Pith Number

pith:SH4M5UBV

pith:2015:SH4M5UBVHXXXAXKLOMNDJBFI5N

not attested not anchored not stored refs pending

Adjacency matrices of random digraphs: singularity and anti-concentration

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

arxiv:1511.00113 v4 · 2015-10-31 · 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{SH4M5UBVHXXXAXKLOMNDJBFI5N}

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	2026-05-18T01:02:04.837136Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

91f8ced0353def705d4b731a3484a8eb50d41f96f23966ccee0a88443f4ebc35

Aliases

arxiv: 1511.00113 · arxiv_version: 1511.00113v4 · doi: 10.48550/arxiv.1511.00113 · pith_short_12: SH4M5UBVHXXX · pith_short_16: SH4M5UBVHXXXAXKL · pith_short_8: SH4M5UBV

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/SH4M5UBVHXXXAXKLOMNDJBFI5N \
  | 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: 91f8ced0353def705d4b731a3484a8eb50d41f96f23966ccee0a88443f4ebc35

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ef093dfd4b180ae13bdc765b845a82c1a4cd17e55c33870f276b11a9b7580523",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-10-31T11:30:52Z",
    "title_canon_sha256": "3933367602d03cfd454bcd3e145e461d7160b25a075561f0d96ab80b5332311a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.00113",
    "kind": "arxiv",
    "version": 4
  }
}