Pith Number

pith:IT4FCAWG

pith:2008:IT4FCAWG2LDFUMKRMXXMCPA3Q4

not attested not anchored not stored refs pending

Vertex operators and the geometry of moduli spaces of framed torsion-free sheaves

Alistair Savage, Anthony Licata

arxiv:0809.4010 v3 · 2008-09-23 · math.RT · 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{IT4FCAWG2LDFUMKRMXXMCPA3Q4}

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	2026-05-18T04:01:26.760768Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

44f85102c6d2c65a315165eec13c1b8713d2584ba0cb3bc12c1d3700b92f1232

Aliases

arxiv: 0809.4010 · arxiv_version: 0809.4010v3 · doi: 10.48550/arxiv.0809.4010 · pith_short_12: IT4FCAWG2LDF · pith_short_16: IT4FCAWG2LDFUMKR · pith_short_8: IT4FCAWG

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/IT4FCAWG2LDFUMKRMXXMCPA3Q4 \
  | 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: 44f85102c6d2c65a315165eec13c1b8713d2584ba0cb3bc12c1d3700b92f1232

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ff7797dd36b09d3a9172f4233ae8c8e1eb3f2a2ff2ea251f0b5036e4f8045a72",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2008-09-23T20:04:52Z",
    "title_canon_sha256": "ed866cca2f952a703a9434f28d9a38a58f4f973f0633723f366f9d3330033c55"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0809.4010",
    "kind": "arxiv",
    "version": 3
  }
}