Pith Number

pith:BBZAL47I

pith:2011:BBZAL47IVSICKFTPM5CSVP7U6C

not attested not anchored not stored refs pending

Test ideals via a single alteration and discreteness and rationality of $F$-jumping numbers

Karl Schwede, Kevin Tucker, Wenliang Zhang

arxiv:1107.4059 v2 · 2011-07-20 · math.AG · 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{BBZAL47IVSICKFTPM5CSVP7U6C}

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	2026-05-18T03:54:37.654074Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

087205f3e8ac9025166f67452abff4f09ae3dbb4c46cab2f05870b7fc9951a97

Aliases

arxiv: 1107.4059 · arxiv_version: 1107.4059v2 · doi: 10.48550/arxiv.1107.4059 · pith_short_12: BBZAL47IVSIC · pith_short_16: BBZAL47IVSICKFTP · pith_short_8: BBZAL47I

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/BBZAL47IVSICKFTPM5CSVP7U6C \
  | 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: 087205f3e8ac9025166f67452abff4f09ae3dbb4c46cab2f05870b7fc9951a97

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a80c1da4020ebc2ddbd3096030a9ff9780f8cb22a233424bd19d6997ff8ae2f4",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2011-07-20T18:41:37Z",
    "title_canon_sha256": "ea4d55fd108be618a4fbbc8575e7a83117c325da2532b09155005dc16ad8d3a3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.4059",
    "kind": "arxiv",
    "version": 2
  }
}