Pith Number

pith:JI4UBI3H

pith:2010:JI4UBI3HO2TH55TMEGBJHCZ4ED

not attested not anchored not stored refs pending

Bi-Lipschitz Embeddability of the Grushin Plane into Euclidean Space

Jeehyeon Seo

arxiv:1011.0365 v1 · 2010-11-01 · 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{JI4UBI3HO2TH55TMEGBJHCZ4ED}

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	2026-05-18T04:37:23.335219Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4a3940a36776a67ef66c2182938b3c20ce68055e7e77ee0504815b94b8fbacee

Aliases

arxiv: 1011.0365 · arxiv_version: 1011.0365v1 · doi: 10.48550/arxiv.1011.0365 · pith_short_12: JI4UBI3HO2TH · pith_short_16: JI4UBI3HO2TH55TM · pith_short_8: JI4UBI3H

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/JI4UBI3HO2TH55TMEGBJHCZ4ED \
  | 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: 4a3940a36776a67ef66c2182938b3c20ce68055e7e77ee0504815b94b8fbacee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ee2eee66e3fcf2b439c30578578620e80f38e302ea189eb169483d08f13fc340",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2010-11-01T16:19:56Z",
    "title_canon_sha256": "a2d1d444771f136f7b3ce7464f77bf79b30e813edf7e7701bf50c06a797a47de"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.0365",
    "kind": "arxiv",
    "version": 1
  }
}