Pith Number

pith:Z4LZLQG2

pith:2026:Z4LZLQG2NXSCVABBLQXQICPUAY

not attested not anchored not stored refs pending

Extremal graphs with no subgraph admitting $k+1$ edge-disjoint spanning trees

Qinglin Wang, Yingzhi Tian

arxiv:2606.28198 v1 · 2026-06-26 · 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{Z4LZLQG2NXSCVABBLQXQICPUAY}

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	2026-06-29T01:15:09.016143Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf1795c0da6de42a80215c2f0409f4063c3a34e274394c0f89c286d2d82d05b5

Aliases

arxiv: 2606.28198 · arxiv_version: 2606.28198v1 · doi: 10.48550/arxiv.2606.28198 · pith_short_12: Z4LZLQG2NXSC · pith_short_16: Z4LZLQG2NXSCVABB · pith_short_8: Z4LZLQG2

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/Z4LZLQG2NXSCVABBLQXQICPUAY \
  | 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: cf1795c0da6de42a80215c2f0409f4063c3a34e274394c0f89c286d2d82d05b5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bbdc72f4571ed58b1881461670c20a02fe54ff7ea2f3f4575919fe171d8c452f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-26T15:48:16Z",
    "title_canon_sha256": "6bf8559cdcf6c8d3b190d7d5d3edba3c94de05e0538bc341bc18cf0590a59516"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.28198",
    "kind": "arxiv",
    "version": 1
  }
}