Pith Number

pith:W63L5X2M

pith:2014:W63L5X2MNUC6AVXWCAHSFSQSWZ

not attested not anchored not stored refs pending

Improved convergence theorems for bubble clusters. I. The planar case

Francesco Maggi, Gian Paolo Leonardi, Marco Cicalese

arxiv:1409.6652 v3 · 2014-09-23 · math.AP · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{W63L5X2MNUC6AVXWCAHSFSQSWZ}

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	2026-05-18T01:55:53.187294Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7b6bedf4c6d05e056f6100f22ca12b66c0ade82830e959d62010b5ae2110de1

Aliases

arxiv: 1409.6652 · arxiv_version: 1409.6652v3 · doi: 10.48550/arxiv.1409.6652 · pith_short_12: W63L5X2MNUC6 · pith_short_16: W63L5X2MNUC6AVXW · pith_short_8: W63L5X2M

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/W63L5X2MNUC6AVXWCAHSFSQSWZ \
  | 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: b7b6bedf4c6d05e056f6100f22ca12b66c0ade82830e959d62010b5ae2110de1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9679794526a910bc9bc2936837f5d8315efecce6ae63a42d91c57a9c09bab9df",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2014-09-23T16:07:14Z",
    "title_canon_sha256": "d8ed4a0494749b6c9976c78238ecc8fc3ae9df97a5aa02dc711deb914db19b1e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.6652",
    "kind": "arxiv",
    "version": 3
  }
}