Pith Number

pith:KTD5LZPC

pith:2026:KTD5LZPCKMXTTSDRUDXO7W7JQ3

not attested not anchored not stored refs pending

A Lam--Postnikov--Pylyavskyy inequality for hybrid Grothendieck polynomials

Jiaji Liu, Mingyang Kang, Peter L. Guo

arxiv:2607.03116 v1 · 2026-07-03 · 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{KTD5LZPCKMXTTSDRUDXO7W7JQ3}

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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.

Receipt and verification

First computed	2026-07-07T01:16:43.516398Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

54c7d5e5e2532f39c871a0eeefdbe986f1ff0c3f42b33c370bbfd95445e0cd3f

Aliases

arxiv: 2607.03116 · arxiv_version: 2607.03116v1 · doi: 10.48550/arxiv.2607.03116 · pith_short_12: KTD5LZPCKMXT · pith_short_16: KTD5LZPCKMXTTSDR · pith_short_8: KTD5LZPC

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/KTD5LZPCKMXTTSDRUDXO7W7JQ3 \
  | 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: 54c7d5e5e2532f39c871a0eeefdbe986f1ff0c3f42b33c370bbfd95445e0cd3f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1f4cb66c3eebc1b2e80d1e118c3ab45c8eb3195dfacce36a3fed4ec8e25d3599",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-03T08:56:29Z",
    "title_canon_sha256": "1dfc352cf03a22c67d8b8b6f98bc307a12b7902986d335c7bd88fc5414489dcf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.03116",
    "kind": "arxiv",
    "version": 1
  }
}