Pith Number

pith:PJQQBQ7I

pith:2021:PJQQBQ7IVSB4NFL6YL7I7CBNUK

not attested not anchored not stored refs pending

Extending higher Bruhat orders to non-longest words in $S_n$

Daniel Hothem

arxiv:2105.15181 v1 · 2021-05-31 · 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{PJQQBQ7IVSB4NFL6YL7I7CBNUK}

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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.

Cited by

1 paper in Pith

Commutation classes of reduced words and higher Bruhat orders for affine permutations

Receipt and verification

First computed	2026-07-05T02:44:45.714112Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a6100c3e8ac83c6957ec2fe8f882da288ab23058c2a7110a3cb14440535d918

Aliases

arxiv: 2105.15181 · arxiv_version: 2105.15181v1 · doi: 10.48550/arxiv.2105.15181 · pith_short_12: PJQQBQ7IVSB4 · pith_short_16: PJQQBQ7IVSB4NFL6 · pith_short_8: PJQQBQ7I

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/PJQQBQ7IVSB4NFL6YL7I7CBNUK \
  | 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: 7a6100c3e8ac83c6957ec2fe8f882da288ab23058c2a7110a3cb14440535d918

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3ac67c7be84168a97c9f3a75742d6e9cea495ec3f3511cccf09eadf1f50d6167",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2021-05-31T17:45:02Z",
    "title_canon_sha256": "b5a44abb015923861acf466a575f1efc68f1d344a6c586db07bdc009d1505d9e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2105.15181",
    "kind": "arxiv",
    "version": 1
  }
}