Pith Number

pith:4ZEUKYLJ

pith:2019:4ZEUKYLJ7IN7WQS5F3PRXLZEFU

not attested not anchored not stored refs pending

On the cohomology of line bundles over certain flag schemes II

Linyuan Liu, Patrick Polo

arxiv:1908.08432 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{4ZEUKYLJ7IN7WQS5F3PRXLZEFU}

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	2026-07-05T01:41:28.455987Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e649456169fa1bfb425d2edf1baf242d28e2a3bb9e51033f6bcfe305850b418b

Aliases

arxiv: 1908.08432 · arxiv_version: 1908.08432v4 · doi: 10.48550/arxiv.1908.08432 · pith_short_12: 4ZEUKYLJ7IN7 · pith_short_16: 4ZEUKYLJ7IN7WQS5 · pith_short_8: 4ZEUKYLJ

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/4ZEUKYLJ7IN7WQS5F3PRXLZEFU \
  | 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: e649456169fa1bfb425d2edf1baf242d28e2a3bb9e51033f6bcfe305850b418b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "129ce4c95010fd71dcf50b5423e1a27d6c1278e7d0a08b589ef88c38135be84d",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2019-08-22T15:08:35Z",
    "title_canon_sha256": "0278903a1e9001f454f5f978fa365356887362b3f21dd7a7c03b5c817cca5c2c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.08432",
    "kind": "arxiv",
    "version": 4
  }
}