Pith Number

pith:N4FRSSTY

pith:2016:N4FRSSTYKVG6BHPTCX7ML3WQUY

not attested not anchored not stored refs pending

A necessary and sufficient condition for edge universality at the largest singular values of covariance matrices

Fan Yang, Xiucai Ding

arxiv:1607.06873 v2 · 2016-07-23 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{N4FRSSTYKVG6BHPTCX7ML3WQUY}

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	2026-05-18T00:14:29.233112Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6f0b194a78554de09df315fec5eed0a62da71ad59c4f40a8c6103022aa20c445

Aliases

arxiv: 1607.06873 · arxiv_version: 1607.06873v2 · doi: 10.48550/arxiv.1607.06873 · pith_short_12: N4FRSSTYKVG6 · pith_short_16: N4FRSSTYKVG6BHPT · pith_short_8: N4FRSSTY

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/N4FRSSTYKVG6BHPTCX7ML3WQUY \
  | 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: 6f0b194a78554de09df315fec5eed0a62da71ad59c4f40a8c6103022aa20c445

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a85eadd542ecaea10dd820f60e6358780a00a9b5b5b040100588ec2e937d1efb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-07-23T01:19:38Z",
    "title_canon_sha256": "044f4fddf61eaa645627152c7520144b303f2b77e13c9f89a2c770da6e22975b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.06873",
    "kind": "arxiv",
    "version": 2
  }
}