Pith Number

pith:XJEW7GGW

pith:2017:XJEW7GGWQ4TPEKB6RVVMA4UXAC

not attested not anchored not stored refs pending

A bijective proof of Macdonald's reduced word formula

Alexander E. Holroyd, Benjamin Young, Sara C. Billey

arxiv:1702.02936 v1 · 2017-02-09 · 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{XJEW7GGWQ4TPEKB6RVVMA4UXAC}

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	2026-05-18T00:51:02.011855Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba496f98d68726f2283e8d6ac0729700b777f52b9dce206605630b042cadaecc

Aliases

arxiv: 1702.02936 · arxiv_version: 1702.02936v1 · doi: 10.48550/arxiv.1702.02936 · pith_short_12: XJEW7GGWQ4TP · pith_short_16: XJEW7GGWQ4TPEKB6 · pith_short_8: XJEW7GGW

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/XJEW7GGWQ4TPEKB6RVVMA4UXAC \
  | 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: ba496f98d68726f2283e8d6ac0729700b777f52b9dce206605630b042cadaecc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ff677b78a82a05004eb5ae4bc67549a5a2224251bd22b11b968930208fe9c308",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-02-09T18:45:18Z",
    "title_canon_sha256": "ad4d17bdc98dc7fef4852901e09e28917f16c776a400acb93a3c35cf2ba3bd04"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1702.02936",
    "kind": "arxiv",
    "version": 1
  }
}