Vertical-Slice Growth Protocol

• Vertical-Slice Growth Protocol is a methodological framework that decomposes a system into vertically-resolved layers or service bundles, linking formal models to staged operational execution across diverse fields.
• It integrates a reduced state representation, minimal control variables, and stage-wise execution to translate theoretical models into practical actions in domains from agriculture to telecommunications.
• The protocol enhances optimization and efficiency while addressing domain-specific challenges, from cost reductions in indoor crop control to performance tuning in CVD, atmospheric, and network slicing applications.

Vertical-Slice Growth Protocol denotes, across several technical literatures, a class of end-to-end procedures organized around a vertically resolved slice, a vertically stacked layer system, or a per-vertical service bundle. The surveyed usages indicate that the label does not name a single canonical method; rather, it refers to domain-specific workflows that connect formal models to operational decisions in indoor crop control, chemical vapor deposition of van der Waals materials, atmospheric slice dynamics, 5G network slicing for vertical industries, and height-aware 3D semantic occupancy prediction (Daniels et al., 2023, Guo et al., 2019, Cotter et al., 2012, Habibi et al., 2021, Huang et al., 4 Sep 2025).

1. Terminological scope and core meanings

The collected literature exhibits two distinct senses of vertical. In indoor farming, van der Waals growth, atmospheric slice modeling, and semantic occupancy, the term refers to a geometric height or stacking direction. In 5G network slicing, it refers to a vertical industry such as automobile, manufacturing, or power grid. In all cases, the protocol is an implementable synthesis that begins from a structured model and ends in staged execution, monitoring, and adaptation.

Domain	Vertical-slice object	Primary objective
Indoor vertical farming	Daily controls and annual crop schedule	Resource–yield–duration trade-off
van der Waals materials	Stacked layers and step boundaries	Vertical versus lateral growth control
Atmospheric dynamics	$x$–$z$ slice with three velocity components	Frontogenesis and baroclinic-instability analysis
5G network slicing	Per-vertical NSIs, US-NSIs, GN-NSIs, S-NSIs	Provisioning and life-cycle management
3D semantic occupancy	Height-axis slices of voxel features	Height-aware multimodal representation

A plausible synthesis is that a Vertical-Slice Growth Protocol is characterized by five recurrent elements: a reduced but explicit state representation; a small set of control or design variables; stage-wise execution; constraints tied to physics, service guarantees, or geometry; and a translation layer that maps the formal model to operational practice.

2. Indoor vertical farms: optimal-control scheduling for wheat

In "Optimal Control for Indoor Vertical Farms Based on Crop Growth" (Daniels et al., 2023), the protocol operationalizes an optimal-control formulation for indoor wheat cultivation, using cultivar Batten as the reference crop. The daily control vector is

$u_i = [T_i, D_i, R_i]^\mathsf{T},$

where $T_i$ is the mean air/leaf temperature setpoint, $D_i$ is the drought or soil-moisture stress index ARID in $[0,1]$, and $R_i$ is artificial plant-available radiation expressed as daily SRAD in MJ m$^{-2}$ d$^{-1}$. The state vector is

$x_i = [m_{B,i}, \tau_i, I_{50B,i}]^\mathsf{T},$

with biomass, cumulative temperature, and cumulative temperature to accelerate senescence. The paper fixes $z$0 enrichment at $z$1 ppm rather than optimizing it.

The crop dynamics are cast as a nonlinear, discrete-time hybrid model derived from SIMPLE, with a smooth approximation SIMPLE-SC used in optimization: $z$2 Non-smooth $z$3 operators are replaced by

$z$4

with $z$5. Maturity is defined phenologically through the canopy radiation interception fraction $z$6, and harvest is enforced by the terminal equality

$z$7

Two optimal-control problems are posed. For fixed final time,

$z$8

where $z$9 encodes energy and water costs and $u_i = [T_i, D_i, R_i]^\mathsf{T},$0 encodes crop revenue. For free final time, the dynamics become

$u_i = [T_i, D_i, R_i]^\mathsf{T},$1

and the annualized objective is

$u_i = [T_i, D_i, R_i]^\mathsf{T},$2

The stage-cost weights used are $u_i = [T_i, D_i, R_i]^\mathsf{T},$3, $u_i = [T_i, D_i, R_i]^\mathsf{T},$4, $u_i = [T_i, D_i, R_i]^\mathsf{T},$5, $u_i = [T_i, D_i, R_i]^\mathsf{T},$6, $u_i = [T_i, D_i, R_i]^\mathsf{T},$7, and $u_i = [T_i, D_i, R_i]^\mathsf{T},$8.

The optimization is implemented in Python with automatic differentiation through CasADi; standard gradient-based NLP solvers such as IPOPT can be used within CasADi. The free-final-time routine initializes $u_i = [T_i, D_i, R_i]^\mathsf{T},$9, solves the OCP, updates $T_i$0, sets $T_i$1, and repeats until $T_i$2 with $T_i$3. The protocol uses a daily time step and modest computational resources, which the paper states are suitable for iterative annual scheduling updates or periodic re-optimization.

