Pith Number

pith:YU47HQBK

pith:2014:YU47HQBKOYMTKQLHH5XJMGWZNK

not attested not anchored not stored refs pending

Congruences involving product of intervals and sets with small multiplicative doubling modulo a prime and applications

J. Cilleruelo, M. Z. Garaev

arxiv:1404.5070 v2 · 2014-04-20 · 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{YU47HQBKOYMTKQLHH5XJMGWZNK}

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	2026-05-18T01:17:44.328947Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c539f3c02a76193541673f6e961ad96a984360ebea74428aed77e017384a28ec

Aliases

arxiv: 1404.5070 · arxiv_version: 1404.5070v2 · doi: 10.48550/arxiv.1404.5070 · pith_short_12: YU47HQBKOYMT · pith_short_16: YU47HQBKOYMTKQLH · pith_short_8: YU47HQBK

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/YU47HQBKOYMTKQLHH5XJMGWZNK \
  | 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: c539f3c02a76193541673f6e961ad96a984360ebea74428aed77e017384a28ec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2fa6c03d3c2f538107bbdb6ef1a0949ce79c92dd977ea4217af5ba50bb829454",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-04-20T20:39:09Z",
    "title_canon_sha256": "0cd306bb115eb76ef2854329938414547dca4ecca412bf77d1905f759925c490"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1404.5070",
    "kind": "arxiv",
    "version": 2
  }
}