Pith Number

pith:AKCOKL6M

pith:2018:AKCOKL6MLDDKXELPAGWOPVTWOF

not attested not anchored not stored refs pending

A generalized Lieb's theorem and its applications to spectrum estimates for a sum of random matrices

De Huang

arxiv:1808.05550 v2 · 2018-08-10 · math.ST · cs.IT · math.IT · math.PR · 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{AKCOKL6MLDDKXELPAGWOPVTWOF}

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	2026-05-17T23:59:32.281002Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0284e52fcc58c6ab916f01ace7d676715d487e3b9d2eb3e5f9fdc1c95d9f03eb

Aliases

arxiv: 1808.05550 · arxiv_version: 1808.05550v2 · doi: 10.48550/arxiv.1808.05550 · pith_short_12: AKCOKL6MLDDK · pith_short_16: AKCOKL6MLDDKXELP · pith_short_8: AKCOKL6M

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/AKCOKL6MLDDKXELPAGWOPVTWOF \
  | 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: 0284e52fcc58c6ab916f01ace7d676715d487e3b9d2eb3e5f9fdc1c95d9f03eb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "17056e44494840ff2b0d377eeb140deb437ad4ffe0fd67fcc2be6a8c18bb9f66",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT",
      "math.PR",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2018-08-10T02:57:49Z",
    "title_canon_sha256": "75d2bb528c4cfe967fe7526669e575d11309b3ded8a182de5cd8eac73dcf3b43"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.05550",
    "kind": "arxiv",
    "version": 2
  }
}