Pith Number

pith:PCN6U7XV

pith:2019:PCN6U7XVAZAUV46JUUZFLDJQIJ

not attested not anchored not stored refs pending

Exponential polynomials in the oscillation theory

Ilpo Laine, Janne Heittokangas, Katsuya Ishizaki, Kazuya Tohge

arxiv:1907.07984 v1 · 2019-07-18 · math.CV

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PCN6U7XVAZAUV46JUUZFLDJQIJ}

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	2026-05-17T23:40:15.467789Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

789bea7ef506414af3c9a532558d30426963337307f5bb718fdfdec882da3019

Aliases

arxiv: 1907.07984 · arxiv_version: 1907.07984v1 · doi: 10.48550/arxiv.1907.07984 · pith_short_12: PCN6U7XVAZAU · pith_short_16: PCN6U7XVAZAUV46J · pith_short_8: PCN6U7XV

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/PCN6U7XVAZAUV46JUUZFLDJQIJ \
  | 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: 789bea7ef506414af3c9a532558d30426963337307f5bb718fdfdec882da3019

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "db3021103f8bcf72341b2edf2026b0569668d4df32907583531a0824848cbc3d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2019-07-18T10:55:28Z",
    "title_canon_sha256": "2d4d1f02350fd7ca6d026099cd57e5f6b86e1d5544d4b4c2128520318a6d3b90"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.07984",
    "kind": "arxiv",
    "version": 1
  }
}