Pith Number

pith:WBBATPQP

pith:2025:WBBATPQPIR4XR7DRCWZPEJ5AE3

not attested not anchored not stored refs pending

Newton polytopes of fireworks Grothendieck polynomials

Jack Chen-An Chou, Linus Setiabrata

arxiv:2508.09107 v2 · 2025-08-12 · 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{WBBATPQPIR4XR7DRCWZPEJ5AE3}

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

Injectivity of symmetric polynomial maps on partitions

Receipt and verification

First computed	2026-07-05T11:53:08.639606Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b04209be0f447978fc7115b2f227a026fd41db5dc4ff7aa73d70eaaadf30f092

Aliases

arxiv: 2508.09107 · arxiv_version: 2508.09107v2 · doi: 10.48550/arxiv.2508.09107 · pith_short_12: WBBATPQPIR4X · pith_short_16: WBBATPQPIR4XR7DR · pith_short_8: WBBATPQP

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/WBBATPQPIR4XR7DRCWZPEJ5AE3 \
  | 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: b04209be0f447978fc7115b2f227a026fd41db5dc4ff7aa73d70eaaadf30f092

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4e57589c11ee654bfafc677a8595ff255474b03bd42f1c488493785f7ce37780",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-08-12T17:37:20Z",
    "title_canon_sha256": "f10f5ca929d794c987872ffa57aa0a7f7a71d5e149b22569305e291015648375"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.09107",
    "kind": "arxiv",
    "version": 2
  }
}