Pith Number

pith:GOUP6HDQ

pith:2010:GOUP6HDQTYMYIDOQHARJ3H4GYJ

not attested not anchored not stored refs pending

The Weak Bruhat Order and Separable Permutations

Fan Wei

arxiv:1009.5740 v1 · 2010-09-29 · 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{GOUP6HDQTYMYIDOQHARJ3H4GYJ}

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	2026-05-18T04:40:09.035034Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

33a8ff1c709e19840dd038229d9f86c24c226796a08b09ca68668a11b3fae523

Aliases

arxiv: 1009.5740 · arxiv_version: 1009.5740v1 · doi: 10.48550/arxiv.1009.5740 · pith_short_12: GOUP6HDQTYMY · pith_short_16: GOUP6HDQTYMYIDOQ · pith_short_8: GOUP6HDQ

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/GOUP6HDQTYMYIDOQHARJ3H4GYJ \
  | 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: 33a8ff1c709e19840dd038229d9f86c24c226796a08b09ca68668a11b3fae523

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c1fd85f111191bef3b9b190406d7594775363d1f2882633a75ab530568816bf3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-09-29T01:59:21Z",
    "title_canon_sha256": "2bf49e2c3ffc7a3f4100d501455fccb86cb13901282ac16cee3b5950b8bc2ae5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.5740",
    "kind": "arxiv",
    "version": 1
  }
}