Pith Number

pith:423CEAH4

pith:2026:423CEAH4O47AGAN3H3XVBAKFEC

not attested not anchored not stored refs pending

Monotonicity of the rank functions for concave compositions

Nian Hong Zhou

arxiv:2606.13274 v1 · 2026-06-11 · 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{423CEAH4O47AGAN3H3XVBAKFEC}

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	2026-06-12T01:09:50.030727Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e6b62200fc773e0301bb3eef50814520b39819a0e7f10af7dc22fd860a82c378

Aliases

arxiv: 2606.13274 · arxiv_version: 2606.13274v1 · doi: 10.48550/arxiv.2606.13274 · pith_short_12: 423CEAH4O47A · pith_short_16: 423CEAH4O47AGAN3 · pith_short_8: 423CEAH4

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/423CEAH4O47AGAN3H3XVBAKFEC \
  | 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: e6b62200fc773e0301bb3eef50814520b39819a0e7f10af7dc22fd860a82c378

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3fa92ad42dc70cf77b340a4b5af7cee6be4cd981ff1421f773d932eb22e73655",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-11T12:27:41Z",
    "title_canon_sha256": "d75f71c69dd203845a2ec43c47b74aed1946c6f6bd887d0b0393de7586a14d4b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.13274",
    "kind": "arxiv",
    "version": 1
  }
}