Pith Number

pith:SA2SYBWZ

pith:2009:SA2SYBWZCIIRWTKZXJVCEELVWU

not attested not anchored not stored refs pending

The smooth structure set of $S^p \times S^q$

Diarmuid Crowley

arxiv:0904.1370 v2 · 2009-04-08 · 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{SA2SYBWZCIIRWTKZXJVCEELVWU}

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.

Cited by

1 paper in Pith

Smooth manifolds homotopy equivalent to products of spheres

Receipt and verification

First computed	2026-07-04T17:30:35.905241Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

90352c06d912111b4d59ba6a221175b514e7220fbd33eae168a3f8dca0147529

Aliases

arxiv: 0904.1370 · arxiv_version: 0904.1370v2 · doi: 10.48550/arxiv.0904.1370 · pith_short_12: SA2SYBWZCIIR · pith_short_16: SA2SYBWZCIIRWTKZ · pith_short_8: SA2SYBWZ

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/SA2SYBWZCIIRWTKZXJVCEELVWU \
  | 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: 90352c06d912111b4d59ba6a221175b514e7220fbd33eae168a3f8dca0147529

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ec403743ed43be701c1ed6e00aa3b73f150b9bd8f69fd6dbc73b0ba7960a68ff",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2009-04-08T15:45:37Z",
    "title_canon_sha256": "c2047ac042d05ecf1383a0f9c3ae14566541371898b59a077527159b7e75fc62"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0904.1370",
    "kind": "arxiv",
    "version": 2
  }
}