Pith Number

pith:64UHJ3GK

pith:2016:64UHJ3GKZI5R2Q3QTOAKFSXKVM

not attested not anchored not stored refs pending

Invariant measures and measurable projective factors for actions of higher-rank lattices on manifolds

Aaron Brown, Federico Rodriguez Hertz, Zhiren Wang

arxiv:1609.05565 v2 · 2016-09-18 · math.DS

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{64UHJ3GKZI5R2Q3QTOAKFSXKVM}

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	2026-05-18T00:53:20.672374Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f72874eccaca3b1d43709b80a2caeaab370693d4fc083a209fc47be21d4ffa54

Aliases

arxiv: 1609.05565 · arxiv_version: 1609.05565v2 · doi: 10.48550/arxiv.1609.05565 · pith_short_12: 64UHJ3GKZI5R · pith_short_16: 64UHJ3GKZI5R2Q3Q · pith_short_8: 64UHJ3GK

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/64UHJ3GKZI5R2Q3QTOAKFSXKVM \
  | 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: f72874eccaca3b1d43709b80a2caeaab370693d4fc083a209fc47be21d4ffa54

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "51f07a992c6aa9ff9f934bab6fb2781012d90278711c410bbe017dc29719325a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2016-09-18T23:08:11Z",
    "title_canon_sha256": "5ea31192d66228f1c6250f54353b0de8a6af0450cc3b36ab4d34e7aa70cde9ea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.05565",
    "kind": "arxiv",
    "version": 2
  }
}