Pith Number

pith:O63W7T45

pith:2015:O63W7T45ROUTMRYKZSCVB3I6W6

not attested not anchored not stored refs pending

Essential normality of homogenous quotient modules over the polydisc: distinguished variety case

Chong Zhao, Penghui Wang

arxiv:1508.03481 v1 · 2015-08-14 · math.FA · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{O63W7T45ROUTMRYKZSCVB3I6W6}

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	2026-05-18T01:35:17.644787Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

77b76fcf9d8ba936470acc8550ed1eb7b64d71790a04741f11ebd357075bfbca

Aliases

arxiv: 1508.03481 · arxiv_version: 1508.03481v1 · doi: 10.48550/arxiv.1508.03481 · pith_short_12: O63W7T45ROUT · pith_short_16: O63W7T45ROUTMRYK · pith_short_8: O63W7T45

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/O63W7T45ROUTMRYKZSCVB3I6W6 \
  | 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: 77b76fcf9d8ba936470acc8550ed1eb7b64d71790a04741f11ebd357075bfbca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dd9957662f8f5ccdb2b3c20db110028344eece147ec8fc9ec49e980aa509d44e",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-08-14T12:42:41Z",
    "title_canon_sha256": "5b3d79164029a223c04db6e8f3ef66201f386b4f6822faccf6fe5d2cb56f318b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.03481",
    "kind": "arxiv",
    "version": 1
  }
}