Pith Number

pith:4HMYMI2F

pith:2022:4HMYMI2F2RVIJUDJSNOG4V3FBX

not attested not anchored not stored refs pending

On the multiplicative independence between $n$ and $\lfloor \alpha n\rfloor$

David Crn\v{c}evi\'c, Felipe Hern\'andez, Kevin Rizk, Khunpob Sereesuchart, Ran Tao

arxiv:2211.15830 v4 · 2022-11-28 · 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{4HMYMI2F2RVIJUDJSNOG4V3FBX}

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	2026-07-05T07:21:24.873472Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1d9862345d46a84d069935c6e57650dc5cfe30f4f440e97494b62e1b867aa65

Aliases

arxiv: 2211.15830 · arxiv_version: 2211.15830v4 · doi: 10.48550/arxiv.2211.15830 · pith_short_12: 4HMYMI2F2RVI · pith_short_16: 4HMYMI2F2RVIJUDJ · pith_short_8: 4HMYMI2F

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/4HMYMI2F2RVIJUDJSNOG4V3FBX \
  | 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: e1d9862345d46a84d069935c6e57650dc5cfe30f4f440e97494b62e1b867aa65

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f712690077c30122544b251b2604fa3665e79222650e62b38b383e99bc44c5fa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2022-11-28T23:41:17Z",
    "title_canon_sha256": "986ee0c58d70c71e701769cc7cbff78b1d4ba1e9bc6d73898ff72366e75324e7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2211.15830",
    "kind": "arxiv",
    "version": 4
  }
}