Pith Number

pith:XSF2UTVO

pith:2015:XSF2UTVOVKOTIF6VK7RCX3OWNR

not attested not anchored not stored refs pending

On the unramified spherical automorphic spectrum

Eric Opdam, Marcelo De Martino, Volker Heiermann

arxiv:1512.08566 v4 · 2015-12-29 · 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{XSF2UTVOVKOTIF6VK7RCX3OWNR}

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.

Cited by

1 paper in Pith

On Arthur's unitarity conjecture for split real groups

Receipt and verification

First computed	2026-07-05T04:40:41.188828Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bc8baa4eaeaa9d3417d557e22bedd66c57986c43ca3b4d397dacc82bab26ea91

Aliases

arxiv: 1512.08566 · arxiv_version: 1512.08566v4 · doi: 10.48550/arxiv.1512.08566 · pith_short_12: XSF2UTVOVKOT · pith_short_16: XSF2UTVOVKOTIF6V · pith_short_8: XSF2UTVO

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/XSF2UTVOVKOTIF6VK7RCX3OWNR \
  | 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: bc8baa4eaeaa9d3417d557e22bedd66c57986c43ca3b4d397dacc82bab26ea91

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e6b628a405ab9a10180a7c06760b9513b22d656300d7c8d22e0e7813e10be555",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2015-12-29T00:24:22Z",
    "title_canon_sha256": "c686288cbcefb40e37c46ff72508f61888c63a13e3eb4469b6070297932e3a4e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.08566",
    "kind": "arxiv",
    "version": 4
  }
}