Pith Number

pith:DXLQMU6B

pith:2015:DXLQMU6BIVNT3QI3KA66KEUS67

not attested not anchored not stored refs pending

Multiple ergodic theorems for arithmetic sets

Bernard Host, Nikos Frantzikinakis

arxiv:1503.07154 v3 · 2015-03-24 · math.DS · math.CO · 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{DXLQMU6BIVNT3QI3KA66KEUS67}

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	2026-05-18T01:26:34.281810Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1dd70653c1455b3dc11b503de51292f7fcec6a9c50579bd4414f1da86e505dae

Aliases

arxiv: 1503.07154 · arxiv_version: 1503.07154v3 · doi: 10.48550/arxiv.1503.07154 · pith_short_12: DXLQMU6BIVNT · pith_short_16: DXLQMU6BIVNT3QI3 · pith_short_8: DXLQMU6B

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/DXLQMU6BIVNT3QI3KA66KEUS67 \
  | 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: 1dd70653c1455b3dc11b503de51292f7fcec6a9c50579bd4414f1da86e505dae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "469773c4067a1515d9d21a84d94511e218f82a66b8603a5b02f82e47198f4ea7",
    "cross_cats_sorted": [
      "math.CO",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-03-24T19:54:17Z",
    "title_canon_sha256": "a44c21ccabed0b989bc4af753419b9c2d09fff9203baced366623f54a37186c8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.07154",
    "kind": "arxiv",
    "version": 3
  }
}