Pith Number

pith:WYRK5DFU

pith:2008:WYRK5DFU4SARJLPV2QWSDWPCII

not attested not anchored not stored refs pending

The stable free rank of symmetry of products of spheres

Bernhard Hanke

arxiv:0803.3572 v3 · 2008-03-25 · 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{WYRK5DFU4SARJLPV2QWSDWPCII}

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	2026-05-18T02:15:59.834552Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b622ae8cb4e48114adf5d42d21d9e242101717ea5decc3fe4cebd66845415b1d

Aliases

arxiv: 0803.3572 · arxiv_version: 0803.3572v3 · doi: 10.48550/arxiv.0803.3572 · pith_short_12: WYRK5DFU4SAR · pith_short_16: WYRK5DFU4SARJLPV · pith_short_8: WYRK5DFU

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/WYRK5DFU4SARJLPV2QWSDWPCII \
  | 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: b622ae8cb4e48114adf5d42d21d9e242101717ea5decc3fe4cebd66845415b1d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aa91bd97061be2a88082c301d0a32aa4fcca49cc1cc8873008a1c9826f862894",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2008-03-25T15:03:43Z",
    "title_canon_sha256": "e0d3256a828334e88bc68648ff3cd10174ea808ee71bf3157b89a3b163b6229f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0803.3572",
    "kind": "arxiv",
    "version": 3
  }
}