Pith Number

pith:DQUYN56N

pith:2024:DQUYN56NOQVH6KOSNXZCNHCI5P

not attested not anchored not stored refs pending

Lipschitz functions on weak expanders

Jinyoung Park, Lina Li, Robert A. Krueger

arxiv:2408.14702 v1 · 2024-08-27 · math.PR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DQUYN56NOQVH6KOSNXZCNHCI5P}

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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

3 papers in Pith

Random homomorphisms and Lipschitz functions on trees

Lipschitz Functions on Sparse Graphs II

Range of random $\mathbb Z$-homomorphisms on weak expanders

Receipt and verification

First computed	2026-07-05T08:59:37.822055Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1c2986f7cd742a7f29d26df2269c48ebcb70cba7405a88490ea3c5467089fe32

Aliases

arxiv: 2408.14702 · arxiv_version: 2408.14702v1 · doi: 10.48550/arxiv.2408.14702 · pith_short_12: DQUYN56NOQVH · pith_short_16: DQUYN56NOQVH6KOS · pith_short_8: DQUYN56N

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/DQUYN56NOQVH6KOSNXZCNHCI5P \
  | 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: 1c2986f7cd742a7f29d26df2269c48ebcb70cba7405a88490ea3c5467089fe32

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "703f5f516fe43bbc55c40f8bff8e72ce9eff9b35a1d47ae317e27c850186a5b1",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2024-08-27T00:00:41Z",
    "title_canon_sha256": "93c414bda11a3479978fe949a9416ac4473be10262ed952d34faefc6563a847b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2408.14702",
    "kind": "arxiv",
    "version": 1
  }
}