Pith Number

pith:QRYOFU77

pith:2025:QRYOFU77FTD7XPGJUETVRHLLHT

not attested not anchored not stored refs pending

Asymmetry for the Riemann Hypothesis

Walid Oukil

The Riemann zeta function cannot have both zeta(s) and zeta(1 minus conjugate s) equal to zero except on the critical line.

arxiv:2511.13496 v12 · 2025-11-17 · math.DS

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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.

Claims

C1strongest claim

we show that the Riemann zeta function satisfies (ζ(s),ζ(1-¯s))≠(0,0) for any s in the critical strip, except on the critical line. This still holds even when the fractional part function is replaced by a function satisfying a specific 'Rotation Number Hypothesis'.

C2weakest assumption

The Rotation Number Hypothesis holds for the function that replaces the fractional part function; without an independent justification or verification of this hypothesis, the asymmetry claim does not follow.

C3one line summary

The Riemann zeta function satisfies (ζ(s), ζ(1-¯s)) ≠ (0,0) off the critical line, even under a Rotation Number Hypothesis replacing the fractional part.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-22T01:03:49.736014Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8470e2d3ff2cc7fbbcc9a127589d6b3ce867b69b6fe0a70cb3815dd4eba0a9b7

Aliases

arxiv: 2511.13496 · arxiv_version: 2511.13496v12 · doi: 10.48550/arxiv.2511.13496 · pith_short_12: QRYOFU77FTD7 · pith_short_16: QRYOFU77FTD7XPGJ · pith_short_8: QRYOFU77

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/QRYOFU77FTD7XPGJUETVRHLLHT \
  | 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: 8470e2d3ff2cc7fbbcc9a127589d6b3ce867b69b6fe0a70cb3815dd4eba0a9b7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6c76d45c725e7ab83a6ec9d5048932f2d582db72855a037964dff61dda130a0f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2025-11-17T15:36:07Z",
    "title_canon_sha256": "a1950ea9270e6ce955188fb366d3db6522efe06c20fe86313c2ee814b2885c74"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2511.13496",
    "kind": "arxiv",
    "version": 12
  }
}