Pith Number

pith:WWMHYFAQ

pith:2013:WWMHYFAQLBEH3MNMCFWZQGXW4Y

not attested not anchored not stored refs pending

A note on power instability of linear discrete-time systems in Banach spaces

Ioan-Lucian Popa

arxiv:1305.2064 v1 · 2013-05-09 · 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{WWMHYFAQLBEH3MNMCFWZQGXW4Y}

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	2026-05-18T03:26:09.431798Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b5987c141058487db1ac116d981af6e631f3541969b3db9482936ddfab5c0788

Aliases

arxiv: 1305.2064 · arxiv_version: 1305.2064v1 · doi: 10.48550/arxiv.1305.2064 · pith_short_12: WWMHYFAQLBEH · pith_short_16: WWMHYFAQLBEH3MNM · pith_short_8: WWMHYFAQ

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/WWMHYFAQLBEH3MNMCFWZQGXW4Y \
  | 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: b5987c141058487db1ac116d981af6e631f3541969b3db9482936ddfab5c0788

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4692d9a6a693adc53329a259af8e8b14e433d54b2bb31dcc1c8d395a4f16f7ee",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2013-05-09T12:05:19Z",
    "title_canon_sha256": "124d2f4c0274db76582dd5b57eb3d964ff067f5e07a76fbfcc775eaa78f0d89f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.2064",
    "kind": "arxiv",
    "version": 1
  }
}