Pith Number

pith:QDZ5MMC3

pith:2012:QDZ5MMC3GJ5MBRBE32RAIAXLUW

not attested not anchored not stored refs pending

Vector Valued Martingale-Ergodic and Ergodic-Martingale Theorems

Farruh Shahidi, Inomjon Ganiev

arxiv:1201.1682 v1 · 2012-01-09 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QDZ5MMC3GJ5MBRBE32RAIAXLUW}

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	2026-05-18T04:05:02.818173Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

80f3d6305b327ac0c424dea20402eba5a98ebc6878230d08239f0b4faa7a2379

Aliases

arxiv: 1201.1682 · arxiv_version: 1201.1682v1 · doi: 10.48550/arxiv.1201.1682 · pith_short_12: QDZ5MMC3GJ5M · pith_short_16: QDZ5MMC3GJ5MBRBE · pith_short_8: QDZ5MMC3

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/QDZ5MMC3GJ5MBRBE32RAIAXLUW \
  | 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: 80f3d6305b327ac0c424dea20402eba5a98ebc6878230d08239f0b4faa7a2379

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0fa3acf8f8f873cdfe38846a181248444b40996dffc53ca74b8d89ac4126951f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-01-09T03:00:50Z",
    "title_canon_sha256": "4e39f266f5a651f5a2e06c92125ef9037e8cba0b9a9d59467f2995c2ee1b82a0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.1682",
    "kind": "arxiv",
    "version": 1
  }
}