Pith Number

pith:4IHCXA2X

pith:2011:4IHCXA2XC22DABQUIOETNNHDNJ

not attested not anchored not stored refs pending

A note on the direct limit of increasing sequences of completely decomposable modules over integral domains

J. E. Mac\'ias-D\'iaz

arxiv:1112.0608 v1 · 2011-12-02 · math.AC · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4IHCXA2XC22DABQUIOETNNHDNJ}

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	2026-05-18T04:07:06.171286Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e20e2b835716b4300614438936b4e36a5be5ac6a25b2c2c66dcbc5d52164aaff

Aliases

arxiv: 1112.0608 · arxiv_version: 1112.0608v1 · doi: 10.48550/arxiv.1112.0608 · pith_short_12: 4IHCXA2XC22D · pith_short_16: 4IHCXA2XC22DABQU · pith_short_8: 4IHCXA2X

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/4IHCXA2XC22DABQUIOETNNHDNJ \
  | 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: e20e2b835716b4300614438936b4e36a5be5ac6a25b2c2c66dcbc5d52164aaff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7e0432bd1643590a9d8e82b4a76e3d2d386fd83863eb116347c9d823478ebc17",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2011-12-02T23:17:31Z",
    "title_canon_sha256": "40b8876dd14695f3d4e787b0365a1eb8fab5a17fcb88d536a15e295d12fc595a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.0608",
    "kind": "arxiv",
    "version": 1
  }
}