Pith Number

pith:JXMP6RX6

pith:2014:JXMP6RX6XLR5WUEHROJ4ESVWVV

not attested not anchored not stored refs pending

On the Real-rootedness of the Descent Polynomials of $(n-2)$-Stack Sortable Permutations

Philip B. Zhang

arxiv:1408.4235 v2 · 2014-08-19 · 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{JXMP6RX6XLR5WUEHROJ4ESVWVV}

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	2026-05-18T01:21:16.194782Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4dd8ff46febae3db50878b93c24ab6ad5ff9ddb7085c42a1a59923f69225e087

Aliases

arxiv: 1408.4235 · arxiv_version: 1408.4235v2 · doi: 10.48550/arxiv.1408.4235 · pith_short_12: JXMP6RX6XLR5 · pith_short_16: JXMP6RX6XLR5WUEH · pith_short_8: JXMP6RX6

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/JXMP6RX6XLR5WUEHROJ4ESVWVV \
  | 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: 4dd8ff46febae3db50878b93c24ab6ad5ff9ddb7085c42a1a59923f69225e087

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1586d172870e8aa208a7512a62d585072eba3fa04f995a171bf1ebe016337116",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-08-19T07:30:37Z",
    "title_canon_sha256": "db6d53485a6e93ce9e4c535fedd128a98b8025df8a048bafd50f7d0dfe2e3c6a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1408.4235",
    "kind": "arxiv",
    "version": 2
  }
}