Pith Number

pith:KFBGRNXV

pith:2018:KFBGRNXVJBVLSN6LGIRKD2Q4VB

not attested not anchored not stored refs pending

Singularity of random Bernoulli matrices

Konstantin Tikhomirov

arxiv:1812.09016 v4 · 2018-12-21 · 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{KFBGRNXVJBVLSN6LGIRKD2Q4VB}

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

An algebraic inverse theorem for the quadratic Littlewood-Offord problem, and an application to Ramsey graphs

Receipt and verification

First computed	2026-07-04T23:59:29.841158Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

514268b6f5486ab937cb3222a1ea1ca8628ae30184c27a4e469b03fa93d78bf1

Aliases

arxiv: 1812.09016 · arxiv_version: 1812.09016v4 · doi: 10.48550/arxiv.1812.09016 · pith_short_12: KFBGRNXVJBVL · pith_short_16: KFBGRNXVJBVLSN6L · pith_short_8: KFBGRNXV

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/KFBGRNXVJBVLSN6LGIRKD2Q4VB \
  | 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: 514268b6f5486ab937cb3222a1ea1ca8628ae30184c27a4e469b03fa93d78bf1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9fe08f547890d9e9f89dae792e5ca0805af9a7fdcfe02921ad28ca51b290cbd8",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2018-12-21T09:39:37Z",
    "title_canon_sha256": "a3e056c608a91052fd0cf53e8692fa8905aec09a242edcb0225e3ea96c64e28a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.09016",
    "kind": "arxiv",
    "version": 4
  }
}