Pith Number

pith:QPPZAZPH

pith:2015:QPPZAZPHS5XSZHDJHOXTGUS5HC

not attested not anchored not stored refs pending

Dimension and cut vertices: an application of Ramsey theory

Bartosz Walczak, Ruidong Wang, William T. Trotter

arxiv:1505.08162 v4 · 2015-05-29 · math.CO · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QPPZAZPHS5XSZHDJHOXTGUS5HC}

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	2026-05-17T23:58:50.676671Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

83df9065e7976f2c9c693baf33525d38bdbffb9e4efd50357d407e41e6a25b1f

Aliases

arxiv: 1505.08162 · arxiv_version: 1505.08162v4 · doi: 10.48550/arxiv.1505.08162 · pith_short_12: QPPZAZPHS5XS · pith_short_16: QPPZAZPHS5XSZHDJ · pith_short_8: QPPZAZPH

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/QPPZAZPHS5XSZHDJHOXTGUS5HC \
  | 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: 83df9065e7976f2c9c693baf33525d38bdbffb9e4efd50357d407e41e6a25b1f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5052295dbe4ab4b6b361d80f0939e8bf9b191398a3b8a7ae664fd2f7268a969f",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-05-29T19:36:02Z",
    "title_canon_sha256": "52f48b3d0c069dc6e754f388361ead2ec6ab6ea008638fc2affbbabf20601a67"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.08162",
    "kind": "arxiv",
    "version": 4
  }
}