Pith Number

pith:ADBGHYG3

pith:2019:ADBGHYG3VFDVPSHBBTLUCWUETL

not attested not anchored not stored refs pending

An Omega(n^2) Lower Bound for Random Universal Sets for Planar Graphs

Alexander Choi, Kevin Costello, Marek Chrobak

arxiv:1908.07097 v2 · 2019-08-19 · cs.DM · cs.CG · 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{ADBGHYG3VFDVPSHBBTLUCWUETL}

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	2026-07-05T00:03:58.273261Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

00c263e0dba94757c8e10cd7415a849ac203ac510fa422ed0d00f8089f1dd103

Aliases

arxiv: 1908.07097 · arxiv_version: 1908.07097v2 · doi: 10.48550/arxiv.1908.07097 · pith_short_12: ADBGHYG3VFDV · pith_short_16: ADBGHYG3VFDVPSHB · pith_short_8: ADBGHYG3

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/ADBGHYG3VFDVPSHBBTLUCWUETL \
  | 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: 00c263e0dba94757c8e10cd7415a849ac203ac510fa422ed0d00f8089f1dd103

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "167526aba8878f608e2e8d65144b6424a7446719538e49f8afab7b54f92d9578",
    "cross_cats_sorted": [
      "cs.CG",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2019-08-19T22:57:53Z",
    "title_canon_sha256": "ef3feb39a273c70a165442b2feaf56816f977b565e142b2de21233bebe575a56"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.07097",
    "kind": "arxiv",
    "version": 2
  }
}