Pith Number

pith:43CODRU6

pith:2004:43CODRU6D45NALM2ASOKVGRWVR

not attested not anchored not stored refs pending

Proof of the Double Bubble Conjecture

Antonio Ros, Frank Morgan, Manuel Ritor\'e, Michael Hutchings

arxiv:math/0406017 v1 · 2004-06-01 · math.DG · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{43CODRU6D45NALM2ASOKVGRWVR}

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

2 papers in Pith

The lens cluster and triod cluster uniquely minimize the anisotropic perimeter in $\mathbb{R}^2$

Receipt and verification

First computed	2026-07-04T14:38:40.472484Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e6c4e1c69e1f3ad02d9a049caa9a36ac539240aa2b1e35e4a0b4f4986a7b9317

Aliases

arxiv: math/0406017 · arxiv_version: math/0406017v1 · doi: 10.48550/arxiv.math/0406017 · pith_short_12: 43CODRU6D45N · pith_short_16: 43CODRU6D45NALM2 · pith_short_8: 43CODRU6

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/43CODRU6D45NALM2ASOKVGRWVR \
  | 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: e6c4e1c69e1f3ad02d9a049caa9a36ac539240aa2b1e35e4a0b4f4986a7b9317

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f33270ed6073e6ca7c4678e4d63669682ede2a1ed50774e61d949818d333efab",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "",
    "primary_cat": "math.DG",
    "submitted_at": "2004-06-01T16:10:48Z",
    "title_canon_sha256": "1f228f600646013d1b6e871dbbc7a6cfc321fcff72222a820a3a239442579440"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0406017",
    "kind": "arxiv",
    "version": 1
  }
}