Pith Number

pith:IESUIXNU

pith:2016:IESUIXNUH7UYHSAKSFI6DLCRCZ

not attested not anchored not stored refs pending

Almost sure convergence of the multiple ergodic average for certain weakly mixing systems

Song Shao, Wen Huang, Xiangdong Ye, Yonatan Gutman

arxiv:1612.02873 v2 · 2016-12-09 · 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{IESUIXNUH7UYHSAKSFI6DLCRCZ}

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	2026-05-18T00:42:44.029749Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4125445db43fe983c80a9151e1ac5116426e4681b790cbaef708a634f992f99b

Aliases

arxiv: 1612.02873 · arxiv_version: 1612.02873v2 · doi: 10.48550/arxiv.1612.02873 · pith_short_12: IESUIXNUH7UY · pith_short_16: IESUIXNUH7UYHSAK · pith_short_8: IESUIXNU

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/IESUIXNUH7UYHSAKSFI6DLCRCZ \
  | 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: 4125445db43fe983c80a9151e1ac5116426e4681b790cbaef708a634f992f99b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9299b201e3470a6c9e01ffe122f3a351278f185d08446cee06795ddf9c235207",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2016-12-09T00:01:56Z",
    "title_canon_sha256": "22f5e27b9779dae6e9d7ddb0c32e18a3f05da95dad0306c7d6933371499a8852"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.02873",
    "kind": "arxiv",
    "version": 2
  }
}