Pith Number

pith:WUZY26IE

pith:2026:WUZY26IE3QEQPG6WVT4TJYFTFB

not attested not anchored not stored refs pending

Obstructions for Minor-Closed Classes of limiting Densities Below 3/2

Antonios Kominatos, Dimitrios M. Thilikos, Reem Mahmoud

arxiv:2606.24326 v1 · 2026-06-23 · 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{WUZY26IE3QEQPG6WVT4TJYFTFB}

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	2026-06-24T01:14:50.060561Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b5338d7904dc09079bd6acf934e0b3286dd0bb62ff41388def069353499c8bda

Aliases

arxiv: 2606.24326 · arxiv_version: 2606.24326v1 · doi: 10.48550/arxiv.2606.24326 · pith_short_12: WUZY26IE3QEQ · pith_short_16: WUZY26IE3QEQPG6W · pith_short_8: WUZY26IE

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/WUZY26IE3QEQPG6WVT4TJYFTFB \
  | 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: b5338d7904dc09079bd6acf934e0b3286dd0bb62ff41388def069353499c8bda

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "78d555b6fad7bac2c90b79cfdb3fc6bed8df2829017523275dae4d235b1ff15d",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-23T09:02:50Z",
    "title_canon_sha256": "bdedb6d45b5f541d3170cc50b5a47b8cc84ad8b2ee22e3430790b7ffd8df3909"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.24326",
    "kind": "arxiv",
    "version": 1
  }
}