Pith Number

pith:OGNJTHIL

pith:2017:OGNJTHILZEJWFH3TT4D7DKBLLR

not attested not anchored not stored refs pending

Combinatorics of cyclic shifts in plactic, hypoplactic, sylvester, Baxter, and related monoids

Alan J. Cain, Ant\'onio Malheiro

arxiv:1709.03974 v1 · 2017-09-12 · math.CO · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OGNJTHILZEJWFH3TT4D7DKBLLR}

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	2026-05-18T00:35:28.907233Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

719a999d0bc913629f739f07f1a82b5c7e2de77f41d7f9753e7243a66a7ec2c2

Aliases

arxiv: 1709.03974 · arxiv_version: 1709.03974v1 · doi: 10.48550/arxiv.1709.03974 · pith_short_12: OGNJTHILZEJW · pith_short_16: OGNJTHILZEJWFH3T · pith_short_8: OGNJTHIL

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/OGNJTHILZEJWFH3TT4D7DKBLLR \
  | 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: 719a999d0bc913629f739f07f1a82b5c7e2de77f41d7f9753e7243a66a7ec2c2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d9201da4bfcb32abde2a7884611ecf4bd66a190c72cb19d0d6232545191d5a4a",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-09-12T17:58:28Z",
    "title_canon_sha256": "43cc2e822080e4aa091757c1d5e07a382bcd87246d57a4b8be0d305ab16d5e2a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1709.03974",
    "kind": "arxiv",
    "version": 1
  }
}