Pith Number

pith:QK3I33AJ

pith:2016:QK3I33AJSINFUIS7DILHZ2QDL7

not attested not anchored not stored refs pending

Hardy's function $Z(t)$ - results and problems

Aleksandar Ivi\'c

arxiv:1601.06512 v2 · 2016-01-25 · 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{QK3I33AJSINFUIS7DILHZ2QDL7}

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	2026-05-18T01:21:10.941986Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

82b68dec09921a5a225f1a167cea035ff660b19de5b0fcdb04c23f7a16a4d703

Aliases

arxiv: 1601.06512 · arxiv_version: 1601.06512v2 · doi: 10.48550/arxiv.1601.06512 · pith_short_12: QK3I33AJSINF · pith_short_16: QK3I33AJSINFUIS7 · pith_short_8: QK3I33AJ

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/QK3I33AJSINFUIS7DILHZ2QDL7 \
  | 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: 82b68dec09921a5a225f1a167cea035ff660b19de5b0fcdb04c23f7a16a4d703

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "00836bdb80e874e9f06b97ae299fd115b1d575055e2401eea0ed2e3158c004b8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-01-25T08:46:33Z",
    "title_canon_sha256": "6f52cf0af08dc281dfc35c76053a25a8c027b063c667aa01bdd9a1ec1de21483"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.06512",
    "kind": "arxiv",
    "version": 2
  }
}