Pith Number

pith:AZCA2A3F

pith:2010:AZCA2A3FZME6C5JQLZ6UQ3IEOG

not attested not anchored not stored refs pending

Necessary and sufficient conditions for weak exponential instability of evolution operators

Nicolae Lupa

arxiv:1002.2372 v2 · 2010-02-11 · math.CA · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AZCA2A3FZME6C5JQLZ6UQ3IEOG}

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	2026-05-18T02:32:31.322511Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

06440d0365cb09e175305e7d486d0471a4eb192fdc5f9b8224af2a3e0cbde8f0

Aliases

arxiv: 1002.2372 · arxiv_version: 1002.2372v2 · doi: 10.48550/arxiv.1002.2372 · pith_short_12: AZCA2A3FZME6 · pith_short_16: AZCA2A3FZME6C5JQ · pith_short_8: AZCA2A3F

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/AZCA2A3FZME6C5JQLZ6UQ3IEOG \
  | 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: 06440d0365cb09e175305e7d486d0471a4eb192fdc5f9b8224af2a3e0cbde8f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f1df2514d418d273025716929d5bfcef97090c7b3ba747654e9aae837475bfb3",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2010-02-11T16:22:50Z",
    "title_canon_sha256": "97e1a85e914651d59b516da62e9d2202aa8054459003a69a27a6e9778833b3e9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1002.2372",
    "kind": "arxiv",
    "version": 2
  }
}