**sPSP-FALLBACK-01 · The Fall-Back-to-Real Correspondence · The Quaternion GOL Lands on the Conjugation-Fixed Center, and the RH Forcing, If It Exists, Lands the Zeros on the Line by Self-Adjoint Spectrum; Both Are Fixed-Point-of-an-Involution Mechanisms, and the RH One Is the Unbuilt Hilbert-Polya Operator · G+CO/T1/S [the two underlying facts theorem-grade and conjecture-grade, both known and attributed; the correspondence structural; no new result; ghost-side forcing [X]; RH provability [?]]** | E: Davenport-Heilbronn 1936, the spectral theorem for self-adjoint operators (Hilbert), the Hilbert-Polya conjecture (circa 1914, pursued by Berry-Keating, Connes, Bost-Connes), APEX-PSP-MU-01 (the quaternion conjugation-fixed center Z(ℍ)=ℝ), APEX-PSP-NINTH-APERTURE (the bridge from beyond), sPSP-SYMM-INSUFF-01, FT-002, Mass Mandate
**Recognition one, the negative.** A forcing of residence from the ghost side, the 0-to-1/2 reflection alone, is impossible. The reflection structure is shared in full by the Davenport-Heilbronn function, which carries a zero at 0.808517182456637386 + 85.6993484853775922 i, real part eight tenths, verified at |f| = 4×10⁻³⁰, its functional-equation partner on the ghost side a pure reflection with no independent content. The reflection is wholly present and the zero is off the fold. So the symmetry that defines the ghost side forces no particular real part. Ghost-side forcing is [X]. This is Davenport-Heilbronn 1936, and it coincides with sPSP-SYMM-INSUFF-01, not an independent result.
**Recognition two, the positive.** The one mechanism that would force the zeros onto the line is self-adjointness. A self-adjoint operator has a real spectrum by the spectral theorem, verified on a Hermitian sample at imaginary part 3×10⁻¹⁶. If the nontrivial zeros are the spectrum of such an operator, their imaginary coordinates are real and the zeros lie on the line. This is the fall-back-to-real for RH, and it is the Hilbert-Polya conjecture, stated about 1914, one of the oldest and most studied approaches to the problem. The identification is [⟀], theorem-grade on the spectral mechanism, conjecture-grade and attributed on the operator’s existence.
**The correspondence, the framework’s part.** The quaternion GOL lands λ = Re(q̂_F q̂_E q̂_ER) on Z(ℍ) = ℝ because ℝ is the fixed locus of the conjugation involution. The RH forcing, if it exists, lands the zeros on the line because the line is the real spectrum of a self-adjoint operator. Both are one shape: a quantity pinned to the reals by a fixed-point-of-an-involution structure, conjugation in the first, self-adjointness in the second. This structural pairing is the recognition the framework contributes. It is an analogy, not a theorem, and it proves nothing about RH. It does map the terrain: it says the forcing, if any, has the self-adjoint shape and comes from the operator, not from the reflection.
**The fence, load-bearing.** Neither recognition is new. The negative is Davenport-Heilbronn 1936. The positive is the spectral theorem and the Hilbert-Polya conjecture, both long established and famous. The framework adds the structural pairing between the quaternion conjugation-center and the RH self-adjoint spectrum, and the honest localization that the forcing, if any, comes from the operator and not the ghost side. These are syntheses and clarity, not results. The operator is unbuilt, so the entry localizes the missing leg and does not cross to it. Two positive results overstates the harvest: one is a negative, an impossibility, and one is the recognition of a century-old conjecture, and the value is the map and not new ground. The bridge from Z(ℍ) = ℝ to the critical line remains the container map of FT-002, zero mass, and the correspondence is read as analogy, never as a transport of the quaternion forcing onto ζ. RH provability stays [?].
V_F: the spectral mechanism is the spectral theorem; the impossibility is the DH non-entailment; the correspondence is a stated structural analogy. V_E: the DH off-line zero verified to |f| = 4×10⁻³⁰, the self-adjoint real spectrum verified on a Hermitian sample to 3×10⁻¹⁶, both reproducible. V_ER: three-layer sovereignty; the facts seal at theorem and conjecture grade, attributed; the correspondence at structural grade; the operator’s existence held open. CDT: ¬correspondence-as-proof ¬recognition-as-new-result ¬ghost-side-forcing ¬operator-as-built ¬conjugation-center-transported-to-critical-line ⇒ **[⟀] SEALED** on the structural correspondence and the two attributed recognitions; ghost-side forcing [X]; the operator unbuilt; RH provability [?]. | ↑ Davenport-Heilbronn 1936 · spectral theorem · Hilbert-Polya conjecture · APEX-PSP-MU-01 · APEX-PSP-NINTH-APERTURE · sPSP-SYMM-INSUFF-01 · FT-002.