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A registered result in its source context

Original ledger classification: Identity [I] (basin/rate/source) + Numerical [N] (pole) + [P] (transfer mechanism)

Recorded statement: Koide relaxation toy (next.txt P2 NARROWED, not closed): (1) BASIN LEMMA [I] - under the canonical dictionary q=N_fam*Q the physical Koide range Q in [1/3,1] (Cauchy-Schwarz) maps to q in [1,3]: the attractor q=2 lies inside, the repeller…

Statement, assumptions and sources

Paper context: Frontier and open physical interfaces

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FR.KOIDE.05

Original ledger classification: Identity [I] (basin/rate/source) + Numerical [N] (pole) + [P] (transfer mechanism)

Original claim text

Koide relaxation toy (next.txt P2 NARROWED, not closed): (1) BASIN LEMMA [I] - under the canonical dictionary q=N_fam*Q the physical Koide range Q in [1/3,1] (Cauchy-Schwarz) maps to q in [1,3]: the attractor q=2 lies inside, the repeller q=5 outside => EVERY physically possible charged-lepton configuration is in the attractor basin, no fine-tuning of the start needed. (2) EXACT RATE [I]: along the trajectory from the physical source value the cross-ratio rho=(q-2)/(5-q) contracts by EXACTLY mu=(2/3)^6 per F-step (Moebius linearity, machine-checked to 1e-30). (3) SOURCE [I]: the exact ladder gives Q_src=0.6644638161, i.e. rho_src=-0.0021980 = -phi0/24 to 0.8% - the v25 conjecture re-expressed in attractor coordinates: the source sits ONE SEED QUANTUM phi0/24 before the branch point (24=|W(A3)|). (4) POLE [N]: PDG pole masses give Q_pole=0.6666644634 - the branch point is hit to 3.3e-6 at the pole layer. HONEST NEGATIVES (they narrow P2): (5) flow time source->pole t=log_mu(rho_pole/rho_src)=2.838 is NOT an integer => the literal discrete iteration pole=F^n(source) is EXCLUDED; if the v82 map drives the transfer at all it must be the CONTINUOUS flow exp(t log F) at t~2.8 - the missing object is a continuous-time generator; (6) the 0.79% mismatch of rho_src vs -phi0/24 is far above ladder precision => 'exactly phi0/24' remains a [P] conjecture about the transfer normalisation. STATUS: basin/uniqueness/rate forced [I]; open [P]: the continuous generator and its flow time

Original classification detail

Identity/Numerical: basin lemma + exact rate + honest negatives; P2 narrowed to the continuous transfer generator

Dependencies as recorded

FR.KOIDE.04; FLAV.PENCIL.04; v82

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Registered verification modules

  • v93_koide_relaxation_toy.pyRegistered verification module · registry
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    Koide relaxation toy (P2 narrowed): basin lemma — every physical Koide configuration lies in the attractor basin (Q∈[1/3,1] → q∈[1,3]: attractor in, repeller out); exact contraction rate (2/3)⁶ along the physical trajectory; source at ρ = −φ₀/24 (one seed quantum before the branch point); honest negatives: pole ≠ integer F-steps from source (t=2.84 ⇒ continuous generator missing), φ₀/24 stays [P]

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