Pith Number

pith:Z2X3I2JU

pith:2011:Z2X3I2JUERQJ5HNKMLFAB3F27D

not attested not anchored not stored refs pending

$j$-multiplicity and depth of associated graded modules

Claudia Polini, Yu Xie

arxiv:1101.2281 v1 · 2011-01-12 · 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{Z2X3I2JUERQJ5HNKMLFAB3F27D}

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	2026-05-18T04:31:43.205289Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ceafb4693424609e9daa62ca00ecbaf8c2b7df989aabaf2a4811a44b4ff5c81a

Aliases

arxiv: 1101.2281 · arxiv_version: 1101.2281v1 · doi: 10.48550/arxiv.1101.2281 · pith_short_12: Z2X3I2JUERQJ · pith_short_16: Z2X3I2JUERQJ5HNK · pith_short_8: Z2X3I2JU

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/Z2X3I2JUERQJ5HNKMLFAB3F27D \
  | 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: ceafb4693424609e9daa62ca00ecbaf8c2b7df989aabaf2a4811a44b4ff5c81a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "992b5d476c19fa290098c3585572b78b11aef96012e2c06495d5cf1c34e79fab",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2011-01-12T07:39:17Z",
    "title_canon_sha256": "d51228a9b347c03690f7a9d312c8f36c82f9654b6bb32e8aa63f899b9f5bd779"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.2281",
    "kind": "arxiv",
    "version": 1
  }
}