Pith Number

pith:XMHMFL2S

pith:2007:XMHMFL2SPADMH7RJMF6NUBBSB7

not attested not anchored not stored refs pending

Bounding the number of stable homotopy types of a parametrized family of semi-algebraic sets defined by quadratic inequalities

Michael Kettner, Saugata Basu

arxiv:0707.4333 v1 · 2007-07-30 · math.AG · math.AT · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XMHMFL2SPADMH7RJMF6NUBBSB7}

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	2026-05-18T02:58:12.496641Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bb0ec2af527806c3fe29617cda04320ff4f38285b7ff6eb915025f82680d11da

Aliases

arxiv: 0707.4333 · arxiv_version: 0707.4333v1 · doi: 10.48550/arxiv.0707.4333 · pith_short_12: XMHMFL2SPADM · pith_short_16: XMHMFL2SPADMH7RJ · pith_short_8: XMHMFL2S

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/XMHMFL2SPADMH7RJMF6NUBBSB7 \
  | 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: bb0ec2af527806c3fe29617cda04320ff4f38285b7ff6eb915025f82680d11da

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d1bdb120e9479749b76168e1d6ac10b3f4acb230462b88bbf3fd68acc05ec554",
    "cross_cats_sorted": [
      "math.AT",
      "math.GT"
    ],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2007-07-30T15:06:15Z",
    "title_canon_sha256": "d08ba958fc5319c2d95e10bcc5504313c248fa3c37daae92606c0fd31fab7bd2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0707.4333",
    "kind": "arxiv",
    "version": 1
  }
}