Pith Number

pith:LCOYWE4R

pith:2012:LCOYWE4R4PEFH3QHBKFVFNQRWM

not attested not anchored not stored refs pending

Local rings of embedding codepth 3. Examples

Lars Winther Christensen, Oana Veliche

arxiv:1209.4256 v2 · 2012-09-19 · math.AC · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LCOYWE4R4PEFH3QHBKFVFNQRWM}

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	2026-05-18T03:40:50.988250Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

589d8b1391e3c853ee070a8b52b611b32c2690f3946e8e27692ebfeae2a2aaa8

Aliases

arxiv: 1209.4256 · arxiv_version: 1209.4256v2 · doi: 10.48550/arxiv.1209.4256 · pith_short_12: LCOYWE4R4PEF · pith_short_16: LCOYWE4R4PEFH3QH · pith_short_8: LCOYWE4R

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/LCOYWE4R4PEFH3QHBKFVFNQRWM \
  | 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: 589d8b1391e3c853ee070a8b52b611b32c2690f3946e8e27692ebfeae2a2aaa8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c56cc455916706704c9b7cc30c4d39bb520e51e13f428c934093e0d2c6e41a99",
    "cross_cats_sorted": [
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2012-09-19T14:29:28Z",
    "title_canon_sha256": "c363972c458abb966e25c6e23614fb05201bce292994fed6f28e97c6fb331244"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.4256",
    "kind": "arxiv",
    "version": 2
  }
}