Pith Number

pith:QSAZZLUK

pith:2010:QSAZZLUKP3BFR3KJ4USVPFYLDE

not attested not anchored not stored refs pending

Invariant measures on homogeneous spaces, with applications to function spaces and lattice counting

Bernhard Kr\"otz, Eitan Sayag, Henrik Schlichtkrull

arxiv:1004.1942 v2 · 2010-04-12 · 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{QSAZZLUKP3BFR3KJ4USVPFYLDE}

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	2026-05-18T04:19:43.802621Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

84819cae8a7ec258ed49e52557970b19347d4b0d02117abd7d6604b1a82bcd65

Aliases

arxiv: 1004.1942 · arxiv_version: 1004.1942v2 · doi: 10.48550/arxiv.1004.1942 · pith_short_12: QSAZZLUKP3BF · pith_short_16: QSAZZLUKP3BFR3KJ · pith_short_8: QSAZZLUK

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/QSAZZLUKP3BFR3KJ4USVPFYLDE \
  | 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: 84819cae8a7ec258ed49e52557970b19347d4b0d02117abd7d6604b1a82bcd65

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c87d88db7c80dbf7caae089082d37003a8f6e21ccd423254e6cb3832ce071e5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2010-04-12T12:53:28Z",
    "title_canon_sha256": "d0102d3dc1be789eebe8dbd3d302e9072e2b46b0e3d1c82b7719a949e6a87cc8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.1942",
    "kind": "arxiv",
    "version": 2
  }
}