Pith Number

pith:4ZQPQ5V4

pith:2017:4ZQPQ5V4YWQVF2ZWXOSOR4SGYH

not attested not anchored not stored refs pending

Complete minimal submanifolds with nullity in Euclidean spheres

A. Savas-Halilaj, M. Dajczer, Th. Kasioumis, Th. Vlachos

arxiv:1704.06401 v2 · 2017-04-21 · 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{4ZQPQ5V4YWQVF2ZWXOSOR4SGYH}

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	2026-05-18T00:40:46.177145Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e660f876bcc5a152eb36bba4e8f246c1ca0188eb0c6b2875ade85965357721db

Aliases

arxiv: 1704.06401 · arxiv_version: 1704.06401v2 · doi: 10.48550/arxiv.1704.06401 · pith_short_12: 4ZQPQ5V4YWQV · pith_short_16: 4ZQPQ5V4YWQVF2ZW · pith_short_8: 4ZQPQ5V4

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/4ZQPQ5V4YWQVF2ZWXOSOR4SGYH \
  | 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: e660f876bcc5a152eb36bba4e8f246c1ca0188eb0c6b2875ade85965357721db

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9d3cb61eee6e8cc7e1379aeceb2fb3cb743ef22ae0ef2c0fe1083dc1b27b90a8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2017-04-21T05:28:44Z",
    "title_canon_sha256": "bf990fe7ce9502331f106f13b40aaa814cbc9a6ffeb367a615a9112f5e3aa960"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1704.06401",
    "kind": "arxiv",
    "version": 2
  }
}