Pith Number

pith:WAS24E3K

pith:2019:WAS24E3KRWIN7M4WZC35LJF2BT

not attested not anchored not stored refs pending

$X$-Ramanujan Graphs

Ryan O'Donnell, Sidhanth Mohanty

arxiv:1904.03500 v2 · 2019-04-06 · math.CO · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WAS24E3KRWIN7M4WZC35LJF2BT}

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

Ramanujan Graphs and Interlacing Families

Receipt and verification

First computed	2026-05-17T23:48:49.888478Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b025ae136a8d90dfb396c8b7d5a4ba0cce9827fcbc416b15ecf5374b5d5cfc7e

Aliases

arxiv: 1904.03500 · arxiv_version: 1904.03500v2 · doi: 10.48550/arxiv.1904.03500 · pith_short_12: WAS24E3KRWIN · pith_short_16: WAS24E3KRWIN7M4W · pith_short_8: WAS24E3K

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/WAS24E3KRWIN7M4WZC35LJF2BT \
  | 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: b025ae136a8d90dfb396c8b7d5a4ba0cce9827fcbc416b15ecf5374b5d5cfc7e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3c57238e17f1a0e8768678c96988e3e053cceb8fe2688952b5ff16b6e3855104",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-04-06T17:36:33Z",
    "title_canon_sha256": "de4dc9eea90272944abc95c1ca5fa781255a560e4d967564f7ae859bb5ff67b9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1904.03500",
    "kind": "arxiv",
    "version": 2
  }
}