Pith Number

pith:BVAQ45P2

pith:2025:BVAQ45P2G74QL3S67XYGCXC424

not attested not anchored not stored refs pending

Grothendieck positivity for normal square root crystals

Eric Marberg, Kam Hung Tong, Tianyi Yu

arxiv:2501.16640 v2 · 2025-01-28 · math.CO · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BVAQ45P2G74QL3S67XYGCXC424}

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 Grothendieck polynomials

Receipt and verification

First computed	2026-06-19T16:11:09.621801Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0d410e75fa37f905ee5efdf0615c5cd735a5e38b83946d936a092920e7e79ca2

Aliases

arxiv: 2501.16640 · arxiv_version: 2501.16640v2 · doi: 10.48550/arxiv.2501.16640 · pith_short_12: BVAQ45P2G74Q · pith_short_16: BVAQ45P2G74QL3S6 · pith_short_8: BVAQ45P2

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/BVAQ45P2G74QL3S67XYGCXC424 \
  | 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: 0d410e75fa37f905ee5efdf0615c5cd735a5e38b83946d936a092920e7e79ca2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "66643bd6426931a0b857d6bb07df316528b1d30dfd47329689d62a1186e73c01",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-01-28T02:23:15Z",
    "title_canon_sha256": "2eb3415437a08017e609ed9339cf11dc0e43f40b2ee1ec84effdc10eead6cddd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2501.16640",
    "kind": "arxiv",
    "version": 2
  }
}