Pith Number

pith:5EIUU3TQ

pith:2019:5EIUU3TQYGXBJNUCXMZOB2Z6IL

not attested not anchored not stored refs pending

On the Relativized Alon Second Eigenvalue Conjecture I: Main Theorems, Examples, and Outline of Proof

David Kohler, Joel Friedman

arxiv:1911.05688 v1 · 2019-11-13 · cs.DM · 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{5EIUU3TQYGXBJNUCXMZOB2Z6IL}

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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

1 paper in Pith

Ramanujan Graphs and Interlacing Families

Receipt and verification

First computed	2026-07-05T00:19:00.006390Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e9114a6e70c1ae14b682bb32e0eb3e42c20aa83668dc86b3f295281d5ae5b520

Aliases

arxiv: 1911.05688 · arxiv_version: 1911.05688v1 · doi: 10.48550/arxiv.1911.05688 · pith_short_12: 5EIUU3TQYGXB · pith_short_16: 5EIUU3TQYGXBJNUC · pith_short_8: 5EIUU3TQ

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/5EIUU3TQYGXBJNUCXMZOB2Z6IL \
  | 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: e9114a6e70c1ae14b682bb32e0eb3e42c20aa83668dc86b3f295281d5ae5b520

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2a9e13dfe39c21893cbdf04aaa6257a9a768caa432aa0e6441c1e3bdda2a8564",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2019-11-13T18:11:09Z",
    "title_canon_sha256": "794a3fa2ae061465af7b7258310a42918d1c24cb5481bd113d26c0733320d1ab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1911.05688",
    "kind": "arxiv",
    "version": 1
  }
}