Pith Number

pith:4C5FBB3X

pith:2000:4C5FBB3XTTEUP4RKGG26F7NSQL

not attested not anchored not stored refs pending

A classification of $S^3$-bundles over $S^4$

Christine M. Escher, Diarmuid Crowley

arxiv:math/0004147 v1 · 2000-04-24 · math.AT · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4C5FBB3XTTEUP4RKGG26F7NSQL}

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	2026-07-04T14:34:28.563243Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e0ba5087779cc947f22a31b5e2fdb282e0a7c6de620ad392ea86c69c0ff5d382

Aliases

arxiv: math/0004147 · arxiv_version: math/0004147v1 · doi: 10.48550/arxiv.math/0004147 · pith_short_12: 4C5FBB3XTTEU · pith_short_16: 4C5FBB3XTTEUP4RK · pith_short_8: 4C5FBB3X

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/4C5FBB3XTTEUP4RKGG26F7NSQL \
  | 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: e0ba5087779cc947f22a31b5e2fdb282e0a7c6de620ad392ea86c69c0ff5d382

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d633dfedd4beb26a372fab782a3117ea0eef7063fbf3b965f85a608fb261be7e",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "",
    "primary_cat": "math.AT",
    "submitted_at": "2000-04-24T20:26:45Z",
    "title_canon_sha256": "c08b83db2521cd7fd9c5023f964a894304343ad086ee2ce575b818dee77a781a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0004147",
    "kind": "arxiv",
    "version": 1
  }
}