Pith Number

pith:ZG3VCZJX

pith:2026:ZG3VCZJX5IJJPNYVAVDPNBPCTG

not attested not anchored not stored refs pending

On separable permutations and three other pairs in the Schr\"oder class

Juan B. Gil, Michael D. Weiner, Oscar A. Lopez

arxiv:2603.25528 v2 · 2026-03-26 · 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{ZG3VCZJX5IJJPNYVAVDPNBPCTG}

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	2026-06-08T01:04:02.352855Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c9b7516537ea1297b7150546f685e2998c928152f6ac78dbd2369c2292e06440

Aliases

arxiv: 2603.25528 · arxiv_version: 2603.25528v2 · doi: 10.48550/arxiv.2603.25528 · pith_short_12: ZG3VCZJX5IJJ · pith_short_16: ZG3VCZJX5IJJPNYV · pith_short_8: ZG3VCZJX

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/ZG3VCZJX5IJJPNYVAVDPNBPCTG \
  | 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: c9b7516537ea1297b7150546f685e2998c928152f6ac78dbd2369c2292e06440

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f341f2106999d4f5529778c6cdcbc236543d6f1378f49f78e34e8182de6d942b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-03-26T15:00:56Z",
    "title_canon_sha256": "12120fc6821135b2a519519263b318060a96cbb8b77cf4c2a3f3f4a0b2d9c029"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.25528",
    "kind": "arxiv",
    "version": 2
  }
}