Pith Number

pith:FPZNQMFK

pith:2014:FPZNQMFKLOAKKHQLMVCG22G7G7

not attested not anchored not stored refs pending

Higher order Fourier analysis of multiplicative functions and applications

Bernard Host, Nikos Frantzikinakis

arxiv:1403.0945 v2 · 2014-03-04 · math.NT · 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{FPZNQMFKLOAKKHQLMVCG22G7G7}

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	2026-05-18T01:22:03.515066Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2bf2d830aa5b80a51e0b65446d68df37cd3cd5182714c57ca122ca397a51d6f5

Aliases

arxiv: 1403.0945 · arxiv_version: 1403.0945v2 · doi: 10.48550/arxiv.1403.0945 · pith_short_12: FPZNQMFKLOAK · pith_short_16: FPZNQMFKLOAKKHQL · pith_short_8: FPZNQMFK

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/FPZNQMFKLOAKKHQLMVCG22G7G7 \
  | 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: 2bf2d830aa5b80a51e0b65446d68df37cd3cd5182714c57ca122ca397a51d6f5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3d792ff4cef19bff307253a370930168cfccb05aa7f7600a254ed48ee84d0d9a",
    "cross_cats_sorted": [
      "math.CO",
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-03-04T21:02:21Z",
    "title_canon_sha256": "a8bb527710b73e0e4f3f462676a020628faa505548f4d79684feb644c6a50552"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1403.0945",
    "kind": "arxiv",
    "version": 2
  }
}