Pith Number

pith:3X2L7S47

pith:2025:3X2L7S47637EZDALMBBUIKZ5IW

not attested not anchored not stored refs pending

Introduction to the Cohomology of the Flag Variety

Brendan Pawlowski, Sara C. Billey, Yibo Gao

arxiv:2506.21064 v1 · 2025-06-26 · math.CO · math.AC · 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{3X2L7S47637EZDALMBBUIKZ5IW}

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

Multigraded Regularity of the Complete Flag Variety

Ideals defining components of two-row Springer fibers

Receipt and verification

First computed	2026-07-05T11:27:39.422583Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ddf4bfcb9ff6fe4c8c0b6043442b3d459734b5b2eebc503eec34f3ac59689ac9

Aliases

arxiv: 2506.21064 · arxiv_version: 2506.21064v1 · doi: 10.48550/arxiv.2506.21064 · pith_short_12: 3X2L7S47637E · pith_short_16: 3X2L7S47637EZDAL · pith_short_8: 3X2L7S47

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/3X2L7S47637EZDALMBBUIKZ5IW \
  | 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: ddf4bfcb9ff6fe4c8c0b6043442b3d459734b5b2eebc503eec34f3ac59689ac9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fa76fa18f2c825198f528bf24ab691a00f3511c2c9d389f4275092fb64526c00",
    "cross_cats_sorted": [
      "math.AC",
      "math.AG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-06-26T07:33:38Z",
    "title_canon_sha256": "24b9f0daddbaf977d3529e45cfd249ec66b143e6d527503d6a6e5a740ebd3343"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.21064",
    "kind": "arxiv",
    "version": 1
  }
}