Pith Number

pith:PX3XWJE5

pith:2016:PX3XWJE5OLRYCSWFNJGHKV6PTK

not attested not anchored not stored refs pending

Lefschetz properties of balanced 3-polytopes

David Cook II, Eran Nevo, Martina Juhnke-Kubitzke, Satoshi Murai

arxiv:1606.02028 v1 · 2016-06-07 · math.CO · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PX3XWJE5OLRYCSWFNJGHKV6PTK}

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	2026-05-18T01:12:44.763616Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7df77b249d72e3814ac56a4c7557cf9abd50a14e033869cf1c1dc4e5b1d89094

Aliases

arxiv: 1606.02028 · arxiv_version: 1606.02028v1 · doi: 10.48550/arxiv.1606.02028 · pith_short_12: PX3XWJE5OLRY · pith_short_16: PX3XWJE5OLRYCSWF · pith_short_8: PX3XWJE5

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/PX3XWJE5OLRYCSWFNJGHKV6PTK \
  | 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: 7df77b249d72e3814ac56a4c7557cf9abd50a14e033869cf1c1dc4e5b1d89094

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d6d1d0776d93cf3383329854ce00fee34634fa41f454fe9b7340705186d961e8",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-06-07T04:38:50Z",
    "title_canon_sha256": "87500d04e30620b45dab98d6e4585486cf14f4be6df19fbc55539e22287e342c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.02028",
    "kind": "arxiv",
    "version": 1
  }
}