Pith Number

pith:DRNHNDZP

pith:2018:DRNHNDZPTYLHFMRP2JF6JKWKR3

not attested not anchored not stored refs pending

On the discrete mean of the derivative of Hardy's $Z$-function

Hirotaka Kobayashi

arxiv:1811.04530 v2 · 2018-11-12 · 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{DRNHNDZPTYLHFMRP2JF6JKWKR3}

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	2026-05-18T00:00:12.650223Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1c5a768f2f9e1672b22fd24be4aaca8efa706f9c5c61cc4dd2b886c874f0d04b

Aliases

arxiv: 1811.04530 · arxiv_version: 1811.04530v2 · doi: 10.48550/arxiv.1811.04530 · pith_short_12: DRNHNDZPTYLH · pith_short_16: DRNHNDZPTYLHFMRP · pith_short_8: DRNHNDZP

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/DRNHNDZPTYLHFMRP2JF6JKWKR3 \
  | 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: 1c5a768f2f9e1672b22fd24be4aaca8efa706f9c5c61cc4dd2b886c874f0d04b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9e7fe59334216db8d8342ef2beaa6f19a8c23f21156b04f6ae0571a2a6deb539",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-11-12T02:09:51Z",
    "title_canon_sha256": "ef3b5d552aa1595e383ca5ea003296f612fbfccdfaac9d3940ad1b7cc8c4c21b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.04530",
    "kind": "arxiv",
    "version": 2
  }
}