Pith Number

pith:AZ7KWVKF

pith:2009:AZ7KWVKFQLXVVXAYW7R6C6BB6F

not attested not anchored not stored refs pending

On locally constructible spheres and balls

Bruno Benedetti, G\"unter M. Ziegler

arxiv:0902.0436 v4 · 2009-02-03 · math.CO · hep-th · math.AT · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AZ7KWVKFQLXVVXAYW7R6C6BB6F}

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	2026-05-18T04:15:17.173946Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

067eab554582ef5adc18b7e3e17821f17f88ee659a4a89b0daf3b59c3aa33aaf

Aliases

arxiv: 0902.0436 · arxiv_version: 0902.0436v4 · doi: 10.48550/arxiv.0902.0436 · pith_short_12: AZ7KWVKFQLXV · pith_short_16: AZ7KWVKFQLXVVXAY · pith_short_8: AZ7KWVKF

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/AZ7KWVKFQLXVVXAYW7R6C6BB6F \
  | 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: 067eab554582ef5adc18b7e3e17821f17f88ee659a4a89b0daf3b59c3aa33aaf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "47ac88c334cd59d0f91e290595fc8487c2ba11c4022f5853c1c05b8a828635f5",
    "cross_cats_sorted": [
      "hep-th",
      "math.AT",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2009-02-03T07:15:19Z",
    "title_canon_sha256": "c8c1ec5f99da189d34b4b4950930b5ce2b8a8488f1178cbcaaa7c8560a126d60"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0902.0436",
    "kind": "arxiv",
    "version": 4
  }
}