Pith Number

pith:SXJSBVVI

pith:2010:SXJSBVVITPF4NY263SPIPOKSB5

not attested not anchored not stored refs pending

Random Sequences and Pointwise Convergence of Multiple Ergodic Averages

Emmanuel Lesigne (LMPT), Mate Wierdl, Nikos Frantzikinakis

arxiv:1012.1130 v3 · 2010-12-06 · math.DS · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SXJSBVVITPF4NY263SPIPOKSB5}

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	2026-05-18T04:24:06.032065Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

95d320d6a89bcbc6e35edc9e87b9520f53104c2f542b3ed171158622fc7ddb91

Aliases

arxiv: 1012.1130 · arxiv_version: 1012.1130v3 · doi: 10.48550/arxiv.1012.1130 · pith_short_12: SXJSBVVITPF4 · pith_short_16: SXJSBVVITPF4NY26 · pith_short_8: SXJSBVVI

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/SXJSBVVITPF4NY263SPIPOKSB5 \
  | 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: 95d320d6a89bcbc6e35edc9e87b9520f53104c2f542b3ed171158622fc7ddb91

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d7fa9ec600c431f9e813c0edd285fa097f63b2ec77a03732c20448e98fb12858",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2010-12-06T11:12:46Z",
    "title_canon_sha256": "fb110e14dc5f886377af94fca4330b8867d911f413fc796da37153f3b0affe88"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.1130",
    "kind": "arxiv",
    "version": 3
  }
}