Pith Number

pith:VPBYKMC6

pith:2020:VPBYKMC6TOK3COO3N2OHIBQ5XD

not attested not anchored not stored refs pending

On regular and random two-dimensional packing of crosses

Jonas Schulze, Ralf Stannarius

arxiv:2011.06581 v3 · 2020-11-07 · cond-mat.stat-mech

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VPBYKMC6TOK3COO3N2OHIBQ5XD}

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	2026-07-05T03:30:50.556956Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

abc385305e9b95b139db6e9c74061db8d83a70ab18bff4b0e95dc97d4141312f

Aliases

arxiv: 2011.06581 · arxiv_version: 2011.06581v3 · doi: 10.48550/arxiv.2011.06581 · pith_short_12: VPBYKMC6TOK3 · pith_short_16: VPBYKMC6TOK3COO3 · pith_short_8: VPBYKMC6

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/VPBYKMC6TOK3COO3N2OHIBQ5XD \
  | 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: abc385305e9b95b139db6e9c74061db8d83a70ab18bff4b0e95dc97d4141312f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3f9ea5f8458f6a827c9836a7a45c34f19718708709292ecde6806e89e646a7ee",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2020-11-07T19:19:27Z",
    "title_canon_sha256": "f83501ddb9e72dcc612c1fd88dfead8cfc81561f626b000116ec9758f6f97f58"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2011.06581",
    "kind": "arxiv",
    "version": 3
  }
}