Pith Number

pith:CKWEZZ2O

pith:2026:CKWEZZ2OQXQR52JQTV3IULC6PL

not attested not anchored not stored refs pending

Comparison theorems for the extreme eigenvalues of a random symmetric matrix

Joel A. Tropp

arxiv:2603.04365 v3 · 2026-03-04 · math.PR · cs.NA · math.NA · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CKWEZZ2OQXQR52JQTV3IULC6PL}

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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

Well-invertible column subsets of sparse matrices are rare

Receipt and verification

First computed	2026-07-07T02:18:36.404712Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12ac4ce74e85e11ee9309d768a2c5e7ad6e9d4061c2804cc1bd21f5df4178a5a

Aliases

arxiv: 2603.04365 · arxiv_version: 2603.04365v3 · doi: 10.48550/arxiv.2603.04365 · pith_short_12: CKWEZZ2OQXQR · pith_short_16: CKWEZZ2OQXQR52JQ · pith_short_8: CKWEZZ2O

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/CKWEZZ2OQXQR52JQTV3IULC6PL \
  | 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: 12ac4ce74e85e11ee9309d768a2c5e7ad6e9d4061c2804cc1bd21f5df4178a5a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "630ea065d2fe48c86f9310fdaa0af49a287f7eb42a2797994f898d8d35f4b377",
    "cross_cats_sorted": [
      "cs.NA",
      "math.NA",
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-03-04T18:30:04Z",
    "title_canon_sha256": "eee4193c823f266b2c8e677e2b42585b4c42badb8cbdef8d0dd4ac84b4b452ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.04365",
    "kind": "arxiv",
    "version": 3
  }
}