Pith Number

pith:SBWOCVEQ

pith:2011:SBWOCVEQC3NFAWKV5NQ3QYTWZ7

not attested not anchored not stored refs pending

Some open problems on multiple ergodic averages

Nikos Frantzikinakis

arxiv:1103.3808 v3 · 2011-03-19 · math.DS · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SBWOCVEQC3NFAWKV5NQ3QYTWZ7}

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	2026-05-18T01:02:14.527734Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

906ce1549016da505955eb61b86276cfed3ad5a0cb3d715f2726969574ed146d

Aliases

arxiv: 1103.3808 · arxiv_version: 1103.3808v3 · doi: 10.48550/arxiv.1103.3808 · pith_short_12: SBWOCVEQC3NF · pith_short_16: SBWOCVEQC3NFAWKV · pith_short_8: SBWOCVEQ

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/SBWOCVEQC3NFAWKV5NQ3QYTWZ7 \
  | 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: 906ce1549016da505955eb61b86276cfed3ad5a0cb3d715f2726969574ed146d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6e21e605fdbe1399fa0badca9d8132949cc73eca06daf9128eca1912167a725c",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-03-19T20:55:49Z",
    "title_canon_sha256": "fa7fc1338c756732041ea5192d7cb91fe1e16c8e19c6f54458f9b2db4c87382f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.3808",
    "kind": "arxiv",
    "version": 3
  }
}