version: 1508.07518v2 · doi: 10.48550/arxiv.1508.07518 · pith_short_12: MTPXUWK3NRIE · pith_short_16: MTPXUWK3NRIE7IP6 · pith_short_8: MTPXUWK3

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/MTPXUWK3NRIE7IP6RW273OQU7L \
  | 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: 64df7a595b6c504fa1fe8db5fdba14fadef894715e2be296dea89612c36c2e86

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c43b479e575c223943abae695ae9a436d7bdcbf1b7e0e9f6ad598f6044e9ca50",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2015-08-30T00:39:02Z",
    "title_canon_sha256": "21211945594121f65800f2814634d0c4374d63cf521f92c7e1f1fb473bf6a2f9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.07518",
    "kind": "arxiv",
    "version": 2
  }
}