Pith Number

pith:Z5RLSSVX

pith:2020:Z5RLSSVXMFW7N3KTX4YFR2YPVI

not attested not anchored not stored refs pending

Minimal $2$-Spheres and Optimal Foliations in $3$-Spheres with Arbitrary Metric

Salim Deaibes

arxiv:2001.07695 v2 · 2020-01-21 · 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{Z5RLSSVXMFW7N3KTX4YFR2YPVI}

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.

Cited by

1 paper in Pith

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

Receipt and verification

First computed	2026-07-05T03:36:50.947417Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf62b94ab7616df6ed53bf3058eb0faa168d345590b72f217d226c9629620b8f

Aliases

arxiv: 2001.07695 · arxiv_version: 2001.07695v2 · doi: 10.48550/arxiv.2001.07695 · pith_short_12: Z5RLSSVXMFW7 · pith_short_16: Z5RLSSVXMFW7N3KT · pith_short_8: Z5RLSSVX

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/Z5RLSSVXMFW7N3KTX4YFR2YPVI \
  | 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: cf62b94ab7616df6ed53bf3058eb0faa168d345590b72f217d226c9629620b8f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d21b0988b564114a2517a8f81ef3cc0ba1c5ae7b2abfb69b90bb3245bae34996",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2020-01-21T18:53:58Z",
    "title_canon_sha256": "64526ad57ff9d770767d3f7cf4a4342d2e250664d60b38a4daea47fd18e33154"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2001.07695",
    "kind": "arxiv",
    "version": 2
  }
}