Pith Number

pith:GWL4OODU

pith:2011:GWL4OODURET64SXMG3RXCFKE6P

not attested not anchored not stored refs pending

A planar bi-Lipschitz extension Theorem

Aldo Pratelli, Sara Daneri

arxiv:1110.6124 v2 · 2011-10-27 · math.FA · 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{GWL4OODURET64SXMG3RXCFKE6P}

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	2026-05-18T04:10:08.296725Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3597c738748927ee4aec36e3711544f3efb47843f338f9f2bff2eb8201069725

Aliases

arxiv: 1110.6124 · arxiv_version: 1110.6124v2 · doi: 10.48550/arxiv.1110.6124 · pith_short_12: GWL4OODURET6 · pith_short_16: GWL4OODURET64SXM · pith_short_8: GWL4OODU

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/GWL4OODURET64SXMG3RXCFKE6P \
  | 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: 3597c738748927ee4aec36e3711544f3efb47843f338f9f2bff2eb8201069725

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cb3b1513f9c208d59dfd3e5293c9b2762105022917903b64b3821c084e964e3a",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-10-27T15:49:41Z",
    "title_canon_sha256": "9de0455411de5a750aef21e5f3ff753144abe284bb82798c62697adf2e0c068f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.6124",
    "kind": "arxiv",
    "version": 2
  }
}