Pith Number

pith:MTPJ45IF

pith:2009:MTPJ45IFBJKHS75HVDY7776OGP

not attested not anchored not stored refs pending

Frobenius maps on injective hulls and their applications to tight closure

Mordechai Katzman

arxiv:0902.3110 v2 · 2009-02-18 · 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{MTPJ45IFBJKHS75HVDY7776OGP}

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	2026-05-18T02:58:10.648965Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

64de9e75050a54797fa7a8f1ffffce33f10431f3fc9d03c1f6da5ecf7fa3490e

Aliases

arxiv: 0902.3110 · arxiv_version: 0902.3110v2 · doi: 10.48550/arxiv.0902.3110 · pith_short_12: MTPJ45IFBJKH · pith_short_16: MTPJ45IFBJKHS75H · pith_short_8: MTPJ45IF

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/MTPJ45IFBJKHS75HVDY7776OGP \
  | 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: 64de9e75050a54797fa7a8f1ffffce33f10431f3fc9d03c1f6da5ecf7fa3490e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d12f475c563528e0526882f2ea073bafd361c18967f5424a390b4b2f0e06d073",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2009-02-18T12:04:58Z",
    "title_canon_sha256": "89e2bca4c79dd7ae6ba0f042e1aeb92f5cdbc77f4154f7eac640d8197cc29e67"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0902.3110",
    "kind": "arxiv",
    "version": 2
  }
}