Pith Number

pith:HAI7ICCP

pith:2011:HAI7ICCPKNPUKEW2BJ7QKR6RW2

not attested not anchored not stored refs pending

Koszul dual 2-functors and extension algebras of simple modules for $GL_2$

Vanessa Miemietz, Will Turner

arxiv:1106.5411 v3 · 2011-06-27 · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HAI7ICCPKNPUKEW2BJ7QKR6RW2}

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	2026-05-18T02:48:02.530678Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3811f4084f535f4512da0a7f0547d1b6abb834a8c0c244d0afcb8f631ba58f87

Aliases

arxiv: 1106.5411 · arxiv_version: 1106.5411v3 · doi: 10.48550/arxiv.1106.5411 · pith_short_12: HAI7ICCPKNPU · pith_short_16: HAI7ICCPKNPUKEW2 · pith_short_8: HAI7ICCP

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/HAI7ICCPKNPUKEW2BJ7QKR6RW2 \
  | 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: 3811f4084f535f4512da0a7f0547d1b6abb834a8c0c244d0afcb8f631ba58f87

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c3a66dace7dbf6b234cc765c0368a16e173e9005585d63739c1ce68789ef3190",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2011-06-27T15:01:34Z",
    "title_canon_sha256": "5e67bd6450cf9dbf9b50041326682e35e32063f1bc88d1ceac0df52519c39fce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.5411",
    "kind": "arxiv",
    "version": 3
  }
}