Pith Number

pith:Z4YQIUTE

pith:2014:Z4YQIUTE6DRSC6IC6SQX7W4NNI

not attested not anchored not stored refs pending

Maximal Cohen-Macaulay approximations and Serre's condition

Hiroki Matsui, Ryo Takahashi

arxiv:1412.8046 v1 · 2014-12-27 · math.AC · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Z4YQIUTE6DRSC6IC6SQX7W4NNI}

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	2026-05-18T02:30:24.303093Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf31045264f0e3217902f4a17fdb8d6a16e5cf73e32fa57efa88fc3668c27ad5

Aliases

arxiv: 1412.8046 · arxiv_version: 1412.8046v1 · doi: 10.48550/arxiv.1412.8046 · pith_short_12: Z4YQIUTE6DRS · pith_short_16: Z4YQIUTE6DRSC6IC · pith_short_8: Z4YQIUTE

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/Z4YQIUTE6DRSC6IC6SQX7W4NNI \
  | 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: cf31045264f0e3217902f4a17fdb8d6a16e5cf73e32fa57efa88fc3668c27ad5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "caa15610be8c496efd52fb5a03314d0f8a3db5a07afaf657b1b0353f0d2a5c3d",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2014-12-27T13:42:33Z",
    "title_canon_sha256": "638fbf9d3bb3db24eefe87736647e828a72b57846fc0417ff7f11520689ae1c1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.8046",
    "kind": "arxiv",
    "version": 1
  }
}