Pith Number

pith:3VW6LI6O

pith:2022:3VW6LI6OPLYAANAY2DYVCMASMR

not attested not anchored not stored refs pending

Pattern bounds for principal specializations of $\beta$-Grothendieck Polynomials

Hugh Dennin

arxiv:2206.10017 v1 · 2022-06-20 · 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{3VW6LI6OPLYAANAY2DYVCMASMR}

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

Schubert polynomials and patterns in permutations

Receipt and verification

First computed	2026-07-05T04:33:42.484978Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd6de5a3ce7af0003418d0f15130126469c63286b969341109423eab14202c50

Aliases

arxiv: 2206.10017 · arxiv_version: 2206.10017v1 · doi: 10.48550/arxiv.2206.10017 · pith_short_12: 3VW6LI6OPLYA · pith_short_16: 3VW6LI6OPLYAANAY · pith_short_8: 3VW6LI6O

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/3VW6LI6OPLYAANAY2DYVCMASMR \
  | 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: dd6de5a3ce7af0003418d0f15130126469c63286b969341109423eab14202c50

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b91a7e4dcf451a515559d87e503f16214ebe9a94b0d87e7deb01c438d758dcaf",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2022-06-20T21:40:57Z",
    "title_canon_sha256": "46a6fb94f4a769770f4e5d5db100ed81e422a1c4367fac596cfd0e32b1908a8d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2206.10017",
    "kind": "arxiv",
    "version": 1
  }
}