Pith Number

pith:4LWZ5EH7

pith:2013:4LWZ5EH7MJJIGN2EYEESU3TTTB

not attested not anchored not stored refs pending

A simple proof of the formula for the Betti numbers of the quasihomogeneous Hilbert schemes

A. Buryak, B. L. Feigin, H. Nakajima

arxiv:1302.2789 v3 · 2013-02-12 · math.AG · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4LWZ5EH7MJJIGN2EYEESU3TTTB}

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	2026-05-18T01:36:31.787572Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e2ed9e90ff6252833744c1092a6e73985e162f6e0b916c222e94acc66209bf30

Aliases

arxiv: 1302.2789 · arxiv_version: 1302.2789v3 · doi: 10.48550/arxiv.1302.2789 · pith_short_12: 4LWZ5EH7MJJI · pith_short_16: 4LWZ5EH7MJJIGN2E · pith_short_8: 4LWZ5EH7

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/4LWZ5EH7MJJIGN2EYEESU3TTTB \
  | 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: e2ed9e90ff6252833744c1092a6e73985e162f6e0b916c222e94acc66209bf30

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fe7516a5e71e0e404304e3f2b8b54d2d3063edd3d3b262d28f61a35668a44dec",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2013-02-12T13:39:34Z",
    "title_canon_sha256": "60a6a5550b5a6cbb06334d2dc8edb25fce8e5e7edcf805bc21a54b25ce63c646"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.2789",
    "kind": "arxiv",
    "version": 3
  }
}