Pith Number

pith:JIJX7DYB

pith:2013:JIJX7DYBO6L2GGDKYY4UU3OEU2

not attested not anchored not stored refs pending

On the uniform bound of the index of reducibility of parameter ideals of a module whose polynomial type is at most one

Pham Hung Quy

arxiv:1311.0987 v1 · 2013-11-05 · 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{JIJX7DYBO6L2GGDKYY4UU3OEU2}

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	2026-05-18T03:07:55.808876Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4a137f8f017797a3186ac6394a6dc4a684675ae347459a5edb8ac71f3d4eda21

Aliases

arxiv: 1311.0987 · arxiv_version: 1311.0987v1 · doi: 10.48550/arxiv.1311.0987 · pith_short_12: JIJX7DYBO6L2 · pith_short_16: JIJX7DYBO6L2GGDK · pith_short_8: JIJX7DYB

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/JIJX7DYBO6L2GGDKYY4UU3OEU2 \
  | 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: 4a137f8f017797a3186ac6394a6dc4a684675ae347459a5edb8ac71f3d4eda21

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ee5884496f5ebd749919e2447a353c8d2f7ad969a3263a2c4d6224e6c7bf2ec",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2013-11-05T08:26:44Z",
    "title_canon_sha256": "24d8c871c2dbe63a12d6e0d167f46ce6af0fdec9f59255a32c8f10ef1e662b4f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.0987",
    "kind": "arxiv",
    "version": 1
  }
}