Pith Number

pith:XAWIA7OE

pith:2016:XAWIA7OEXPELH7DZXZ6XYPUT24

not attested not anchored not stored refs pending

Existence of minimizing Willmore Klein bottles in Euclidean four-space

Elena M\"ader-Baumdicker, Jonas Hirsch, Patrick Breuning

arxiv:1604.01906 v2 · 2016-04-07 · math.AP · 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{XAWIA7OEXPELH7DZXZ6XYPUT24}

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	2026-05-18T00:42:33.022532Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b82c807dc4bbc8b3fc79be7d7c3e93d72d4ee98d02d7d2d679e5d5a44062399f

Aliases

arxiv: 1604.01906 · arxiv_version: 1604.01906v2 · doi: 10.48550/arxiv.1604.01906 · pith_short_12: XAWIA7OEXPEL · pith_short_16: XAWIA7OEXPELH7DZ · pith_short_8: XAWIA7OE

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/XAWIA7OEXPELH7DZXZ6XYPUT24 \
  | 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: b82c807dc4bbc8b3fc79be7d7c3e93d72d4ee98d02d7d2d679e5d5a44062399f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4d566af40385097da106f660b52d9af53d9150af66353aec107354f5219e94fa",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-04-07T07:56:30Z",
    "title_canon_sha256": "c9d4cd9ffc3d2b11cd60ad3439be899a112c12130f32461127320e363a8e087b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.01906",
    "kind": "arxiv",
    "version": 2
  }
}