Pith Number

pith:WFMUDOJH

pith:2008:WFMUDOJH7B2RKFY57U5D67FHKL

not attested not anchored not stored refs pending

On some modular representations of the Borel subgroup of GL_2(Q_p)

Laurent Berger

arxiv:0810.5083 v5 · 2008-10-28 · 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{WFMUDOJH7B2RKFY57U5D67FHKL}

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	2026-05-17T23:53:39.475944Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b15941b927f87515171dfd3a3f7ca752c58c064205381956b60b0aedf0c94afa

Aliases

arxiv: 0810.5083 · arxiv_version: 0810.5083v5 · doi: 10.48550/arxiv.0810.5083 · pith_short_12: WFMUDOJH7B2R · pith_short_16: WFMUDOJH7B2RKFY5 · pith_short_8: WFMUDOJH

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/WFMUDOJH7B2RKFY57U5D67FHKL \
  | 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: b15941b927f87515171dfd3a3f7ca752c58c064205381956b60b0aedf0c94afa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb701b9a05a0893211579bc74885c9aeaeee03fe788c4f794edd3e47cfed7e09",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2008-10-28T16:59:11Z",
    "title_canon_sha256": "2c6199c9503cb06b92b7f3ff85c873a16b26d26e2ad2a421f5846f0a73c65c13"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0810.5083",
    "kind": "arxiv",
    "version": 5
  }
}