Pith Number

pith:55ARXSWS

pith:2022:55ARXSWS7UNUEY4XUVMCJ6NBJU

not attested not anchored not stored refs pending

Pseudodifferential arithmetic, Riemann and Lindel\"of hypotheses

Andr\'e Unterberger

The Riemann hypothesis is equivalent to estimates on a Weyl-calculus operator from zeta zeros, and explicit construction via pseudodifferential arithmetic disproves a measure conjecture on zero real parts while proving the Lindelöf

arxiv:2208.12937 v46 · 2022-08-27 · math.NT

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\usepackage{pith}
\pithnumber{55ARXSWS7UNUEY4XUVMCJ6NBJU}

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Record completeness

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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.

Claims

C1strongest claim

The closure of the set of real parts of non-trivial zeros of zeta has measure at least 0.5 is disproved, and the Lindelöf hypothesis is proved, via explicit construction of an operator whose estimates are controlled by pseudodifferential arithmetic.

C2weakest assumption

That the pseudodifferential arithmetic construction yields an operator whose explicit form permits direct verification or refutation of the stated estimates without hidden circular dependence on the distribution of the zeros themselves.

C3one line summary

Claims to disprove that the closure of real parts of non-trivial zeta zeros has measure at least 0.5 and to prove the Lindelöf hypothesis via pseudodifferential arithmetic applied to an operator built from zeta zeros.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-01T01:02:11.070989Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ef411bcad2fd1b426397a55824f9a14d0deddf405a32e949646b2a53a476dbd2

Aliases

arxiv: 2208.12937 · arxiv_version: 2208.12937v46 · doi: 10.48550/arxiv.2208.12937 · pith_short_12: 55ARXSWS7UNU · pith_short_16: 55ARXSWS7UNUEY4X · pith_short_8: 55ARXSWS

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/55ARXSWS7UNUEY4XUVMCJ6NBJU \
  | 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: ef411bcad2fd1b426397a55824f9a14d0deddf405a32e949646b2a53a476dbd2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "862d8a53fe6afbd8981929eb9d07db4f18270c20e94d991b188daf3596a8151f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2022-08-27T06:41:32Z",
    "title_canon_sha256": "007a3c2710ed7f29ccabdf7df957bd3e3bd62ebf7de15e9bb0fe1fb442760453"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2208.12937",
    "kind": "arxiv",
    "version": 46
  }
}