Pith Number

pith:WQSH5BLY

pith:2024:WQSH5BLYCQMUSUFWXUCM7QAJW7

not attested not anchored not stored refs pending

Embedded minimal surfaces in $\mathbb{S}^3$ and $\mathbb{B}^3$ via equivariant eigenvalue optimization

Daniel Stern, Mikhail Karpukhin, Peter McGrath, Robert Kusner

arxiv:2402.13121 v1 · 2024-02-20 · math.DG · math.AP · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WQSH5BLYCQMUSUFWXUCM7QAJW7}

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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

2 papers in Pith

Eigenvalue optimization via a first-variation formula

Embedded minimal $S^1$-bundles in $\mathbb{S}^4$

Receipt and verification

First computed	2026-07-05T07:47:21.074014Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b4247e857814194950b6bd04cfc009b7ec2ad5dc2cf5f9fcef5baa16340ff6d0

Aliases

arxiv: 2402.13121 · arxiv_version: 2402.13121v1 · doi: 10.48550/arxiv.2402.13121 · pith_short_12: WQSH5BLYCQMU · pith_short_16: WQSH5BLYCQMUSUFW · pith_short_8: WQSH5BLY

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/WQSH5BLYCQMUSUFWXUCM7QAJW7 \
  | 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: b4247e857814194950b6bd04cfc009b7ec2ad5dc2cf5f9fcef5baa16340ff6d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "52d49184f4c19e49574fba769b21e61ce037cbd392ac44542ebf86d4b48d3b70",
    "cross_cats_sorted": [
      "math.AP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2024-02-20T16:32:47Z",
    "title_canon_sha256": "9792f61e27fa16ae5af15c6c52715b45cf1d1ed8fd1f60635131437cb81016d1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2402.13121",
    "kind": "arxiv",
    "version": 1
  }
}