Pith Number

pith:2ZRL3VHK

pith:2026:2ZRL3VHKPUJYJWPPB5KJTZULYO

not attested not anchored not stored refs pending

Intersecting Families of Spanning Trees of $K_{n,n}$

Alexander L. Gavrilyuk, Dheer Noal Desai, Gordian C. Bruns, Josias Gomez, Nathan Lindzey

arxiv:2606.22697 v1 · 2026-06-21 · 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{2ZRL3VHKPUJYJWPPB5KJTZULYO}

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	2026-06-23T02:13:45.122470Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d662bdd4ea7d1384d9ef0f5499e68bc3a30ebd4ab1dd5727f8dab4abba6a0075

Aliases

arxiv: 2606.22697 · arxiv_version: 2606.22697v1 · doi: 10.48550/arxiv.2606.22697 · pith_short_12: 2ZRL3VHKPUJY · pith_short_16: 2ZRL3VHKPUJYJWPP · pith_short_8: 2ZRL3VHK

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/2ZRL3VHKPUJYJWPPB5KJTZULYO \
  | 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: d662bdd4ea7d1384d9ef0f5499e68bc3a30ebd4ab1dd5727f8dab4abba6a0075

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "26fee71aaca66a22783ab91ac0affc508510ce83efacf960ed3ae444a0ba005c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-21T22:23:59Z",
    "title_canon_sha256": "ccdca2ec4667fd9ea30b2444bb50e1954b03daea624a6a1f70bf67510d2bfb45"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.22697",
    "kind": "arxiv",
    "version": 1
  }
}