Pith Number

pith:WZSUV6PK

pith:2015:WZSUV6PK5VDS4LRCJJ4BGHYAJS

not attested not anchored not stored refs pending

On the stable hom relation and stable degenerations of Cohen-Macaulay modules

Naoya Hiramatsu

arxiv:1501.05027 v4 · 2015-01-21 · 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{WZSUV6PK5VDS4LRCJJ4BGHYAJS}

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	2026-05-18T00:34:05.395671Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b6654af9eaed472e2e224a78131f004c933abab5750a769a68330816f98b5d47

Aliases

arxiv: 1501.05027 · arxiv_version: 1501.05027v4 · doi: 10.48550/arxiv.1501.05027 · pith_short_12: WZSUV6PK5VDS · pith_short_16: WZSUV6PK5VDS4LRC · pith_short_8: WZSUV6PK

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/WZSUV6PK5VDS4LRCJJ4BGHYAJS \
  | 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: b6654af9eaed472e2e224a78131f004c933abab5750a769a68330816f98b5d47

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a534bd117b3c713033d766eab0adfbc2613c9df9dd10af1908ab7a26b5f1d712",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2015-01-21T00:22:22Z",
    "title_canon_sha256": "70d73a4ef04408f730cedc6f110770ea189877bf26648e3d6a864278b9c984dd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.05027",
    "kind": "arxiv",
    "version": 4
  }
}