Pith Number

pith:GCLTY4JZ

pith:2012:GCLTY4JZ6GC7Q5ZP6WOVIZ6MLI

not attested not anchored not stored refs pending

Descent polynomials for k bubble-sortable permutations of type B

Matthew Hyatt

arxiv:1205.1014 v1 · 2012-05-04 · 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{GCLTY4JZ6GC7Q5ZP6WOVIZ6MLI}

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	2026-05-18T03:56:23.350922Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

30973c7139f185f8772ff59d5467cc5a2efb9d5db4a83fecd2a847e70b00edbe

Aliases

arxiv: 1205.1014 · arxiv_version: 1205.1014v1 · doi: 10.48550/arxiv.1205.1014 · pith_short_12: GCLTY4JZ6GC7 · pith_short_16: GCLTY4JZ6GC7Q5ZP · pith_short_8: GCLTY4JZ

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/GCLTY4JZ6GC7Q5ZP6WOVIZ6MLI \
  | 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: 30973c7139f185f8772ff59d5467cc5a2efb9d5db4a83fecd2a847e70b00edbe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bdd937bfe9c3de8afde049eeecf8b62f6e7060e502485d2d0f20922139ff775d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-05-04T17:25:10Z",
    "title_canon_sha256": "acd6849b3039f30d79bd727af77720d886b9f3280b652f65cc534959052fec0b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.1014",
    "kind": "arxiv",
    "version": 1
  }
}