Pith Number

pith:D5PWSWSE

pith:2012:D5PWSWSE3Y3ITMA3BQTDMYTIZP

not attested not anchored not stored refs pending

Mean Ergodic Theorems in Hilbert-Kaplansky spaces

Farruh Shahidi, Inomjon Ganiev

arxiv:1208.5561 v1 · 2012-08-28 · math.FA · 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{D5PWSWSE3Y3ITMA3BQTDMYTIZP}

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	2026-05-18T03:46:58.364351Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1f5f695a44de3689b01b0c26366268cbe52fde46da87ea8def55e8c7c1d01826

Aliases

arxiv: 1208.5561 · arxiv_version: 1208.5561v1 · doi: 10.48550/arxiv.1208.5561 · pith_short_12: D5PWSWSE3Y3I · pith_short_16: D5PWSWSE3Y3ITMA3 · pith_short_8: D5PWSWSE

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/D5PWSWSE3Y3ITMA3BQTDMYTIZP \
  | 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: 1f5f695a44de3689b01b0c26366268cbe52fde46da87ea8def55e8c7c1d01826

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8dec24dd4edad05d65114b6cdd4d1d8188880d1b96ee72f39ee9c0149631c3e6",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-08-28T05:56:08Z",
    "title_canon_sha256": "9d6b5b3110e46f3be75fa7b2a36a16979fab1656fae916417409f27667e9c4d5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.5561",
    "kind": "arxiv",
    "version": 1
  }
}