Pith Number

pith:62UUOOEU

pith:2017:62UUOOEUFHFZ64RFKTKN3NREKP

not attested not anchored not stored refs pending

Counting submodules of a module over a noetherian commutative ring

Yves Cornulier

arxiv:1705.09224 v2 · 2017-05-25 · 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{62UUOOEUFHFZ64RFKTKN3NREKP}

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	2026-05-17T23:41:47.225248Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f6a947389429cb9f722554d4ddb62453da90c72b4eee99d6d94087d2b7b80119

Aliases

arxiv: 1705.09224 · arxiv_version: 1705.09224v2 · doi: 10.48550/arxiv.1705.09224 · pith_short_12: 62UUOOEUFHFZ · pith_short_16: 62UUOOEUFHFZ64RF · pith_short_8: 62UUOOEU

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/62UUOOEUFHFZ64RFKTKN3NREKP \
  | 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: f6a947389429cb9f722554d4ddb62453da90c72b4eee99d6d94087d2b7b80119

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3197da01c7cbc6ba177617f0fa3775c2b1f8e1b6d9c651193a5dc27d382e47a3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2017-05-25T15:25:43Z",
    "title_canon_sha256": "80e668f604a0ff978e550fb3b4018f98e6ab495c13a7e014413d9ec16a742251"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.09224",
    "kind": "arxiv",
    "version": 2
  }
}