Pith Number

pith:P4O5YOTN

pith:2014:P4O5YOTN452I2Z37O2JEKUUMHJ

not attested not anchored not stored refs pending

A concise proof of the Multiplicative Ergodic Theorem on Banach spaces

Anthony Quas, Cecilia Gonz\'alez-Tokman

arxiv:1406.1955 v2 · 2014-06-08 · 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{P4O5YOTN452I2Z37O2JEKUUMHJ}

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	2026-05-18T00:56:04.841250Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7f1ddc3a6de7748d677f769245528c3a76e9b3d18db50e998141382fba404916

Aliases

arxiv: 1406.1955 · arxiv_version: 1406.1955v2 · doi: 10.48550/arxiv.1406.1955 · pith_short_12: P4O5YOTN452I · pith_short_16: P4O5YOTN452I2Z37 · pith_short_8: P4O5YOTN

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/P4O5YOTN452I2Z37O2JEKUUMHJ \
  | 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: 7f1ddc3a6de7748d677f769245528c3a76e9b3d18db50e998141382fba404916

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "140b90df3b68fe52302ae7ea4bd6c1119124210aa548d98714d940bec18df05d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2014-06-08T07:44:38Z",
    "title_canon_sha256": "5dd24c4e5a7e2fac4fb43cd3c798bae94a89880ea13cacb45baaca9b7b059695"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1406.1955",
    "kind": "arxiv",
    "version": 2
  }
}