Pith Number

pith:XM6GSYR2

pith:2010:XM6GSYR2DGGZITTA7MPTWBUBFI

not attested not anchored not stored refs pending

An upper bound on the number of F-jumping coefficients of a principal ideal

Gennady Lyubeznik, Mordechai Katzman, Wenliang Zhang

arxiv:1010.1890 v1 · 2010-10-10 · 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{XM6GSYR2DGGZITTA7MPTWBUBFI}

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	2026-05-18T04:39:30.136889Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bb3c69623a198d944e60fb1f3b06812a2c9a6aa955edda27fcb98f18728aecb1

Aliases

arxiv: 1010.1890 · arxiv_version: 1010.1890v1 · doi: 10.48550/arxiv.1010.1890 · pith_short_12: XM6GSYR2DGGZ · pith_short_16: XM6GSYR2DGGZITTA · pith_short_8: XM6GSYR2

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/XM6GSYR2DGGZITTA7MPTWBUBFI \
  | 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: bb3c69623a198d944e60fb1f3b06812a2c9a6aa955edda27fcb98f18728aecb1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d0b1f10ff8df7ad1b1729f7b9397d564b94b32b781c3ee670c3fa370996ccc7f",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2010-10-10T03:36:11Z",
    "title_canon_sha256": "89a70b650833fd08d19240dab27309c7f5723016eba457098dd70af9aff73818"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.1890",
    "kind": "arxiv",
    "version": 1
  }
}