Pith Number

pith:DN6EX3VA

pith:2015:DN6EX3VA2FXFF2YMKHQCSW7T56

not attested not anchored not stored refs pending

A warped product version of the Cheeger-Gromoll splitting theorem

William Wylie

arxiv:1506.03800 v2 · 2015-06-11 · 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{DN6EX3VA2FXFF2YMKHQCSW7T56}

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	2026-05-18T01:11:43.832900Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1b7c4beea0d16e52eb0c51e0295bf3ef8a233d4ee1be368cc81b483e33720e7a

Aliases

arxiv: 1506.03800 · arxiv_version: 1506.03800v2 · doi: 10.48550/arxiv.1506.03800 · pith_short_12: DN6EX3VA2FXF · pith_short_16: DN6EX3VA2FXFF2YM · pith_short_8: DN6EX3VA

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/DN6EX3VA2FXFF2YMKHQCSW7T56 \
  | 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: 1b7c4beea0d16e52eb0c51e0295bf3ef8a233d4ee1be368cc81b483e33720e7a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f92ad9e269340de525fc719710740ce623c425f53373aca18afecdb26a9c06ef",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-06-11T19:51:04Z",
    "title_canon_sha256": "b550d948438dcbf85dc57c799e93bd62609ba3b5396d07ac29e2a82fc1ec2a49"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.03800",
    "kind": "arxiv",
    "version": 2
  }
}