Add BodegaFlow horn-fiber refinements

4-Infrastructure/shim/bodegaflow_horn_fiber_refinements.md

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+# BodegaFlow Horn-Fiber Refinements
+
+## Purpose
+
+This note captures the refinements developed after the full-stack load / closure revision. The goal is not to force a one-to-one mapping between external results and the framework. External work is treated as a structural probe: it can provide shape alignment, constraint alignment, residual alignment, probe alignment, or failure-mode alignment without being identical to the model.
+
+Keeper:
+
+```text
+External papers/results do not need to map 1:1 onto the framework.
+The question is whether they expose a compatible shape, boundary condition,
+residual, or testable projection.
+```
+
+## 1. Receipt-Gated Attractor Fiber Complex
+
+The current 16D object is neither a cube nor a torus.
+
+A cube implies independent bounded axes:
+
+```text
+[0,1]^16
+```
+
+A torus implies globally periodic closure:
+
+```text
+(S^1)^16
+```
+
+The current object has conditional closure, attractor routing, nested reduction, residual repair, and terminal receipts. The standards-facing name is:
+
+```text
+Receipt-Gated Attractor Fiber Complex, RG-AFC
+```
+
+Definition:
+
+```text
+A Receipt-Gated Attractor Fiber Complex is a high-dimensional controller space
+partitioned into attractor basins, routed through hub nodes, reduced through
+nested local partitions, and validated by terminal receipts.
+```
+
+Shape:
+
+```text
+forest / unresolved manifold mass
+  -> basin partition
+  -> bodega hub
+  -> fractional horn-like reduction
+  -> shelf-object
+  -> receipt / residual / closure
+```
+
+Compact equation:
+
+```text
+O_16 = [0,1]^16 -> {V_i} -> {b_i} -> {A,S,O} -> {W, epsilon, RRM}
+```
+
+Keeper:
+
+```text
+Not torus, not cube: a fiber-city attractor complex with shelf receipts.
+```
+
+## 2. Bodega Attractor Routing
+
+The bodega metaphor is formalized as hub-attractor manifold routing.
+
+A random math object / market state / probe state begins in an unresolved forest:
+
+```text
+x_0 in M_forest
+```
+
+It is drawn to the nearest bodega hub:
+
+```text
+b(x) = argmin_{b_i in B} d_M(x,b_i)
+```
+
+Soft routing:
+
+```text
+P(b_i | x) = exp(-beta d_M(x,b_i)) / sum_j exp(-beta d_M(x,b_j))
+```
+
+Each bodega owns a Voronoi-like basin:
+
+```text
+V_i = {x in M : d_M(x,b_i) <= d_M(x,b_j), for all j}
+```
+
+Inside the bodega, uncertainty reduces fractionally:
+
+```text
+forest -> city -> bodega -> aisle -> shelf -> object
+```
+
+Formal nesting:
+
+```text
+M_forest superset V_b superset b_i superset A_ij superset S_ijk superset O_ijkell
+```
+
+Fractional reduction:
+
+```text
+H_{t+1} = rho_t H_t, 0 < rho_t < 1
+H_n = H_0 prod_t rho_t
+stop when H_n <= Theta_object
+```
+
+Path receipt:
+
+```text
+Route(x) = (V_i, b_i, A_ij, S_ijk, O*, W, epsilon)
+```
+
+Receipt confidence:
+
+```text
+W = P(b_i | x)
+    P(A_ij | x,b_i)
+    P(S_ijk | x,b_i,A_ij)
+    P(O* | x,b_i,A_ij,S_ijk)
+```
+
+If W is low:
+
+```text
+RRM(epsilon) -> adjacent shelf, adjacent aisle, alternate bodega, or quarantine
+```
+
+Keeper:
+
+```text
+The forest gets you to the bodega; the bodega fractions the search;
+the shelf gives the receipt.
+```
+
+## 3. Fiber-Mass Raytrace Probe Atlas
+
+A single ray is too thin. The hidden object is assessed by a fiber mass: a weighted bundle of probe trajectories through hidden state space.
