Pith Number

pith:OLO6BYKA

pith:2023:OLO6BYKAH6NIEAGA6KYZ547DEN

not attested not anchored not stored refs pending

The Density Formula: One Lemma to Bound Them All

Boris Klemz, Felix Schr\"oder, Kristin Knorr, Meghana M. Reddy, Michael Kaufmann, Torsten Ueckerdt

arxiv:2311.06193 v3 · 2023-11-10 · 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{OLO6BYKAH6NIEAGA6KYZ547DEN}

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.

Cited by

1 paper in Pith

Outer-(ap)RAC Graphs

Receipt and verification

First computed	2026-07-05T09:08:21.648233Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

72dde0e1403f9a8200c0f2b19ef3e323654785f32dbe8eee90137adc45911127

Aliases

arxiv: 2311.06193 · arxiv_version: 2311.06193v3 · doi: 10.48550/arxiv.2311.06193 · pith_short_12: OLO6BYKAH6NI · pith_short_16: OLO6BYKAH6NIEAGA · pith_short_8: OLO6BYKA

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/OLO6BYKAH6NIEAGA6KYZ547DEN \
  | 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: 72dde0e1403f9a8200c0f2b19ef3e323654785f32dbe8eee90137adc45911127

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eb256216576272318ca13f14af582156464f6ad71083497286a092f20a68e740",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2023-11-10T17:18:12Z",
    "title_canon_sha256": "607f0a1cdf6249cd0d91da2a752ae59859db899711800786ddbc4b98a1076e00"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2311.06193",
    "kind": "arxiv",
    "version": 3
  }
}