Pith Number

pith:CJM5HQ6K

pith:2023:CJM5HQ6KTQZ7ZLSQJR3OXCWRCZ

not attested not anchored not stored refs pending

Existence of four minimal spheres in $S^3$ with a bumpy metric

Xin Zhou, Zhichao Wang

arxiv:2305.08755 v2 · 2023-05-15 · math.DG · math.AP · math.GT

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CJM5HQ6KTQZ7ZLSQJR3OXCWRCZ}

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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

5 papers in Pith

Existence of classical minimal surfaces in $4$ and $5$-manifolds

Closed minimal surfaces of index one in Riemannian manifolds

Existence of free boundary minimal disks in convex regions

Minimal spheres and scalar curvature

Infinite existence of equivariant minimal hypersurfaces

Receipt and verification

First computed	2026-07-05T08:32:29.597213Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1259d3c3ca9c33fcae504c76eb8ad11642ccce11945e9280e983c26b7f61f47b

Aliases

arxiv: 2305.08755 · arxiv_version: 2305.08755v2 · doi: 10.48550/arxiv.2305.08755 · pith_short_12: CJM5HQ6KTQZ7 · pith_short_16: CJM5HQ6KTQZ7ZLSQ · pith_short_8: CJM5HQ6K

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/CJM5HQ6KTQZ7ZLSQJR3OXCWRCZ \
  | 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: 1259d3c3ca9c33fcae504c76eb8ad11642ccce11945e9280e983c26b7f61f47b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f321120a6b99b6c6eab1493c44f1fc70efcd648f89e477cbffacc6c0f9f42cff",
    "cross_cats_sorted": [
      "math.AP",
      "math.GT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2023-05-15T16:08:34Z",
    "title_canon_sha256": "c062c00a6eca347366e6a9c01672ed663454f6babf3ef517031392a212b6d680"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2305.08755",
    "kind": "arxiv",
    "version": 2
  }
}