+
+Fiber mass:
+
+```text
+F = {F_1, F_2, ..., F_N}
+F_i = (gamma_i, R_i, Y_i, epsilon_i, W_i)
+```
+
+where:
+- `gamma_i` = path through the manifold
+- `R_i` = ray / carrier / probe packet
+- `Y_i` = observed deformation
+- `epsilon_i` = residual against baseline
+- `W_i` = receipt confidence
+
+A multidimensional TSP-like route chooses which informative hubs to visit:
+
+```text
+pi* = argmin_pi [
+  sum_k d_16(b_{pi_k}, b_{pi_{k+1}})
+  + alpha sum_k C_reduce(b_{pi_k})
+  - beta sum_k I_receipt(b_{pi_k})
+]
+```
+
+Weighted 16D distance:
+
+```text
+d_16(u,v) = sqrt(sum_{a=0}^{15} omega_a (q_a(u)-q_a(v))^2)
+```
+
+Information receipt:
+
+```text
+I_i_receipt = W_i [H(C16) - H(C16 | Y_i)] - rho ||epsilon_i||
+```
+
+Keeper:
+
+```text
+Raytrace the fiber mass; TSP the probe route; receipt the distortions;
+fuse the 16D object.
+```
+
+## 4. Gabriel-Horn Spatial Refinement
+
+Treating the spatial / reduction dimensions like Gabriel's horn strengthens the model.
+
+Classical horn behavior:
+
+```text
+finite enclosed volume, infinite surface area
+```
+
+For the framework:
+
+```text
+finite admissible interior / controller budget
+unbounded or very large boundary exposure / attack surface
+```
+
+A horn-like dimension:
+
+```text
+r_i(x) = a_i / (x + b_i)^{p_i}
+```
+
+The 16D horn object is not a plain product space; it is routed:
+
+```text
+O_16^horn = F -> V -> B -> {H_i}_{i=0}^{15} -> O* -> W
+```
+
+Market/compression interpretation:
+
+```text
+Compression narrows volume, but may increase exploitable boundary exposure.
+```
+
+Horn-aware adversarial leakage:
+
+```text
+Lambda_i = Lambda_0
+           + lambda_A A_boundary_i
+           + lambda_g ||grad r_i||
+           + lambda_c C_crowding
+```
+
+Horn-aware compression score:
+
+```text
+C_horn = DeltaS_minus
+         - DeltaS_plus
+         - Lambda(A_boundary)
+         - ||epsilon||
+         - C_friction
+```
+
+Keeper:
+
+```text
+Compression narrows the volume, but Gabriel-horn geometry warns that the
+boundary may still be infinite.
+```
+
+## 5. Horn/Torsion Cosmology Refinement
+
+As a 16D horn-fiber object, apparent acceleration does not have to mean homogeneous bulk-volume expansion. It can mean selected boundary sectors are changing accessibility conditions faster than others.
+
+Core distinction:
+
+```text
+standard intuition: acceleration = d^2 V / dt^2 > 0
+horn-fiber model: apparent acceleration = d^2 A_boundary^(r) / dt^2 > 0
+```
+
+Bulk can remain bounded while accessible surface changes:
+
+```text
+dV_Omega/dt ~= 0
+
+dA_boundary/dt = alpha A_boundary
+                 + beta ||tau||^2
+                 + gamma RRM(epsilon)
+```
+
+Sector acceleration:
+
+```text
+d^2 A_boundary^(r)/dt^2 =
+  alpha_r A_boundary^(r)
+  + beta_r ||tau_r||^2
+  + chi_r d(||tau_r||^2)/dt
+  + gamma_r RRM(epsilon_r)
+```
+
+Carrier/path observable:
+
+```text
+z_gamma = z_metric + z_torsion + z_boundaryA + z_echo + epsilon_gamma
+```
+
+Interpretation:
+
+```text
+The probe no longer asks: is space expanding?
+It asks: which boundary conditions changed along this path, and by how much?
+```
+
+DESI-style comparison rule:
+
+```text
+DESI and similar results do not need to prove this model 1:1.
+They are useful if they expose a non-constant effective expansion term,
+boundary-condition drift, or residual structure that the 16D model can test.
+```
+
+Keeper:
+
+```text
+Acceleration is not the room getting bigger; it is the boundary rules changing
+faster along certain routes.
