Pith Number

pith:5VI2C6JN

pith:2014:5VI2C6JNQPDGX7GRV4ZMDCMSLF

not attested not anchored not stored refs pending

Intervals of Permutations with a Fixed Number of Descents are Shellable

Jason P. Smith

arxiv:1405.2560 v4 · 2014-05-11 · 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{5VI2C6JNQPDGX7GRV4ZMDCMSLF}

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	2026-05-18T01:36:07.314547Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed51a1792d83c66bfcd1af32c18992594969052f098603e0e6b0969e75706d9c

Aliases

arxiv: 1405.2560 · arxiv_version: 1405.2560v4 · doi: 10.48550/arxiv.1405.2560 · pith_short_12: 5VI2C6JNQPDG · pith_short_16: 5VI2C6JNQPDGX7GR · pith_short_8: 5VI2C6JN

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/5VI2C6JNQPDGX7GRV4ZMDCMSLF \
  | 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: ed51a1792d83c66bfcd1af32c18992594969052f098603e0e6b0969e75706d9c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1891345ea10cb1f5217f857b13e2348fdfcca0c2898eba58c3a2d7f6804875e1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-05-11T18:13:04Z",
    "title_canon_sha256": "c15890020237f2f0f0695662acb145096bdf09c40fa0045268ce4099d40f4a7a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1405.2560",
    "kind": "arxiv",
    "version": 4
  }
}