Pith Number

pith:Z7A3C6RI

pith:2015:Z7A3C6RIGWAYUN5WZ4NLA2FVHI

not attested not anchored not stored refs pending

Modified Linear Programming and Class 0 Bounds for Graph Pebbling

Carl Yerger, Chenxiao Xue, Daniel W. Cranston, Luke Postle

arxiv:1508.07299 v1 · 2015-08-28 · 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{Z7A3C6RIGWAYUN5WZ4NLA2FVHI}

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	2026-05-18T00:42:33.308867Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cfc1b17a2835818a37b6cf1ab068b53a06064ed9d3b340f5196ec4d741ad7048

Aliases

arxiv: 1508.07299 · arxiv_version: 1508.07299v1 · doi: 10.48550/arxiv.1508.07299 · pith_short_12: Z7A3C6RIGWAY · pith_short_16: Z7A3C6RIGWAYUN5W · pith_short_8: Z7A3C6RI

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/Z7A3C6RIGWAYUN5WZ4NLA2FVHI \
  | 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: cfc1b17a2835818a37b6cf1ab068b53a06064ed9d3b340f5196ec4d741ad7048

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "be71674e542f3fa8b76d7e9732c7ecb7df520092d8f9d15abadde6f6fe779dc4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-08-28T18:11:47Z",
    "title_canon_sha256": "c81f731f64fe1ae0115064aefe8dabcbd218a5607ee15ac274f1f9074eef92ad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.07299",
    "kind": "arxiv",
    "version": 1
  }
}