Pith Number

pith:ZL2N5NAJ

pith:2017:ZL2N5NAJJ3ACRA6MNK5SY5A3U2

not attested not anchored not stored refs pending

Distance-like functions and smooth approximations: a correction to "Logarithm laws for flows on homogeneous spaces"

Dmitry Kleinbock, Gregory Margulis

arxiv:1706.08570 v4 · 2017-06-26 · 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{ZL2N5NAJJ3ACRA6MNK5SY5A3U2}

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	2026-05-18T00:36:49.260976Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

caf4deb4094ec02883cc6abb2c741ba684c3e1255262c0b08afe1c15fbc10b96

Aliases

arxiv: 1706.08570 · arxiv_version: 1706.08570v4 · doi: 10.48550/arxiv.1706.08570 · pith_short_12: ZL2N5NAJJ3AC · pith_short_16: ZL2N5NAJJ3ACRA6M · pith_short_8: ZL2N5NAJ

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/ZL2N5NAJJ3ACRA6MNK5SY5A3U2 \
  | 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: caf4deb4094ec02883cc6abb2c741ba684c3e1255262c0b08afe1c15fbc10b96

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "232a3833b3a5ee662b0df593ef6af3bb541075c8e0a40c53d43d0f330713ca02",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2017-06-26T19:28:43Z",
    "title_canon_sha256": "04e9e07d4244fd94290947eb4c07946da64ee7995157c80be705320631d43d74"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1706.08570",
    "kind": "arxiv",
    "version": 4
  }
}