Pith Number

pith:3PKYDXM7

pith:2024:3PKYDXM7CKHIDXUMOGQ7GKAO37

not attested not anchored not stored refs pending

On the Submultiplicativity of Matrix Norms Induced by Random Vectors

Ludovick Bouthat

arxiv:2402.08173 v1 · 2024-02-13 · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3PKYDXM7CKHIDXUMOGQ7GKAO37}

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	2026-06-23T02:13:12.410072Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dbd581dd9f128e81de8c71a1f3280edfc570546a20c80ccdfbf5c8532e6b5b5d

Aliases

arxiv: 2402.08173 · arxiv_version: 2402.08173v1 · doi: 10.48550/arxiv.2402.08173 · pith_short_12: 3PKYDXM7CKHI · pith_short_16: 3PKYDXM7CKHIDXUM · pith_short_8: 3PKYDXM7

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/3PKYDXM7CKHIDXUMOGQ7GKAO37 \
  | 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: dbd581dd9f128e81de8c71a1f3280edfc570546a20c80ccdfbf5c8532e6b5b5d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5284ba709e77a4e94e3eb72a9efad4543a37011875551de1eebdb4d26c11acf0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2024-02-13T02:10:03Z",
    "title_canon_sha256": "c140d1246a5c686089a26b57e06ad039217df3807956929c46789a7395a0b8e7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2402.08173",
    "kind": "arxiv",
    "version": 1
  }
}