Pith Number

pith:RHP3PYLQ

pith:2025:RHP3PYLQSWE5N5ZQXQQXY6VT3B

not attested not anchored not stored refs pending

Explicit Lossless Vertex Expanders

Alexander Lubotzky, Assaf Reiner, Jun-Ting Hsieh, Rachel Yun Zhang, Sidhanth Mohanty

arxiv:2504.15087 v1 · 2025-04-21 · math.CO · cs.CC · cs.DM · cs.DS · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RHP3PYLQSWE5N5ZQXQQXY6VT3B}

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

A Simple Sub-Polynomial Degree Coboundary Expander

Receipt and verification

First computed	2026-07-05T10:51:56.014247Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

89dfb7e1709589d6f730bc217c7ab3d85b23c08e7cfe6961f101c45c6006ebc2

Aliases

arxiv: 2504.15087 · arxiv_version: 2504.15087v1 · doi: 10.48550/arxiv.2504.15087 · pith_short_12: RHP3PYLQSWE5 · pith_short_16: RHP3PYLQSWE5N5ZQ · pith_short_8: RHP3PYLQ

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/RHP3PYLQSWE5N5ZQXQQXY6VT3B \
  | 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: 89dfb7e1709589d6f730bc217c7ab3d85b23c08e7cfe6961f101c45c6006ebc2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3bb669f75e39b5c1065593542599da886ba11dc084566a7fe4ce50161e6f234b",
    "cross_cats_sorted": [
      "cs.CC",
      "cs.DM",
      "cs.DS",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-04-21T13:20:37Z",
    "title_canon_sha256": "6ae2d215f08daeb0a4aacfac9f362f4136bbb9ce814ebe02c031f08c39ac2958"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2504.15087",
    "kind": "arxiv",
    "version": 1
  }
}