Pith Number

pith:P7YZ4EIW

pith:2019:P7YZ4EIW5CXRLK3MPVIEAKHSHA

not attested not anchored not stored refs pending

$\beta$-Packing Sets in Graphs

Benjamin M. Case, Evan M. Haithcock, Renu C. Laskar

arxiv:1906.00073 v1 · 2019-05-31 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{P7YZ4EIW5CXRLK3MPVIEAKHSHA}

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	2026-05-17T23:44:33.536999Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ff19e1116e8af15ab6c7d504028f2382347ad392f58e2ef92414dd6cd1af5d4

Aliases

arxiv: 1906.00073 · arxiv_version: 1906.00073v1 · doi: 10.48550/arxiv.1906.00073 · pith_short_12: P7YZ4EIW5CXR · pith_short_16: P7YZ4EIW5CXRLK3M · pith_short_8: P7YZ4EIW

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/P7YZ4EIW5CXRLK3MPVIEAKHSHA \
  | 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: 7ff19e1116e8af15ab6c7d504028f2382347ad392f58e2ef92414dd6cd1af5d4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e4248447e0113a9c57710f12c0b78f7778434384ee1dbdb08155a45ee55cf4c8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-05-31T20:45:25Z",
    "title_canon_sha256": "a4cfb50401f216e97b0f98841adba4cd031fdfbb6b6725aeff32af2b7970182f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.00073",
    "kind": "arxiv",
    "version": 1
  }
}