Pith Number

pith:ZAAOPTWB

pith:2010:ZAAOPTWBK6W63PHTAYZ54GTX3E

not attested not anchored not stored refs pending

Enumeration of bigrassmannian permutations below a permutation in Bruhat order

Masato Kobayashi

arxiv:1005.3335 v1 · 2010-05-18 · 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{ZAAOPTWBK6W63PHTAYZ54GTX3E}

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	2026-07-04T17:28:56.768955Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c800e7cec157adedbcf30633de1a77d9081bdba289170b65a6260fe978e05674

Aliases

arxiv: 1005.3335 · arxiv_version: 1005.3335v1 · doi: 10.48550/arxiv.1005.3335 · pith_short_12: ZAAOPTWBK6W6 · pith_short_16: ZAAOPTWBK6W63PHT · pith_short_8: ZAAOPTWB

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/ZAAOPTWBK6W63PHTAYZ54GTX3E \
  | 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: c800e7cec157adedbcf30633de1a77d9081bdba289170b65a6260fe978e05674

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "35f412357d6da592b9e442d61cfa5d0cff8164e32aa5ebfbfb16707e8b7accfb",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-05-18T21:38:28Z",
    "title_canon_sha256": "d9a929e418f2f18b707d6488ed99a0f0a37505f68262ff2326d9f944ec36c6ed"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1005.3335",
    "kind": "arxiv",
    "version": 1
  }
}