Pith Number

pith:PZ6UUPPO

pith:2016:PZ6UUPPOFGR6SJVYCNY2AAYBWM

not attested not anchored not stored refs pending

On spectral gap properties and extreme value theory for multivariate affine stochastic recursions

Emile Le Page (UBS Vannes), Yves Guivarc'H (IRMAR)

arxiv:1604.08118 v3 · 2016-04-27 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PZ6UUPPOFGR6SJVYCNY2AAYBWM}

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	2026-05-18T00:28:02.778533Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7e7d4a3dee29a3e926b81371a00301b318c9abe8a52004a585408f84b9ff005a

Aliases

arxiv: 1604.08118 · arxiv_version: 1604.08118v3 · doi: 10.48550/arxiv.1604.08118 · pith_short_12: PZ6UUPPOFGR6 · pith_short_16: PZ6UUPPOFGR6SJVY · pith_short_8: PZ6UUPPO

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/PZ6UUPPOFGR6SJVYCNY2AAYBWM \
  | 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: 7e7d4a3dee29a3e926b81371a00301b318c9abe8a52004a585408f84b9ff005a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cf35c25142d5319ba93a82dc6f3d660e87f96669cedd1cc6e950af50e6968c50",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-04-27T15:46:32Z",
    "title_canon_sha256": "28e4fa2d5bfea2868e00a3c5fc289c70f493cea935a97260be66a3db2d5de2bc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.08118",
    "kind": "arxiv",
    "version": 3
  }
}