Pith Number

pith:CUXLU4UT

pith:2026:CUXLU4UTAT6RZMGFZDIFYJ3L7Q

not attested not anchored not stored refs pending

A Characterization of the $2m-4$ Case of Highly Sorted Permutations

Kai Yi

arxiv:2606.08429 v1 · 2026-06-07 · 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{CUXLU4UTAT6RZMGFZDIFYJ3L7Q}

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	2026-06-09T01:05:36.353572Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

152eba729304fd1cb0c5c8d05c276bfc2d735611cdad61f3b5c33421f6398dbb

Aliases

arxiv: 2606.08429 · arxiv_version: 2606.08429v1 · doi: 10.48550/arxiv.2606.08429 · pith_short_12: CUXLU4UTAT6R · pith_short_16: CUXLU4UTAT6RZMGF · pith_short_8: CUXLU4UT

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/CUXLU4UTAT6RZMGFZDIFYJ3L7Q \
  | 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: 152eba729304fd1cb0c5c8d05c276bfc2d735611cdad61f3b5c33421f6398dbb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c05b44056768631f423ef61142bbb407cd902faddd5129266ecdcde230dd1866",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-07T03:02:28Z",
    "title_canon_sha256": "04800b505ff6792150417288c06181e4b53643c3fb76d45e1fd582be79a3824c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.08429",
    "kind": "arxiv",
    "version": 1
  }
}