Pith Number

pith:TYY7Y3ZF

pith:2026:TYY7Y3ZFX5727ZU5D6CANZE2NI

not attested not anchored not stored refs pending

On the Schur-positivity of various sets of set partitions

David Garber, Eli Bagno

arxiv:2606.20185 v1 · 2026-06-14 · 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{TYY7Y3ZFX5727ZU5D6CANZE2NI}

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	2026-06-19T16:13:05.082758Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e31fc6f25bf7fafe69d1f8406e49a6a2b1bd2f9d42a4568c02baeac1aa69307

Aliases

arxiv: 2606.20185 · arxiv_version: 2606.20185v1 · doi: 10.48550/arxiv.2606.20185 · pith_short_12: TYY7Y3ZFX572 · pith_short_16: TYY7Y3ZFX5727ZU5 · pith_short_8: TYY7Y3ZF

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/TYY7Y3ZFX5727ZU5D6CANZE2NI \
  | 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: 9e31fc6f25bf7fafe69d1f8406e49a6a2b1bd2f9d42a4568c02baeac1aa69307

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dd940990fdd945d996293c07332c022fd32ff869bed80e29093b6cdb52ad388e",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-14T14:22:55Z",
    "title_canon_sha256": "9817230af9682d8ae86e3ce8feb9803d5cf62046d934a457b3205177934d7848"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.20185",
    "kind": "arxiv",
    "version": 1
  }
}