Pith Number

pith:2KF3SMFR

pith:2011:2KF3SMFR4VXIVL6XUCTIXDOCH2

not attested not anchored not stored refs pending

Exponential dichotomies for linear discrete-time systems in Banach spaces

Ioan-Lucian Popa, Mihail Megan, Traian Ceausu

arxiv:1108.5058 v1 · 2011-08-25 · 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{2KF3SMFR4VXIVL6XUCTIXDOCH2}

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	2026-05-18T04:14:45.487712Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d28bb930b1e56e8aafd7a0a68b8dc23ea160969b84a8cc40a7f7aafe8e5241d0

Aliases

arxiv: 1108.5058 · arxiv_version: 1108.5058v1 · doi: 10.48550/arxiv.1108.5058 · pith_short_12: 2KF3SMFR4VXI · pith_short_16: 2KF3SMFR4VXIVL6X · pith_short_8: 2KF3SMFR

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/2KF3SMFR4VXIVL6XUCTIXDOCH2 \
  | 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: d28bb930b1e56e8aafd7a0a68b8dc23ea160969b84a8cc40a7f7aafe8e5241d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "94cdcdfbae48b106cbb265d5671d849a7d7d8de6f275a8589c6de9e9be156cea",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-08-25T11:09:46Z",
    "title_canon_sha256": "74be1fda6c8ff724a386e07a167de23aca778d7121c8f0efe0cbf960bc78aae9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.5058",
    "kind": "arxiv",
    "version": 1
  }
}