From ba20a3cf187fb2559fd018c6e1d6f02f3efa94e7 Mon Sep 17 00:00:00 2001 From: Allaun Silverfox <28494262+allaunthefox@users.noreply.github.com> Date: Tue, 5 May 2026 08:39:39 -0500 Subject: [PATCH] Add q-desic wormhole throat equation update --- .../avmr/q_desic_wormhole_throat_equations.md | 388 ++++++++++++++++++ 1 file changed, 388 insertions(+) create mode 100644 6-Documentation/docs/avmr/q_desic_wormhole_throat_equations.md diff --git a/6-Documentation/docs/avmr/q_desic_wormhole_throat_equations.md b/6-Documentation/docs/avmr/q_desic_wormhole_throat_equations.md new file mode 100644 index 00000000..a7738680 --- /dev/null +++ b/6-Documentation/docs/avmr/q_desic_wormhole_throat_equations.md @@ -0,0 +1,388 @@ +# Q-Desic Wormhole Throat Equations + +Status: EQUATION_UPDATE +Claim state: FORMAL_SCAFFOLD / ANALOGY_BOUNDED + +This note updates the wormhole throat equation system with q-desic routing, interface-gap pricing, FAMM route scars, decode/recovery constraints, and computable temporal bounds. + +This is not a claim that the stack implements physical quantum gravity. The q-desic source pattern is used as an operator-corrected route-selection analogy: visible geometry is not enough; the route must be corrected by hidden connection, torsion, density, interface, scar, and recovery terms. + +--- + +## 1. Existing throat center equation + +The existing contested-center throat equation is: + +```math +\frac{\partial H}{\partial t} += +\Delta_{g_{\mathrm{throat}}}H ++ +2\left\langle +\nabla\log(p_P+p_B+p_N+p_T),\nabla H +\right\rangle +``` + +with: + +```math +g_{\mathrm{throat}} += +w_P g_P + w_B g_B + w_N g_N + w_T g_T +``` + +and: + +```math +w_i = \frac{p_i}{p_P+p_B+p_N+p_T}. +``` + +The torsion-modified version is: + +```math +\frac{\partial H}{\partial t} += +\Delta_g H ++ +2\left\langle +\nabla\log p_0 ++\nabla\log\det(e) ++\widetilde{T}, +\nabla H +\right\rangle +``` + +where: + +```math +p_0 = p_P+p_B+p_N+p_T. +``` + +--- + +## 2. q-desic connection correction + +Define the q/FAMM-corrected effective connection: + +```math +\Gamma_{\mathrm{eff}} += +\Gamma_{LC} ++ +K_T ++Q_\Gamma ++F_\Gamma ++\Omega_\Gamma. +``` + +Terms: + +```text +Γ_LC = Levi-Civita connection of the current throat metric +K_T = contorsion / torsion correction +Q_Γ = q-desic operator-level connection correction +F_Γ = FAMM route-scar correction +Ω_Γ = interface-gap / seam correction +``` + +Use the corrected derivative: + +```math +\nabla \rightarrow \nabla^{(qF\Omega)}. +``` + +--- + +## 3. Q-FAMM throat evolution equation + +The updated throat evolution equation is: + +```math +\boxed{ +\frac{\partial H}{\partial t} += +\Delta_{g,qF\Omega}H ++ +2\left\langle +\nabla^{(qF\Omega)}\log p_{\mathrm{throat}}, +\nabla^{(qF\Omega)}H +\right\rangle +- +\Omega_{\mathrm{gap}}H +} +``` + +where: + +```math +p_{\mathrm{throat}} = p_P+p_B+p_N+p_T +``` + +and: + +```text +Δ_{g,qFΩ} = q/FAMM/interface-corrected Laplace-Beltrami operator +Ω_gap = penalty from representation seam debt or bad boundary coupling +``` + +Interpretation: + +```text +A throat is not admissible merely because it is short. +It is admissible only if the q-corrected route remains stable, recoverable, +and cheaper than the normal manifold path. +``` + +--- + +## 4. Q-desic throat action + +For a route γ through or around a throat: + +```math +C_{QWH}(\gamma) += +\int_\gamma +\left[ + ds_g + +\lambda_Q\lVert Q_\Gamma\rVert + +\lambda_T\lVert T\rVert + +\lambda_p\lVert\nabla\log p_{\mathrm{throat}}\rVert + +\lambda_F