Pith Number

pith:WAGFPZQE

pith:2020:WAGFPZQE243R7EJ24T7P73YVKB

not attested not anchored not stored refs pending

Frozen Pipes: Lattice Models for Grothendieck Polynomials

Andrew Hardt, Ben Brubaker, Claire Frechette, Emily Tibor, Katherine Weber

arxiv:2007.04310 v3 · 2020-07-08 · math.CO · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WAGFPZQE243R7EJ24T7P73YVKB}

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

Quantum integrable model for the quantum cohomology/K-theory of flag varieties and the double $\beta$-Grothendieck polynomials

Receipt and verification

First computed	2026-07-05T03:13:17.629961Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b00c57e604d7371f913ae4feffef15505148fc8f06c804262b5c372e158b486b

Aliases

arxiv: 2007.04310 · arxiv_version: 2007.04310v3 · doi: 10.48550/arxiv.2007.04310 · pith_short_12: WAGFPZQE243R · pith_short_16: WAGFPZQE243R7EJ2 · pith_short_8: WAGFPZQE

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/WAGFPZQE243R7EJ24T7P73YVKB \
  | 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: b00c57e604d7371f913ae4feffef15505148fc8f06c804262b5c372e158b486b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d2443c8a09299999068f1d71c16147e44ee8596b53b6d2b3e2049d226994e684",
    "cross_cats_sorted": [
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2020-07-08T17:58:04Z",
    "title_canon_sha256": "cb7623431f04735acc94b6c8abfce205336eebbaab36b52b25c81348df8b11a2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2007.04310",
    "kind": "arxiv",
    "version": 3
  }
}