Pith Number

pith:PDKGJHNY

pith:2023:PDKGJHNYCWIO6SUPQB4NUVWFLD

not attested not anchored not stored refs pending

Bipartite unique-neighbour expanders via Ramanujan graphs

Irit Dinur, Ron Asherov

arxiv:2301.03072 v1 · 2023-01-08 · math.CO · cs.IT · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PDKGJHNYCWIO6SUPQB4NUVWFLD}

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

Explicit Two-Sided Vertex Expanders Beyond the Spectral Barrier

Receipt and verification

First computed	2026-07-05T05:31:25.437172Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

78d4649db81590ef4a8f8078da56c558ec54dac3e342c57764acde3c27f62f7e

Aliases

arxiv: 2301.03072 · arxiv_version: 2301.03072v1 · doi: 10.48550/arxiv.2301.03072 · pith_short_12: PDKGJHNYCWIO · pith_short_16: PDKGJHNYCWIO6SUP · pith_short_8: PDKGJHNY

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/PDKGJHNYCWIO6SUPQB4NUVWFLD \
  | 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: 78d4649db81590ef4a8f8078da56c558ec54dac3e342c57764acde3c27f62f7e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "657e4ebfd32a5b687799a3a937739ea24732ad0b59ac597aeb8f444a2968b476",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2023-01-08T16:48:36Z",
    "title_canon_sha256": "314021eac81394d53a71873d94b41a13f259e8d96f9b66e3452c6c4ae1ae1c38"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2301.03072",
    "kind": "arxiv",
    "version": 1
  }
}