Pith Number

pith:MQZM3NVY

pith:2013:MQZM3NVYYPKXKDKQ3WHXJOCTJI

not attested not anchored not stored refs pending

Persistence of exponential trichotomy for linear operators: A Lyapunov-Perron approach

Arnaud Ducrot, Ousmane Seydi, Pierre Magal

arxiv:1311.2713 v1 · 2013-11-12 · 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{MQZM3NVYYPKXKDKQ3WHXJOCTJI}

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	2026-05-18T03:07:22.060666Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6432cdb6b8c3d5750d50dd8f74b8534a3ae2d6c34a48223de82ba84175ae2f4b

Aliases

arxiv: 1311.2713 · arxiv_version: 1311.2713v1 · doi: 10.48550/arxiv.1311.2713 · pith_short_12: MQZM3NVYYPKX · pith_short_16: MQZM3NVYYPKXKDKQ · pith_short_8: MQZM3NVY

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/MQZM3NVYYPKXKDKQ3WHXJOCTJI \
  | 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: 6432cdb6b8c3d5750d50dd8f74b8534a3ae2d6c34a48223de82ba84175ae2f4b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e616f090cc907797727ec40d7e051f0f88351daa1cbdfc39bc36110451babb00",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2013-11-12T08:51:48Z",
    "title_canon_sha256": "5f9b29fb6febd00cca91215b65a8986b59604f666f0b24292cce65edeaff48f9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.2713",
    "kind": "arxiv",
    "version": 1
  }
}