Pith Number

pith:5NRILYUI

pith:2015:5NRILYUIJGM67HA5Y6BLQ5BNAP

not attested not anchored not stored refs pending

Sequences from zero entropy noncommutative toral automorphisms and Sarnak Conjecture

Song Shao, Wen Huang, Xiangdong Ye, Zhengxing Lian

arxiv:1510.06022 v1 · 2015-10-19 · math.OA · math.DS · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5NRILYUIJGM67HA5Y6BLQ5BNAP}

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	2026-05-18T01:29:38.979923Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eb6285e2884999ef9c1dc782b8742d03d1cf1ed945d49ba48339103286489bc9

Aliases

arxiv: 1510.06022 · arxiv_version: 1510.06022v1 · doi: 10.48550/arxiv.1510.06022 · pith_short_12: 5NRILYUIJGM6 · pith_short_16: 5NRILYUIJGM67HA5 · pith_short_8: 5NRILYUI

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/5NRILYUIJGM67HA5Y6BLQ5BNAP \
  | 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: eb6285e2884999ef9c1dc782b8742d03d1cf1ed945d49ba48339103286489bc9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "232d0c3319d52068ac0f771af20d06f5ce6941268dd87fd39218320112998cd3",
    "cross_cats_sorted": [
      "math.DS",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2015-10-19T08:14:25Z",
    "title_canon_sha256": "d849ec2f17bc40d4bde0537a264ccd83eb108864edadd06cf2f6f78e57334089"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.06022",
    "kind": "arxiv",
    "version": 1
  }
}