A registered result in its source context
Original ledger classification: Physical (conjecture sharpened) + Identity [I]
Recorded statement: Koide RG attractor is FORCED, not postulated [I] + ONE [P] identification (sharpens FR.KOIDE.01/02/03 via the v81 double cover): a branch-divisor-preserving Moebius map of the pencil line that fixes BOTH branch points q=2 (Koide) and q=5…
Statement, assumptions and sources
Paper context: Frontier and open physical interfaces
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FR.KOIDE.04
Original ledger classification: Physical (conjecture sharpened) + Identity [I]
Original claim text
Koide RG attractor is FORCED, not postulated [I] + ONE [P] identification (sharpens FR.KOIDE.01/02/03 via the v81 double cover): a branch-divisor-preserving Moebius map of the pencil line that fixes BOTH branch points q=2 (Koide) and q=5 (carrier) is, in the cross-ratio coordinate rho=(q-2)/(5-q), EXACTLY rho->mu*rho, hence UNIQUE once mu is fixed [I]. The multiplier is NOT a new input: mu=(2/3)^6 is the subleading eigenvalue lambda2 of the THEORY'S OWN unique gapped boundary transfer operator (v54/v56, spectrum {1,(2/3)^6,(1/3)^6}, gap 6 log(3/2)>0), and the Koide branch x=-2/3=-|Z2|/N_fam IS its cusp weight 2/3={0,1,|Z2|}/N_fam; carrier q=5 -> Koide q=2 under the deck period q->q-N_fam (shared cusp class 2/3). With mu=(2/3)^6 the unique map is the integer Moebius map F(q)=2(569q-3325)/(665q-3517), F(2)=2, F(5)=5, F'(2)=(2/3)^6<1 (Koide is the ATTRACTOR), F'(5)=(3/2)^6>1 (carrier the REPELLER), so q_n->2 i.e. x->-2/3 at the SAME rate that governs SM flavor and horizon recovery. NET: the three 'structural postulates' for a Koide derivation collapse to ONE physical identification - source->pole transfer = branch-preserving relaxation of the established transfer operator; rate, uniqueness and direction then follow. NOT a closure: the single identification stays [P]
Original classification detail
Identity [I] (map uniqueness + multiplier = the established transfer gap) + Physical [P] (the one source->pole identification; no closure)
Dependencies as recorded
FR.KOIDE.01; FR.KOIDE.03; FLAV.PENCIL.03; v54; v56; v81
Open the original ledger source, row 149Location recorded in the ledger
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- Frontier and open physical interfaces
Navigation through a shared verification script
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- 2026-06-19 (the discrete [formula in source] dynamic lens on F_transfer: one shape, one seam-rate, v303)Research changelog; TFPT — Introduction and reading guide
- The Sheet Diamond and the Winding Line: masses and transport from one surfacetfpt 2 standard model
- 2026-06-23 (Track 3 — the [formula in source] functor promoted from contracts to TYPED runnable solvers with kill tests: Koide source [formula in source] pole ( v371), [formula in source] Boltzmann ( v372), axion finite- [formula in source] relic ( v373), [formula in source] uncertainty budget ( v374))Research changelog; TFPT — Introduction and reading guide
- 2026-06-24 (Lean 4: FORM.SPECTRALGAP.01 extended to the finite-dimensional Perron–Frobenius case)Research changelog; TFPT — Introduction and reading guide
- Certifiability and recommended ordertfpt research contracts
- 2026-06-25 (F_pole external: the Koide source [formula in source] pole transfer is one-loop EM: v420)Research changelog; TFPT — Introduction and reading guide
- 2026-06-23 (Bird's-eye synthesis: two new structural patterns — v383 the universal spectral-gap principle and v384 the residual is certification, not construction)Research changelog; TFPT — Introduction and reading guide
- Front matter / supportStandard Model and flavor structure
Registered verification modules
- v82_koide_attractor_splitting.pyRegistered verification module · frontier
Read the description recorded in the module registry
Koide attractor FORCED, not postulated: the branch-preserving map fixing q=2,5 is unique, and its multiplier (2/3)⁶ = the established transfer gap λ₂ (v54/56) ⇒ 3 Koide postulates → 1; + splitting trichotomy disc 81/49/40 (clean split is non-generic)
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