Pith Number

pith:E2OP4HVE

pith:1999:E2OP4HVEEMNBZGH3QGULTMICGL

not attested not anchored not stored refs pending

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

Boris Botvinnik, Christine Escher

arxiv:math/9911039 v2 · 1999-11-07 · math.AT · math.DG · 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{E2OP4HVEEMNBZGH3QGULTMICGL}

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	2026-05-18T04:02:12.517032Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

269cfe1ea4231a1c98fb81a8b9b10232e839e35573151c94b6ed7f757be1bea6

Aliases

arxiv: math/9911039 · arxiv_version: math/9911039v2 · doi: 10.48550/arxiv.math/9911039 · pith_short_12: E2OP4HVEEMNB · pith_short_16: E2OP4HVEEMNBZGH3 · pith_short_8: E2OP4HVE

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/E2OP4HVEEMNBZGH3QGULTMICGL \
  | 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: 269cfe1ea4231a1c98fb81a8b9b10232e839e35573151c94b6ed7f757be1bea6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d4a1ae462f0200cc255fb0d8dfcea9cea9c5b89a677d6760648b3fc55e7de903",
    "cross_cats_sorted": [
      "math.DG",
      "math.GT"
    ],
    "license": "",
    "primary_cat": "math.AT",
    "submitted_at": "1999-11-07T05:33:08Z",
    "title_canon_sha256": "00a48e040ad3c27c3edfad375d861607c977103dbcd959b68762f7b5991ee516"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9911039",
    "kind": "arxiv",
    "version": 2
  }
}