Pith Number

pith:TTQ3OASF

pith:2025:TTQ3OASFYPWTGOSMAWDUSRVMDA

not attested not anchored not stored refs pending

Graham positivity of triple Schubert calculus

Rui Xiong, Yibo Gao

arxiv:2506.09421 v1 · 2025-06-11 · math.CO · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TTQ3OASFYPWTGOSMAWDUSRVMDA}

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

2 papers in Pith

A Littlewood-Richardson Rule for Forest Polynomials via the Schubert Bialgebra

Equivariant Quantum Cohomology of Grassmannians via the Clifford algebra

Receipt and verification

First computed	2026-07-05T11:19:36.902670Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9ce1b70245c3ed333a4c05874946ac183527b648eb44b12348638cdb3efe2613

Aliases

arxiv: 2506.09421 · arxiv_version: 2506.09421v1 · doi: 10.48550/arxiv.2506.09421 · pith_short_12: TTQ3OASFYPWT · pith_short_16: TTQ3OASFYPWTGOSM · pith_short_8: TTQ3OASF

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/TTQ3OASFYPWTGOSMAWDUSRVMDA \
  | 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: 9ce1b70245c3ed333a4c05874946ac183527b648eb44b12348638cdb3efe2613

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0888007f3c6fb96ce4c4f0cce5df02a5965ea2c9ee1c5419134352012c2fed08",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-06-11T06:09:52Z",
    "title_canon_sha256": "c9bc99ced3cb84c86319b424cd219b9dd03d0dc6f30c3228c60991d3ceb2a63c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.09421",
    "kind": "arxiv",
    "version": 1
  }
}