Pith Number

pith:LT4WA6BG

pith:2026:LT4WA6BGC7TSOL5QGPDX3L4QNG

not attested not anchored not stored refs pending

Contractions and applications of crystal skeletons: Young quasisymmetric and Stanley symmetric functions

Anne Schilling, Sarah Brauner, Sarah Mason, Zajj Daugherty

arxiv:2607.12232 v1 · 2026-07-14 · math.CO · math.QA · math.RT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LT4WA6BGC7TSOL5QGPDX3L4QNG}

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	2026-07-15T00:21:39.767834Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5cf960782617e7272fb033c77daf9069a04eae365bb1d2e8c7dbc369c5d58f23

Aliases

arxiv: 2607.12232 · arxiv_version: 2607.12232v1 · doi: 10.48550/arxiv.2607.12232 · pith_short_12: LT4WA6BGC7TS · pith_short_16: LT4WA6BGC7TSOL5Q · pith_short_8: LT4WA6BG

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/LT4WA6BGC7TSOL5QGPDX3L4QNG \
  | 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: 5cf960782617e7272fb033c77daf9069a04eae365bb1d2e8c7dbc369c5d58f23

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "12734b9eded3785ff43016f1a42c0c1b1679c6da7a25aad3bc557c4c33d81ef1",
    "cross_cats_sorted": [
      "math.QA",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-14T00:26:36Z",
    "title_canon_sha256": "61e06c6e7d7712aa83c53962e1f8c2f6935f04dfe859628ed904482c0f57c0c1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.12232",
    "kind": "arxiv",
    "version": 1
  }
}