Pith Number

pith:3H6UD3Y5

pith:2014:3H6UD3Y5O656CXTOX2CIWOIOBE

not attested not anchored not stored refs pending

Consequences of the Lakshmibai-Sandhya Theorem: the ubiquity of permutation patterns in Schubert calculus and related geometry

Hiraku Abe, Sara Billey

arxiv:1403.4345 v1 · 2014-03-18 · math.CO · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3H6UD3Y5O656CXTOX2CIWOIOBE}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T02:56:05.970847Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d9fd41ef1d77bbe15e6ebe848b390e091becc845b35b77fa615b0967a5078631

Aliases

arxiv: 1403.4345 · arxiv_version: 1403.4345v1 · doi: 10.48550/arxiv.1403.4345 · pith_short_12: 3H6UD3Y5O656 · pith_short_16: 3H6UD3Y5O656CXTO · pith_short_8: 3H6UD3Y5

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/3H6UD3Y5O656CXTOX2CIWOIOBE \
  | 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: d9fd41ef1d77bbe15e6ebe848b390e091becc845b35b77fa615b0967a5078631

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aa61e9647186975da048bf796c8ae47cabd5f581b039a655a0749440115ba6cd",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-03-18T05:19:47Z",
    "title_canon_sha256": "5559fa13e4e40ee7799468ca57d9b0457fb0631075f039b2a5412840f8622ba8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1403.4345",
    "kind": "arxiv",
    "version": 1
  }
}