Pith Number

pith:KKZZT2SE

pith:2026:KKZZT2SEOEKMCDQL2PWGE752KP

not attested not anchored not stored refs pending

The density of $k$-cacti via excluding minors

Licheng Zhang, Yuanqiu Huang

arxiv:2606.06298 v1 · 2026-06-04 · 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{KKZZT2SEOEKMCDQL2PWGE752KP}

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	2026-06-05T01:15:40.887892Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

52b399ea447114c10e0bd3ec627fba53f968fec20d07ab9ed8e228064bf7aca7

Aliases

arxiv: 2606.06298 · arxiv_version: 2606.06298v1 · doi: 10.48550/arxiv.2606.06298 · pith_short_12: KKZZT2SEOEKM · pith_short_16: KKZZT2SEOEKMCDQL · pith_short_8: KKZZT2SE

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/KKZZT2SEOEKMCDQL2PWGE752KP \
  | 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: 52b399ea447114c10e0bd3ec627fba53f968fec20d07ab9ed8e228064bf7aca7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb942155cce0b37c2794ab9c09a5b5439b0ebc0a565e3d3f7a49c29f9d461f3d",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-04T15:36:57Z",
    "title_canon_sha256": "578cd7452c6ecd1a857a37f37e91d0c530085b1cb4646f1b37b5c205ca4bac12"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.06298",
    "kind": "arxiv",
    "version": 1
  }
}