Pith Number

pith:L5OWUCA7

pith:2016:L5OWUCA7SHH2UJJIWPGDUSHHGS

not attested not anchored not stored refs pending

Euler-Mahonian statistics and descent bases for semigroup algebras

Benjamin Braun, McCabe Olsen

arxiv:1606.03007 v3 · 2016-06-09 · math.CO · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{L5OWUCA7SHH2UJJIWPGDUSHHGS}

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	2026-05-18T00:18:54.207186Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5f5d6a081f91cfaa2528b3cc3a48e734b613ef06689d4ae35be9eb6e64953443

Aliases

arxiv: 1606.03007 · arxiv_version: 1606.03007v3 · doi: 10.48550/arxiv.1606.03007 · pith_short_12: L5OWUCA7SHH2 · pith_short_16: L5OWUCA7SHH2UJJI · pith_short_8: L5OWUCA7

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/L5OWUCA7SHH2UJJIWPGDUSHHGS \
  | 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: 5f5d6a081f91cfaa2528b3cc3a48e734b613ef06689d4ae35be9eb6e64953443

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0f9abb6ddbbeef3f88b05a47ba382a64cd9378abbb31968f0e7b16ad362ff375",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-06-09T15:54:00Z",
    "title_canon_sha256": "a49ad643ae79fd5b6045e6d760fd95e7706a2f645a29f7fbf391eab96e341e9a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.03007",
    "kind": "arxiv",
    "version": 3
  }
}