Pith Number

pith:PSE73NPN

pith:2017:PSE73NPNPVJ5AHQCRAQZKI5GZS

not attested not anchored not stored refs pending

The smallest singular value of a shifted $d$-regular random square matrix

Alexander Litvak, Anna Lytova, Konstantin Tikhomirov, Nicole Tomczak-Jaegermann, Pierre Youssef

arxiv:1707.02635 v3 · 2017-07-09 · 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{PSE73NPNPVJ5AHQCRAQZKI5GZS}

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.

Receipt and verification

First computed	2026-05-18T00:10:24.427323Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7c89fdb5ed7d53d01e0288219523a6cc875e1f990482955a5fc22749a75ab581

Aliases

arxiv: 1707.02635 · arxiv_version: 1707.02635v3 · doi: 10.48550/arxiv.1707.02635 · pith_short_12: PSE73NPNPVJ5 · pith_short_16: PSE73NPNPVJ5AHQC · pith_short_8: PSE73NPN

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/PSE73NPNPVJ5AHQCRAQZKI5GZS \
  | 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: 7c89fdb5ed7d53d01e0288219523a6cc875e1f990482955a5fc22749a75ab581

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1ea4ef6aa245d452b8cd6333fe209306975d81d8a927c2ee1b5d3e909b8f1fdf",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2017-07-09T20:40:44Z",
    "title_canon_sha256": "cbf6318db4f2b59270337c44c7855b0939481b598adaa64e160c57496e498a4b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1707.02635",
    "kind": "arxiv",
    "version": 3
  }
}