Pith Number

pith:IJMXWIQK

pith:2010:IJMXWIQKPVDTBC3DECDN4VMZFR

not attested not anchored not stored refs pending

Ordinary varieties and the comparison between multiplier ideals and test ideals II

Mircea Mustata

arxiv:1012.2915 v2 · 2010-12-14 · math.AC · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IJMXWIQKPVDTBC3DECDN4VMZFR}

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	2026-05-18T04:20:58.983120Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

42597b220a7d47308b632086de55992c7b1b775a98ede46e0fd69c55fb663aae

Aliases

arxiv: 1012.2915 · arxiv_version: 1012.2915v2 · doi: 10.48550/arxiv.1012.2915 · pith_short_12: IJMXWIQKPVDT · pith_short_16: IJMXWIQKPVDTBC3D · pith_short_8: IJMXWIQK

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/IJMXWIQKPVDTBC3DECDN4VMZFR \
  | 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: 42597b220a7d47308b632086de55992c7b1b775a98ede46e0fd69c55fb663aae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cd4a518d9dfdb0803911ecff20ee507254372f02905663c4212623cdad6baecf",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2010-12-14T02:03:11Z",
    "title_canon_sha256": "ea25f1bff42c1b4135b39e5145c7e769add5a729dcb730749418c85db66f643a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.2915",
    "kind": "arxiv",
    "version": 2
  }
}