Pith Number

pith:5WJ2JCOU

pith:2015:5WJ2JCOUTUZWNTNZU3NBGB2UJ7

not attested not anchored not stored refs pending

Generalizing the Single-Crossing Property on Lines and Trees to Intermediate Preferences on Median Graphs

Adam Clearwater, Arkadii Slinko, Clemens Puppe

arxiv:1505.06982 v1 · 2015-05-25 · cs.GT · 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{5WJ2JCOUTUZWNTNZU3NBGB2UJ7}

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	2026-05-18T02:03:27.393556Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed93a489d49d3366cdb9a6da1307544ffc9cc1760e5f28665e4746a55d60fbf1

Aliases

arxiv: 1505.06982 · arxiv_version: 1505.06982v1 · doi: 10.48550/arxiv.1505.06982 · pith_short_12: 5WJ2JCOUTUZW · pith_short_16: 5WJ2JCOUTUZWNTNZ · pith_short_8: 5WJ2JCOU

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/5WJ2JCOUTUZWNTNZU3NBGB2UJ7 \
  | 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: ed93a489d49d3366cdb9a6da1307544ffc9cc1760e5f28665e4746a55d60fbf1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e7c9ccd6ba70663dc337dd9e3ff9e678ed9c73969960e85516e595c0e0f42703",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.GT",
    "submitted_at": "2015-05-25T18:32:54Z",
    "title_canon_sha256": "695ec02daaaa47f4e74f7f51359faeb7db81be7aea86e0112e09d06bdb5c6f46"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.06982",
    "kind": "arxiv",
    "version": 1
  }
}