Pith Number

pith:4T6R3OPJ

pith:2025:4T6R3OPJN26J3APUWNMOKM7XDZ

not attested not anchored not stored refs pending

Operator $\ell_p\to\ell_q$ norms of Gaussian matrices

Marta Strzelecka, Rafa{\l} Lata{\l}a

arxiv:2502.02186 v3 · 2025-02-04 · math.PR · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4T6R3OPJN26J3APUWNMOKM7XDZ}

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	2026-06-10T01:09:15.050518Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e4fd1db9e96ebc9d81f4b358e533f71e5c9f53af8e6ba676ef141ec822492400

Aliases

arxiv: 2502.02186 · arxiv_version: 2502.02186v3 · doi: 10.48550/arxiv.2502.02186 · pith_short_12: 4T6R3OPJN26J · pith_short_16: 4T6R3OPJN26J3APU · pith_short_8: 4T6R3OPJ

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/4T6R3OPJN26J3APUWNMOKM7XDZ \
  | 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: e4fd1db9e96ebc9d81f4b358e533f71e5c9f53af8e6ba676ef141ec822492400

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aa2b7b0c6fbf78f746aa072f5890e6992e17818ef446ba8db7e5ed1d5a03ccd9",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-02-04T10:01:59Z",
    "title_canon_sha256": "b826b6d9400bd7ba329de7a5b610213b15cc6a0bb74b61016b666d7d42be4487"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2502.02186",
    "kind": "arxiv",
    "version": 3
  }
}