Pith Number

pith:L2LG6TP6

pith:2026:L2LG6TP6U2YDMRZ6ELKUXY7AXR

not attested not anchored not stored refs pending

Almost-perfect packings and Tuza's conjecture in the random geometric graph

Andrzej Dudek, Patrick Bennett, Ryan Cushman, Xavier P\'erez-Gim\'enez

arxiv:2606.09736 v1 · 2026-06-08 · 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{L2LG6TP6U2YDMRZ6ELKUXY7AXR}

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	2026-06-09T02:09:06.820827Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5e966f4dfea6b036473e22d54be3e0bc53b136c99fc123e4d71c3ef9a7e0f280

Aliases

arxiv: 2606.09736 · arxiv_version: 2606.09736v1 · doi: 10.48550/arxiv.2606.09736 · pith_short_12: L2LG6TP6U2YD · pith_short_16: L2LG6TP6U2YDMRZ6 · pith_short_8: L2LG6TP6

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/L2LG6TP6U2YDMRZ6ELKUXY7AXR \
  | 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: 5e966f4dfea6b036473e22d54be3e0bc53b136c99fc123e4d71c3ef9a7e0f280

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "49feec2ac49331c1249aff34c27ec27f10286d4f1090193037e728b72be202af",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-08T17:00:40Z",
    "title_canon_sha256": "6c4075a4f128689389eb910a2b16e5d651e7456e55e25521aef192e30035a22b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.09736",
    "kind": "arxiv",
    "version": 1
  }
}