Pith Number

pith:Q3XGI4XP

pith:2018:Q3XGI4XPYQVZ3ICOCEI5V4LOEM

not attested not anchored not stored refs pending

Pair correlation of sequences $(\lbrace a_n \alpha \rbrace)_{n \in \mathbb{N}}$ with maximal order of additive energy

Gerhard Larcher, Wolfgang Stockinger

arxiv:1802.02901 v2 · 2018-02-07 · 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{Q3XGI4XPYQVZ3ICOCEI5V4LOEM}

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	2026-05-18T00:15:04.980104Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

86ee6472efc42b9da04e1111daf16e232f723d9482c1b79b77a8ebb617708b7e

Aliases

arxiv: 1802.02901 · arxiv_version: 1802.02901v2 · doi: 10.48550/arxiv.1802.02901 · pith_short_12: Q3XGI4XPYQVZ · pith_short_16: Q3XGI4XPYQVZ3ICO · pith_short_8: Q3XGI4XP

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/Q3XGI4XPYQVZ3ICOCEI5V4LOEM \
  | 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: 86ee6472efc42b9da04e1111daf16e232f723d9482c1b79b77a8ebb617708b7e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "314f9b1eea137aa59b1e4aff635f9d808802d1aa5dd7eb714d826a8cdd59a5ad",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-02-07T11:58:18Z",
    "title_canon_sha256": "d452778edcd022e53b6c6c2511537a050dd7bd0f28d3e4b5b7dc78a3178ef265"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1802.02901",
    "kind": "arxiv",
    "version": 2
  }
}