Pith Number

pith:JYU2GHHM

pith:2015:JYU2GHHMOFVMSMQSMP3IHBQXTA

not attested not anchored not stored refs pending

Isoperimetric domains in homogeneous three-manifolds and the isoperimetric constant of the Heisenberg group $\mathsf{H}^1$

Andrea Malchiodi, Jih-Hsin Cheng, Paul Yang

arxiv:1501.07357 v2 · 2015-01-29 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JYU2GHHMOFVMSMQSMP3IHBQXTA}

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	2026-05-18T02:27:00.498796Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4e29a31cec716ac9321263f68386179810f848184e9a5c702ce7852b12a6bd72

Aliases

arxiv: 1501.07357 · arxiv_version: 1501.07357v2 · doi: 10.48550/arxiv.1501.07357 · pith_short_12: JYU2GHHMOFVM · pith_short_16: JYU2GHHMOFVMSMQS · pith_short_8: JYU2GHHM

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/JYU2GHHMOFVMSMQSMP3IHBQXTA \
  | 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: 4e29a31cec716ac9321263f68386179810f848184e9a5c702ce7852b12a6bd72

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "006bc69314e674c8f5f03c204aed2c20aa8b95b8404008cdde96aafd7fca18bf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-01-29T07:18:34Z",
    "title_canon_sha256": "7bd2a877b66bdbd17c7a97ccb8bc3707512f1344ab5125f8b3902793992ae336"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.07357",
    "kind": "arxiv",
    "version": 2
  }
}