Pith Number

pith:X737DHXN

pith:2019:X737DHXNCABDY6723TK4KESVR2

not attested not anchored not stored refs pending

On the cohomology of line bundles over certain flag schemes

Linyuan Liu

arxiv:1908.08438 v4 · 2019-08-22 · math.RT · 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{X737DHXNCABDY6723TK4KESVR2}

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.

Receipt and verification

First computed	2026-07-05T01:41:28.471979Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bff7f19eed10023c7bfadcd5c512558ebadf714cea9fb8b6b288016c215ef6d1

Aliases

arxiv: 1908.08438 · arxiv_version: 1908.08438v4 · doi: 10.48550/arxiv.1908.08438 · pith_short_12: X737DHXNCABD · pith_short_16: X737DHXNCABDY672 · pith_short_8: X737DHXN

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/X737DHXNCABDY6723TK4KESVR2 \
  | 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: bff7f19eed10023c7bfadcd5c512558ebadf714cea9fb8b6b288016c215ef6d1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8cec5f5fffeddd246a4d325c757ef738515e68c0d19c2b71fa7fb8e406946267",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2019-08-22T15:14:45Z",
    "title_canon_sha256": "e6637b4eda161e48d5710492eeb75fd40b733fd282fe2af94f272fc0f77f93d5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.08438",
    "kind": "arxiv",
    "version": 4
  }
}