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A registered result in its source context

Original ledger classification: Identity [I] (variational structure both sides) + Physical [P] (common-principle reading)

Recorded statement: ONE ORIENTATION - the anchor is the stationary repeller in BOTH sectors (variational upgrade of the v101 temperature lemma + the v82/v99 flavor flow): FLAVOR [I] - the canonical flow dq/dt = (Delta/N_fam)(q-2)(q-5) is the GRADIENT flow of…

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Paper context: Origin Theory

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HOR.ORIENT.01

Original ledger classification: Identity [I] (variational structure both sides) + Physical [P] (common-principle reading)

Original claim text

ONE ORIENTATION - the anchor is the stationary repeller in BOTH sectors (variational upgrade of the v101 temperature lemma + the v82/v99 flavor flow): FLAVOR [I] - the canonical flow dq/dt = (Delta/N_fam)(q-2)(q-5) is the GRADIENT flow of the cubic V(q) = -(Delta/N_fam)(q^3/3 - 7q^2/2 + 10q); critical points = exactly the two branch points; stationary curvatures = +-the transfer gap (V''(Koide) = +Delta attractor, V''(carrier) = -Delta repeller); inflection at q = 7/2 = scalaron/2 = half the branch-divisor trace; Lyapunov rate d(-ln rho)/dt = Delta exactly and constantly. GRAVITY [I] - d(S_tot/S_dS)/dx = (x-1)(x+1)/Phi_3(x)^2: the Nariai/anchor point is the UNIQUE physical stationary point of the SdS entropy functional, with curvature 2/9 = |Z2|/N_fam^2 = (2/3)(1/3); temperature lemma => evaporation ASCENDS the entropy away from the anchor toward the democratic endpoint. ORIENTATION THEOREM [I]: both sectors flow away from an anchor-stationary configuration with grammar-constant curvatures. HONEST: flavor attractor = a branch point vs gravity attractor = smooth endpoint; flavor functional = potential of a [P] relaxation vs gravity = BH entropy; 'one variational principle of the seam' stays a reading [P]; no open gate touched. Figures: orientation.pdf, cover_twins.pdf, seam_units.pdf

Original classification detail

Identity: anchor = stationary repeller both sectors; principle reading [P]

Dependencies as recorded

HOR.NARIAI.01; FR.KOIDE.04; FR.KOIDE.06 (generator); FLAV.PENCIL.03

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Registered verification modules

  • v102_seam_orientation.pyRegistered verification module · registry
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    One orientation: the anchor is the STATIONARY REPELLER in both sectors — flavor: the canonical flow dq/dt = (Δ/N_fam)(q−2)(q−5) is the gradient flow of a cubic potential whose critical points are exactly the two branch points, with stationary curvatures V''(Koide) = +Δ (attractor) and V''(carrier) = −Δ (repeller) = ±the transfer gap; inflection at q = 7/2 = scalaron/2; Lyapunov rate d(−ln ρ)/dt = Δ exactly constant; gravity: d(S_tot/S_dS)/dx = (x−1)(x+1)/Φ₃(x)² — Nariai is the UNIQUE stationary point of the SdS entropy, curvature 2/9 = |ℤ₂|/N_fam² = (2/3)(1/3); evaporation = entropy ascent away from the anchor [I]; honest disanalogies recorded; 'one variational principle of the seam' stays a reading [P]

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