Pith Number

pith:X55DFIF7

pith:2010:X55DFIF7KOZRX4BLEKXKJDHVAG

not attested not anchored not stored refs pending

When every principal ideal is flat

Fatima Cheniour, Najib Mahdou

arxiv:1012.2538 v2 · 2010-12-12 · 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{X55DFIF7KOZRX4BLEKXKJDHVAG}

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	2026-05-18T04:12:32.360006Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf7a32a0bf53b31bf02b22aea48cf5018ac23a0bd112895b2c2cf8ddec6df170

Aliases

arxiv: 1012.2538 · arxiv_version: 1012.2538v2 · doi: 10.48550/arxiv.1012.2538 · pith_short_12: X55DFIF7KOZR · pith_short_16: X55DFIF7KOZRX4BL · pith_short_8: X55DFIF7

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/X55DFIF7KOZRX4BLEKXKJDHVAG \
  | 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: bf7a32a0bf53b31bf02b22aea48cf5018ac23a0bd112895b2c2cf8ddec6df170

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4ddf0380c1313a964ea7e45c9f6a1f1f6b40abf15dda3951b83b0c1f5854d2db",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2010-12-12T13:16:20Z",
    "title_canon_sha256": "a9e1a85d0c4fddbee8ef401f3f8f9448f66d339fb8f94676da30a8d30a601126"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.2538",
    "kind": "arxiv",
    "version": 2
  }
}