Pith Number

pith:ABW46UUR

pith:2012:ABW46UURNTHSCMRR7BTJ4TGAWY

not attested not anchored not stored refs pending

Any non-monomial polynomial of the Riemann zeta-function has complex zeros off the critical line

{\L}ukasz Pa\'nkowski, Takashi Nakamura

arxiv:1212.5890 v4 · 2012-12-24 · 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{ABW46UURNTHSCMRR7BTJ4TGAWY}

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	2026-05-18T03:12:08.973159Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

006dcf52916ccf213231f8669e4cc0b61d9b4be4e0a3e89c9711eb1d58b55ad0

Aliases

arxiv: 1212.5890 · arxiv_version: 1212.5890v4 · doi: 10.48550/arxiv.1212.5890 · pith_short_12: ABW46UURNTHS · pith_short_16: ABW46UURNTHSCMRR · pith_short_8: ABW46UUR

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/ABW46UURNTHSCMRR7BTJ4TGAWY \
  | 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: 006dcf52916ccf213231f8669e4cc0b61d9b4be4e0a3e89c9711eb1d58b55ad0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3faf819c9064d08ee6b7a65c1bd5061d845a4f5950172d10f8257e4c767a5a67",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-12-24T10:22:39Z",
    "title_canon_sha256": "2a1dedd2102254cf78de026c0bd1bdf3c3a510c38220d062e10b0966bb1a7f9a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.5890",
    "kind": "arxiv",
    "version": 4
  }
}