Pith Number

pith:CRFKEM3V

pith:2020:CRFKEM3VXB452T3IXQJTW27VQP

not attested not anchored not stored refs pending

Bijective Proofs of Monk's rule for Schubert and Double Schubert Polynomials with Bumpless Pipe Dreams

Daoji Huang

arxiv:2010.15048 v1 · 2020-10-28 · 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{CRFKEM3VXB452T3IXQJTW27VQP}

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.

Cited by

1 paper in Pith

Hybrid pipe dreams for the lower-upper scheme

Receipt and verification

First computed	2026-07-05T01:47:27.240840Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

144aa23375b879dd4f68bc133b6bf583f9cae24a4d78ceb2c710c75fdc3861ea

Aliases

arxiv: 2010.15048 · arxiv_version: 2010.15048v1 · doi: 10.48550/arxiv.2010.15048 · pith_short_12: CRFKEM3VXB45 · pith_short_16: CRFKEM3VXB452T3I · pith_short_8: CRFKEM3V

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/CRFKEM3VXB452T3IXQJTW27VQP \
  | 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: 144aa23375b879dd4f68bc133b6bf583f9cae24a4d78ceb2c710c75fdc3861ea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "72baf96d69e17f46929d5b2101afd664544d11c3b7f69f6a443a2cf7c768ff91",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2020-10-28T15:48:10Z",
    "title_canon_sha256": "aa57da58b23aba2fbc224c6907cd952c8df0bdb82f1ff76baad8f6ef11c33e24"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2010.15048",
    "kind": "arxiv",
    "version": 1
  }
}