Pith Number

pith:7H4LLQDO

pith:2010:7H4LLQDO6TFHB3HFBDC4SYOFUY

not attested not anchored not stored refs pending

When an $\mathscr{S}$-closed submodule is a direct summand

Dejun Wu, Yongduo Wang

arxiv:1005.0132 v1 · 2010-05-02 · 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{7H4LLQDO6TFHB3HFBDC4SYOFUY}

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	2026-05-18T02:24:09.433431Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f9f8b5c06ef4ca70ece508c5c961c5a63c27c52a028e5d15e77889c6b5a5c28a

Aliases

arxiv: 1005.0132 · arxiv_version: 1005.0132v1 · doi: 10.48550/arxiv.1005.0132 · pith_short_12: 7H4LLQDO6TFH · pith_short_16: 7H4LLQDO6TFHB3HF · pith_short_8: 7H4LLQDO

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/7H4LLQDO6TFHB3HFBDC4SYOFUY \
  | 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: f9f8b5c06ef4ca70ece508c5c961c5a63c27c52a028e5d15e77889c6b5a5c28a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1972edb20b47f542b401b813c0757bf6bd6dbd7f601fc22cd432208930303890",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2010-05-02T09:43:30Z",
    "title_canon_sha256": "650864d7f107c861c5efc22baea549b2da23ef7f6c9689d90de81f3d90da0476"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1005.0132",
    "kind": "arxiv",
    "version": 1
  }
}