+```
+
+## 6. BodegaFlow Event-Field Refinement
+
+BodegaFlow is a paper-only morphic market geometry engine. It learns what compression means under adversarial deformation; it is not a real-money execution system.
+
+Core event update:
+
+```text
+Every market action is an event update in a live flow field.
+```
+
+Market event:
+
+```text
+e_t = (tau_t, type_t, symbol, DeltaP, DeltaV, DeltaL, DeltaS, DeltaO, metadata)
+```
+
+Live flow field:
+
+```text
+F_t = (U_t, Pi_t, nu_t, omega_t, rho_t, epsilon_t, W_t)
+```
+
+Update:
+
+```text
+F_{t+1} = F_t + K(e_t,x_t) - D(F_t) + RRM(epsilon_t)
+```
+
+Event kernel:
+
+```text
+K(e_t,x) = a_e exp(-d_16(x,x_e)^2 / (2 sigma_e^2)) v_e
+```
+
+Navier-Stokes-like event form:
+
+```text
+U_{t+1} = U_t
+          + sum_{e in E_t} K_U(e)
+          - (U_t . grad) U_t
+          - grad Pi_t
+          + nu_m grad^2 U_t
+          + F_reflexive
+          + F_adversarial
+```
+
+Bodega route:
+
+```text
+raw market outputs
+  -> Market Forest x_t in [0,1]^16
+  -> nearest attractor basin
+  -> Bodega Hub / regime setup family
+  -> Aisle / setup subtype
+  -> Shelf / entry condition
+  -> Object / paper trade candidate
+  -> receipt gate
+  -> paper enter / watch / skip / quarantine
+  -> outcome label
+  -> compression score + competitor-transfer score
+  -> geometry update
+```
+
+Paper-only gate:
+
+```text
+PaperEnter iff
+  W >= Theta_W
+  and SNR >= Theta_SNR
+  and ||epsilon|| <= Theta_epsilon
+  and Lambda <= Theta_Lambda
+```
+
+Compression under adversarial action:
+
+```text
+C_market = DeltaS_minus
+           - DeltaS_plus
+           - Lambda
+           - ||epsilon||
+           - C_friction
+```
+
+Competitor-transfer condition:
+
+```text
+C_market < 0 and Lambda > Theta_Lambda => COMPETITOR_TRANSFER
+```
+
+Route labels:
+
+```text
+TRUE_COMPRESSION
+FALSE_COMPRESSION
+NOISE
+LATE_ENTRY
+CROWDED_EDGE
+LIQUIDITY_TRAP
+STOP_RUN
+ADVERSE_SELECTION
+SPREAD_DONATION
+COMPETITOR_TRANSFER
+VALID_BUT_TOO_EXPENSIVE
+QUARANTINE
+```
+
+Keeper:
+
+```text
+BodegaFlow does not just find the shelf. It learns which aisles turn the
+shopper into inventory.
+```
+
+## 7. Updated 16D Probe Resolution Claim
+
+The 16D horn/fiber shape turns each probe from a ruler into a spectrometer.
+
+Low-resolution probe:
+
+```text
+carrier in -> distorted carrier out -> single inferred cause
+```
+
+High-resolution probe:
+
+```text
+carrier in -> multi-channel deformation receipt -> sector-specific boundary diagnosis
+```
+
+Probe decomposition:
+
+```text
+Y_gamma = Render(g_mu_nu, tau, A_boundary, dA_boundary/dt, echo, epsilon)
+```
+
+Local diagnostic estimate:
+
+```text
+C16_hat^(gamma) = argmin_C16 ||
+  Y_gamma - Render(g_mu_nu, tau, A_boundary, dA_boundary/dt, echo, epsilon)
+||
+```
+
+Keeper:
+
+```text
+The probe gets higher resolution because the model stops treating distortion
+as one cause and starts treating it as a 16-channel receipt.
+```
+
+## Claim Boundaries
+
+```text
+This is a control / compression / transition-receipt model.
+It is not a proven financial, cosmological, biological, or physical law without
+calibrated domain instruments, receipts, and falsification tests.
+```
+
+```text
+BodegaFlow is paper-only. It is for geometry learning and adversarial-compression
+labeling, not live financial execution.
+```
+
+```text
+External results are structural probes, not required one-to-one equivalents.
+```