Pith Number

pith:H7K5QLCP

pith:2011:H7K5QLCPMTHF6P25PDQYYGF4S2

not attested not anchored not stored refs pending

Formulas for the multiplicity of graded algebras

Yu Xie

arxiv:1101.2280 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{H7K5QLCPMTHF6P25PDQYYGF4S2}

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	2026-05-18T04:31:43.211480Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3fd5d82c4f64ce5f3f5d78e18c18bc969933225b856de209b33dab35fbe8b6db

Aliases

arxiv: 1101.2280 · arxiv_version: 1101.2280v1 · doi: 10.48550/arxiv.1101.2280 · pith_short_12: H7K5QLCPMTHF · pith_short_16: H7K5QLCPMTHF6P25 · pith_short_8: H7K5QLCP

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/H7K5QLCPMTHF6P25PDQYYGF4S2 \
  | 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: 3fd5d82c4f64ce5f3f5d78e18c18bc969933225b856de209b33dab35fbe8b6db

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "861cc6e11626485bca4ba8d37de83cdf852e4fc0a5f9de445e972382affc9a47",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2011-01-12T07:35:34Z",
    "title_canon_sha256": "a16cc3d991d8474837468da9dd0bf575fe384f91b9afb2ae821ec5754a56dbfc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.2280",
    "kind": "arxiv",
    "version": 1
  }
}