Pith Number

pith:LJF7F3WK

pith:2013:LJF7F3WKEEU6VN5GMEBPJCYMNN

not attested not anchored not stored refs pending

Flat local morphisms of rings with prescribed depth and dimension

Cristodor Ionescu

arxiv:1310.3478 v2 · 2013-10-13 · 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{LJF7F3WKEEU6VN5GMEBPJCYMNN}

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	2026-05-18T00:54:04.875725Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5a4bf2eeca2129eab7a66102f48b0c6b49ffda2311bdea6518ec241f1f27d63c

Aliases

arxiv: 1310.3478 · arxiv_version: 1310.3478v2 · doi: 10.48550/arxiv.1310.3478 · pith_short_12: LJF7F3WKEEU6 · pith_short_16: LJF7F3WKEEU6VN5G · pith_short_8: LJF7F3WK

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/LJF7F3WKEEU6VN5GMEBPJCYMNN \
  | 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: 5a4bf2eeca2129eab7a66102f48b0c6b49ffda2311bdea6518ec241f1f27d63c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c03c556151ed3184fd3e33eaa5ee960a68e0afbc1c6ceb43d885d49396f20eb4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2013-10-13T13:06:42Z",
    "title_canon_sha256": "6f07b9545785dc74eb7d60cc944f4c511cf9a79e1cddec8a6ec419f1aead6922"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.3478",
    "kind": "arxiv",
    "version": 2
  }
}