L_{FAMM} + +\lambda_\Omega\Omega_{gap} + +\lambda_R R_{decode} +\right]ds. +``` + +A q-desic throat is route-admissible iff: + +```math +C_{QWH}(\gamma_{\mathrm{throat}}) +< +C_{normal}(\gamma_{\mathrm{manifold}}). +``` + +For compression routes: + +```math +C_{QWH}(\gamma_{transform}) ++C_{residual} ++C_{decoder} +< +C_{baseline}. +``` + +--- + +## 5. q-corrected throat cost + +Classical throat cost: + +```math +C_{classical} += +C_{exoticMatter}+C_{stabilityPenalty}. +``` + +q-corrected cost: + +```math +C_{qthroat} += +C_{classical} ++C_{connection} ++C_{torsion} ++C_{density} ++C_{interface} ++C_{FAMM} ++C_{decode}. +``` + +Expanded: + +```math +C_{qthroat} += +C_{exoticMatter} ++C_{stabilityPenalty} ++C_{Q_\Gamma} ++C_T ++C_{\nabla\log p} ++C_{\Omega} ++C_{FAMM} ++C_R. +``` + +--- + +## 6. q-efficiency + +Current visible efficiency is: + +```math +\eta_{classical} += +\frac{D_{manifold}}{L_{proper}}. +``` + +q-corrected efficiency is: + +```math +\eta_q += +\frac{D_{manifold}}{L_{proper}+C_{qcorrection}}. +``` + +where: + +```math +C_{qcorrection} += +C_{connection}+C_{torsion}+C_{density}+C_{interface}+C_{FAMM}+C_{decode}. +``` + +This blocks false positives: + +```text +short throat ≠ good throat +``` + +--- + +## 7. Temporal bounds + +Maximum stable temporal component: + +```math +T_{max,q} += +\frac{C_{temporal}}{D_q} +``` + +with: + +```math +D_q += +D_{base} ++D_{connection} ++D_{torsion} ++D_{density} ++D_{interface} ++D_{FAMM} ++D_{decode}. +``` + +Minimum computable bound: + +```math +\boxed{ +T_{min,q} += +\max\left( +\Delta t_{tick}, +\left\lceil\frac{P}{F}\right\rceil, +\left\lceil\frac{W_d}{R_d}\right\rceil, +\left\lceil\frac{G_i}{R_i}\right\rceil, +\left\lceil\frac{L_{FAMM}}{R_f}\right\rceil, +\epsilon_{Q16} +\right) +} +``` + +Definitions: + +```text +P = payload size +F = flux capacity +W_d = decode work +R_d = decode rate +G_i = interface gap cost +R_i = interface crossing rate +L_FAMM = route-scar / frustration load +R_f = repair or stabilization rate +ε_Q16 = smallest Q16.16 representable quantum +``` + +Temporal admissibility condition: + +```math +\boxed{T_{min,q} \le T_{max,q}} +``` + +If: + +```math +T_{min,q} > T_{max,q}, +``` + +then the throat is mathematically describable but computationally unusable. + +--- + +## 8. Full admissible q-throat condition + +```math +AdmissibleQThroat(\gamma,P) +\iff +Traversable(\gamma,P) +\land +C_{QWH}(\gamma) < C_{normal} +\land +T_{min,q}\le T_{max,q} +\land +DecodeConnected(\gamma) +\land +NoOverflow_{Q16}(\gamma). +``` + +--- + +## 9. Compression interpretation + +For compression, a transform throat is admissible iff: + +```math +saved\_bits +> +model\_bits ++residual\_bits ++interface\_bits ++decoder\_bits ++FAMM\_penalty\_bits +``` + +and: + +```math +T_{min,compress}\le T_{max,context}. +``` + +Thus: + +```text +A compression wormhole is useful only when its q-corrected transform shortcut +beats the ordinary route after model, residual, interface, decoder, and FAMM +scar costs are all counted. +``` + +--- + +## 10. Warden boundary + +Allowed: + +```text +Use q-desic as an operator-corrected route-selection analogy. +Use the equations to price hidden route, interface, torsion, and decode costs. +Use the temporal bound as a computable admissibility gate. +``` + +Blocked: + +```text +Do not claim physical wormhole construction. +Do not claim quantum gravity validation of OTOM/FAMM/AVMR. +Do not promote any transform throat unless q-corrected cost, temporal bounds, +and exact recovery are computed or formally gated. +```