Pith Number

pith:523XQXQ3

pith:2006:523XQXQ37K5AATLZ64GZZD3DIX

not attested not anchored not stored refs pending

A sharper estimate on the Betti numbers of sets defined by quadratic inequalities

Michael Kettner, Saugata Basu

arxiv:math/0610954 v2 · 2006-10-31 · math.AG · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{523XQXQ37K5AATLZ64GZZD3DIX}

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	2026-05-18T04:28:20.593057Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eeb7785e1bfaba004d79f70d9c8f6345d0448f95c3dc56b7036a85d3c467cdf0

Aliases

arxiv: math/0610954 · arxiv_version: math/0610954v2 · doi: 10.48550/arxiv.math/0610954 · pith_short_12: 523XQXQ37K5A · pith_short_16: 523XQXQ37K5AATLZ · pith_short_8: 523XQXQ3

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/523XQXQ37K5AATLZ64GZZD3DIX \
  | 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: eeb7785e1bfaba004d79f70d9c8f6345d0448f95c3dc56b7036a85d3c467cdf0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ae7faeeb206e16ce3435508439a4dc3ba0d38e1b55d74923cea8181c9eb4a87c",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2006-10-31T03:46:02Z",
    "title_canon_sha256": "8e81f697a3a5ec73d3a871d58dc09d50835e45b06c1fcfa575ea92bc3166a2d4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0610954",
    "kind": "arxiv",
    "version": 2
  }
}