Pith Number

pith:G46B6X7G

pith:2012:G46B6X7GXZHZRHY7ETMPQ6WRIK

not attested not anchored not stored refs pending

Sharp stability inequalities for planar double bubbles

Francesco Maggi, Gian Paolo Leonardi, Marco Cicalese

arxiv:1211.3698 v2 · 2012-11-15 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{G46B6X7GXZHZRHY7ETMPQ6WRIK}

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	2026-05-18T02:18:13.842249Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

373c1f5fe6be4f989f1f24d8f87ad142979495e6b52d2ab77fbf878a163d83fa

Aliases

arxiv: 1211.3698 · arxiv_version: 1211.3698v2 · doi: 10.48550/arxiv.1211.3698 · pith_short_12: G46B6X7GXZHZ · pith_short_16: G46B6X7GXZHZRHY7 · pith_short_8: G46B6X7G

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/G46B6X7GXZHZRHY7ETMPQ6WRIK \
  | 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: 373c1f5fe6be4f989f1f24d8f87ad142979495e6b52d2ab77fbf878a163d83fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "29634c399bb068318be7705d3794c7c402fba6df520d68814affbfc3ebee7ed6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-11-15T19:12:47Z",
    "title_canon_sha256": "3590500c22a3383b1feda2a49faa6761afe798d185c92a241859155583d83b13"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.3698",
    "kind": "arxiv",
    "version": 2
  }
}