Pith Number

pith:IFAXC6X3

pith:1993:IFAXC6X3U7ZYIIT3E7YKO62ZUU

not attested not anchored not stored refs pending

Lyapunov theorems for Banach spaces

Stephen Montgomery-Smith, Yuri Latushkin

arxiv:math/9302216 v1 · 1993-02-24 · math.FA · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IFAXC6X3U7ZYIIT3E7YKO62ZUU}

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	2026-05-18T01:05:52.283149Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4141717afba7f384227b27f0a77b59a5288021350f57ab11d26a3f63f77b4bc9

Aliases

arxiv: math/9302216 · arxiv_version: math/9302216v1 · doi: 10.48550/arxiv.math/9302216 · pith_short_12: IFAXC6X3U7ZY · pith_short_16: IFAXC6X3U7ZYIIT3 · pith_short_8: IFAXC6X3

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/IFAXC6X3U7ZYIIT3E7YKO62ZUU \
  | 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: 4141717afba7f384227b27f0a77b59a5288021350f57ab11d26a3f63f77b4bc9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3bf7bfcfaea97e17fe865c33fb9dd7a8a72617d073b17b929c9be82e356ba16b",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "",
    "primary_cat": "math.FA",
    "submitted_at": "1993-02-24T00:00:00Z",
    "title_canon_sha256": "9b179e227a5de84eadb7d9496166665fbe25ab4119cfdd54735bcd886e7d8f4e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9302216",
    "kind": "arxiv",
    "version": 1
  }
}