Pith Number

pith:NZF4DWQA

pith:2011:NZF4DWQALIV745FDP6RWAZFVXU

not attested not anchored not stored refs pending

Sheaves on P^1 x P^1, bigraded resolutions, and coadjoint orbits of loop groups

Lorenz Schwachh\"ofer, Roger Bielawski

arxiv:1106.5049 v1 · 2011-06-24 · math.SG · 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{NZF4DWQALIV745FDP6RWAZFVXU}

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	2026-05-18T04:19:22.543933Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6e4bc1da005a2bfe74a37fa36064b5bd0cf9d3f70017ed37bda084b87d1a1fcd

Aliases

arxiv: 1106.5049 · arxiv_version: 1106.5049v1 · doi: 10.48550/arxiv.1106.5049 · pith_short_12: NZF4DWQALIV7 · pith_short_16: NZF4DWQALIV745FD · pith_short_8: NZF4DWQA

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/NZF4DWQALIV745FDP6RWAZFVXU \
  | 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: 6e4bc1da005a2bfe74a37fa36064b5bd0cf9d3f70017ed37bda084b87d1a1fcd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eef20399f169dd9b41d4ed1c9e0d91893b0c4a47eccfbc59afe6169ae3598060",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2011-06-24T19:59:51Z",
    "title_canon_sha256": "535aa480f2cf0f32f372e33474ea972ca30bde1c31eefb260f413ec592111d19"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.5049",
    "kind": "arxiv",
    "version": 1
  }
}