Pith Number

pith:PA4PFSWL

pith:2024:PA4PFSWLCTCGVIECUJYC7COYIG

not attested not anchored not stored refs pending

Existence of 5 minimal tori in 3-spheres of positive Ricci curvature

Adrian Chun-Pong Chu, Yangyang Li

arxiv:2409.09315 v2 · 2024-09-14 · math.DG · math.AP · math.GT

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PA4PFSWLCTCGVIECUJYC7COYIG}

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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

Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric

Minimal spheres and scalar curvature

Receipt and verification

First computed	2026-07-05T11:46:20.156878Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7838f2cacb14c46aa082a2702f89d84198683c37365751921d0cd8d06cc74c4f

Aliases

arxiv: 2409.09315 · arxiv_version: 2409.09315v2 · doi: 10.48550/arxiv.2409.09315 · pith_short_12: PA4PFSWLCTCG · pith_short_16: PA4PFSWLCTCGVIEC · pith_short_8: PA4PFSWL

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/PA4PFSWLCTCGVIECUJYC7COYIG \
  | 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: 7838f2cacb14c46aa082a2702f89d84198683c37365751921d0cd8d06cc74c4f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0a1ca8c59d32fb4d5085a9d54c4a0cec6279cd2eb8e0cf5b2ca403d88f83626a",
    "cross_cats_sorted": [
      "math.AP",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2024-09-14T05:24:48Z",
    "title_canon_sha256": "ee6dbe399a9dd31d265d76516199bd95a6c20f847deab0c4598fd8cb3cfa6f84"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2409.09315",
    "kind": "arxiv",
    "version": 2
  }
}