Pith Number

pith:5PP3IWOE

pith:2016:5PP3IWOETXFIK47ILJZENIDZEO

not attested not anchored not stored refs pending

Sum rules and large deviations for spectral matrix measures

Alain Rouault (LM-Versailles), Fabrice Gamboa (IMT), Jan Nagel

arxiv:1601.08135 v2 · 2016-01-29 · math.PR · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5PP3IWOETXFIK47ILJZENIDZEO}

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	2026-05-18T01:04:21.525448Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ebdfb459c49dca8573e85a7246a079239f12431e4ad022fde707245085649098

Aliases

arxiv: 1601.08135 · arxiv_version: 1601.08135v2 · doi: 10.48550/arxiv.1601.08135 · pith_short_12: 5PP3IWOETXFI · pith_short_16: 5PP3IWOETXFIK47I · pith_short_8: 5PP3IWOE

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/5PP3IWOETXFIK47ILJZENIDZEO \
  | 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: ebdfb459c49dca8573e85a7246a079239f12431e4ad022fde707245085649098

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8b8b8d6813e4e40c66a758a0b8cb2101e888def3ea4ff0b27081741338cafd48",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-01-29T14:45:32Z",
    "title_canon_sha256": "49408f3202b09b4e26b3a477d076b14540cd43a92904dbfd9d93c2becd10790e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.08135",
    "kind": "arxiv",
    "version": 2
  }
}