Pith Number

pith:CNJSZP7E

pith:2013:CNJSZP7ESZTF5636V4KSL5HQAQ

not attested not anchored not stored refs pending

Ergodic Theorem involving additive and multiplicative groups of a field and $\{x+y,xy\}$ patterns

Joel Moreira, Vitaly Bergelson

arxiv:1307.6242 v3 · 2013-07-23 · math.CO · 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{CNJSZP7ESZTF5636V4KSL5HQAQ}

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	2026-05-18T01:30:26.068044Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

13532cbfe496665efb7eaf1525f4f00400c2dba09b55afa01a61854eea5d03d2

Aliases

arxiv: 1307.6242 · arxiv_version: 1307.6242v3 · doi: 10.48550/arxiv.1307.6242 · pith_short_12: CNJSZP7ESZTF · pith_short_16: CNJSZP7ESZTF5636 · pith_short_8: CNJSZP7E

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/CNJSZP7ESZTF5636V4KSL5HQAQ \
  | 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: 13532cbfe496665efb7eaf1525f4f00400c2dba09b55afa01a61854eea5d03d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "57aafd4a00da2de78cf696511bb63bab5c05187ebbddd0df486b93eaa505bc31",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-07-23T20:37:23Z",
    "title_canon_sha256": "83909c71698574b5e3956c70fabacc500ce4ab21bdd3089417117626653d5a69"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.6242",
    "kind": "arxiv",
    "version": 3
  }
}