Pith Number

pith:VGD7MXBL

pith:2010:VGD7MXBLEOH73NO7CI5C5MHIFI

not attested not anchored not stored refs pending

Hall algebras of curves, commuting varieties and Langlands duality

E. Vasserot, O. Schiffmann

arxiv:1009.0678 v1 · 2010-09-03 · math.QA · 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{VGD7MXBLEOH73NO7CI5C5MHIFI}

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	2026-05-18T04:41:25.698102Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a987f65c2b238ffdb5df123a2eb0e82a25ddf76d783c06b399592faedc5c05b0

Aliases

arxiv: 1009.0678 · arxiv_version: 1009.0678v1 · doi: 10.48550/arxiv.1009.0678 · pith_short_12: VGD7MXBLEOH7 · pith_short_16: VGD7MXBLEOH73NO7 · pith_short_8: VGD7MXBL

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/VGD7MXBLEOH73NO7CI5C5MHIFI \
  | 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: a987f65c2b238ffdb5df123a2eb0e82a25ddf76d783c06b399592faedc5c05b0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3d53af1ad828434caf280c005418f1d715fa30b6ed25678ee79af746c4e6bf8d",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2010-09-03T14:09:12Z",
    "title_canon_sha256": "5224ad1f8def922aa41a7ecb975e6fa96f5f7b97908dbd187c331f78f4c756c8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.0678",
    "kind": "arxiv",
    "version": 1
  }
}