Pith Number

pith:XKAMOSYI

pith:2026:XKAMOSYI4DDL6RJNTJTI3AFGZX

not attested not anchored not stored refs pending

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

Xin Zhou, Zhichao Wang

arxiv:2607.08631 v1 · 2026-07-09 · math.DG · math.AP · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XKAMOSYI4DDL6RJNTJTI3AFGZX}

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	2026-07-10T01:19:56.023548Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba80c74b08e0c6bf452d9a668d80a6cdd18fe30081e9e3052b5e13b80716b6bc

Aliases

arxiv: 2607.08631 · arxiv_version: 2607.08631v1 · doi: 10.48550/arxiv.2607.08631 · pith_short_12: XKAMOSYI4DDL · pith_short_16: XKAMOSYI4DDL6RJN · pith_short_8: XKAMOSYI

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/XKAMOSYI4DDL6RJNTJTI3AFGZX \
  | 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: ba80c74b08e0c6bf452d9a668d80a6cdd18fe30081e9e3052b5e13b80716b6bc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2a42db393bd0f31fe10dcbd0567111fff5066ad8f3a737e797fd901e659492d0",
    "cross_cats_sorted": [
      "math.AP",
      "math.GT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-07-09T16:01:30Z",
    "title_canon_sha256": "97f70ab1271f72d4ac7077bbbdad78d6b4a1307d76a4c78d77a12d83f5349abb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.08631",
    "kind": "arxiv",
    "version": 1
  }
}