Pith Number

pith:I74JI6AF

pith:2010:I74JI6AF7HRVYHCIM2EC7DKPPT

not attested not anchored not stored refs pending

Sharp upper bounds of the Betti numbers for a given Hilbert polynomial

Giulio Caviglia, Satoshi Murai

arxiv:1010.0457 v1 · 2010-10-04 · 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{I74JI6AF7HRVYHCIM2EC7DKPPT}

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	2026-05-18T01:22:29.239496Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

47f8947805f9e35c1c4866882f8d4f7cef03833d7f38440c61b53cd69efbef9b

Aliases

arxiv: 1010.0457 · arxiv_version: 1010.0457v1 · doi: 10.48550/arxiv.1010.0457 · pith_short_12: I74JI6AF7HRV · pith_short_16: I74JI6AF7HRVYHCI · pith_short_8: I74JI6AF

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/I74JI6AF7HRVYHCIM2EC7DKPPT \
  | 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: 47f8947805f9e35c1c4866882f8d4f7cef03833d7f38440c61b53cd69efbef9b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b3b4ead6325a13ceafd510986857db5deaf7dc622298371ce447076ce32bf046",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2010-10-04T00:37:49Z",
    "title_canon_sha256": "8946c9ec2d71ab9be862ed0aaafea842fbc5f013d332158c5a824d690c2ce64e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.0457",
    "kind": "arxiv",
    "version": 1
  }
}