Pith Number

pith:6XRGBV2I

pith:2004:6XRGBV2I24O47UDAOBM2YXJJGD

not attested not anchored not stored refs pending

Geometric Langlands duality and representations of algebraic groups over commutative rings

I. Mirkovic, K. Vilonen

arxiv:math/0401222 v5 · 2004-01-18 · 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{6XRGBV2I24O47UDAOBM2YXJJGD}

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	2026-05-18T00:23:41.344164Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f5e260d748d71dcfd0607059ac5d2930fdf874a4ae6fa8b259aaaace1d3daeaf

Aliases

arxiv: math/0401222 · arxiv_version: math/0401222v5 · doi: 10.48550/arxiv.math/0401222 · pith_short_12: 6XRGBV2I24O4 · pith_short_16: 6XRGBV2I24O47UDA · pith_short_8: 6XRGBV2I

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/6XRGBV2I24O47UDAOBM2YXJJGD \
  | 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: f5e260d748d71dcfd0607059ac5d2930fdf874a4ae6fa8b259aaaace1d3daeaf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "724975c423a702dfbe9666bda1052af47e4770f12cb4d1d7aacf02a162599c8a",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2004-01-18T14:02:49Z",
    "title_canon_sha256": "eac922368b59342b3c5f83a7ff95623065b446072b9bf02c117cc16a18d13cdf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0401222",
    "kind": "arxiv",
    "version": 5
  }
}