Pith Number

pith:IUFJC5QB

pith:2013:IUFJC5QB4GYO7BNJDURTUFFHZV

not attested not anchored not stored refs pending

Tight closure with respect to a multiplicatively closed subset of an $F$-pure local ring

Rodney Y. Sharp

arxiv:1301.6890 v1 · 2013-01-29 · 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{IUFJC5QB4GYO7BNJDURTUFFHZV}

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	2026-05-18T03:35:12.005784Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

450a917601e1b0ef85a91d233a14a7cd40c2aa9d483bf8312f4ad23dd08efc82

Aliases

arxiv: 1301.6890 · arxiv_version: 1301.6890v1 · doi: 10.48550/arxiv.1301.6890 · pith_short_12: IUFJC5QB4GYO · pith_short_16: IUFJC5QB4GYO7BNJ · pith_short_8: IUFJC5QB

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/IUFJC5QB4GYO7BNJDURTUFFHZV \
  | 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: 450a917601e1b0ef85a91d233a14a7cd40c2aa9d483bf8312f4ad23dd08efc82

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "65810aa60d70686b5d76bfbac29e42ebd959b48035051cb0ba213df1279efbc9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2013-01-29T10:51:36Z",
    "title_canon_sha256": "e15409df6c9d62ca163bc2ed1bcc29507ce359bc8d1949b386bbf0770bef2c64"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.6890",
    "kind": "arxiv",
    "version": 1
  }
}