Pith Number

pith:OZF3PYEC

pith:2012:OZF3PYECMGJEBQLPXTZ7QOXYI6

not attested not anchored not stored refs pending

Irreducible modular representations of the Borel subgroup of GL_2(Q_p)

Laurent Berger, Mathieu Vienney

arxiv:1202.3609 v2 · 2012-02-16 · math.NT · 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{OZF3PYECMGJEBQLPXTZ7QOXYI6}

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	2026-05-18T03:59:37.840506Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

764bb7e082619240c16fbcf3f83af847bef8d726be85df7985e3add3d5793de4

Aliases

arxiv: 1202.3609 · arxiv_version: 1202.3609v2 · doi: 10.48550/arxiv.1202.3609 · pith_short_12: OZF3PYECMGJE · pith_short_16: OZF3PYECMGJEBQLP · pith_short_8: OZF3PYEC

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/OZF3PYECMGJEBQLPXTZ7QOXYI6 \
  | 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: 764bb7e082619240c16fbcf3f83af847bef8d726be85df7985e3add3d5793de4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "756da021e306e5fed81cac2e38cac21c049be5b22830ee6d43a8099556719412",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-02-16T14:54:36Z",
    "title_canon_sha256": "bebb541a8a4c2e71ed6d968cd4ce6d7a2622967bb62d3f4d41d471c90e27b7c6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.3609",
    "kind": "arxiv",
    "version": 2
  }
}