The reported optimum converges to $T_i$4 days with $T_i$5 after nine iterations, corresponding to about $T_i$6 cycles per year. The stage-wise daily schedule has three phases. During germination and early canopy closure, approximately days $T_i$7–$T_i$8, temperature is near the upper bound at about $T_i$9, drought is near $D_i$0, and radiation rises to $D_i$1 MJ m$D_i$2 d$D_i$3 by about day $D_i$4. During rapid biomass accumulation, approximately days $D_i$5–$D_i$6, temperature is held near $D_i$7, drought remains at $D_i$8, and radiation remains at the upper bound $D_i$9 MJ m$[0,1]$0 d$[0,1]$1. During maturation and drying, approximately days $[0,1]$2–$[0,1]$3, temperature rises gradually to about $[0,1]$4, drought ramps to about $[0,1]$5, and radiation decreases sharply toward zero.

The resulting biomass per cycle is $[0,1]$6 kg m$[0,1]$7, equal to the constant-input case $[0,1]$8 but achieved in fewer days. Annual biomass becomes about $[0,1]$9 kg m$R_i$0 y$R_i$1, compared with about $R_i$2 kg m$R_i$3 y$R_i$4 for constant inputs, an increase of about $R_i$5. The optimized cost per cycle is about $R_i$6, versus $R_i$7 for constant inputs, a reduction of about $R_i$8, and annual energy cost is reduced by about $R_i$9 while biomass increases. A hypothetical zero-energy-cost case yields $^{-2}$0 days and $^{-2}$1 kg m$^{-2}$2, more than $^{-2}$3 above the cost-constrained optimum, illustrating the cost–yield tension.

The implementation layer is explicit. Because the model optimizes SRAD rather than photoperiod, PPFD, or spectrum, the protocol provides a practical conversion through the daily light integral: $^{-2}$4 At $^{-2}$5 MJ m$^{-2}$6 d$^{-2}$7, this implies $^{-2}$8 mol d$^{-2}$9 and, for a 16 h photoperiod, an average PPFD of about $^{-1}$0, which the protocol identifies as very high. It therefore recommends, in practice, capping PPFD and extending photoperiod where necessary. The paper also states strong limitations: nutrients, vernalization, photoperiod, PPFD caps, spectrum, and explicit HVAC energy are omitted; the SIMPLE parameterization is field-calibrated rather than VF-calibrated; and the notional wheat price is set at $^{-1}$1 market to illustrate profitability, while realistic wheat pricing leaves indoor wheat currently unprofitable.

3. van der Waals stacked 2D materials: thermodynamic and kinetic control of vertical growth

In "Modeling the vertical growth of van der Waals stacked 2D materials using the diffuse domain method" (Guo et al., 2019), the protocol concerns CVD growth of vertically stacked monolayers such as graphene and transition-metal dichalcogenides. The physical picture is a Burton–Cabrera–Frank-type model in which adatoms are deposited with flux $^{-1}$2, diffuse with coefficient $^{-1}$3, may desorb at rate $^{-1}$4, and attach to steps with kinetic rates $^{-1}$5. Local thermodynamics are governed by binding energies, edge energies, and curvature through Gibbs–Thomson terms. Lateral growth adds atoms to the perimeter of the first layer $^{-1}$6, whereas vertical stacking adds atoms to the second layer $^{-1}$7 above $^{-1}$8, incurring a new perimeter penalty.

The energetic bias between the two pathways is expressed by

$^{-1}$9

The full free energy includes binding terms, edge terms, and regular-solution entropy. Adatom concentrations satisfy

$x_i = [m_{B,i}, \tau_i, I_{50B,i}]^\mathsf{T},$0

and the step velocities obey

$x_i = [m_{B,i}, \tau_i, I_{50B,i}]^\mathsf{T},$1

Boundary conditions at $x_i = [m_{B,i}, \tau_i, I_{50B,i}]^\mathsf{T},$2 and $x_i = [m_{B,i}, \tau_i, I_{50B,i}]^\mathsf{T},$3 couple adjacent layers through attachment kinetics and local equilibrium densities.

For quasi-steady, isotropic, circular layers, the paper derives an analytic criterion for vertical growth: $x_i = [m_{B,i}, \tau_i, I_{50B,i}]^\mathsf{T},$4 This states that the interlayer binding advantage must exceed the edge-energy penalty per atom associated with creating the upper-layer perimeter. The corresponding critical radii are

$x_i = [m_{B,i}, \tau_i, I_{50B,i}]^\mathsf{T},$5

A kinetic critical radius $x_i = [m_{B,i}, \tau_i, I_{50B,i}]^\mathsf{T},$6 is also identified: when $x_i = [m_{B,i}, \tau_i, I_{50B,i}]^\mathsf{T},$7, transient second-layer growth can occur before the first layer reaches the suppressing threshold $x_i = [m_{B,i}, \tau_i, I_{50B,i}]^\mathsf{T},$8. Increasing $x_i = [m_{B,i}, \tau_i, I_{50B,i}]^\mathsf{T},$9, $z$00, or $z$01 and decreasing $z$02 enlarge this transient window.

To handle arbitrary layer shapes, the model is reformulated by the diffuse domain method. The phase variable $z$03 marks layers with $z$04 in $z$05, $z$06 in $z$07, and $z$08 in $z$09. Adatom fields are solved on a fixed rectangular domain $z$10, and interface motion is governed by a Cahn–Hilliard-type equation with kinetic source terms. The numerical method is mass-conservative, semi-implicit, and second-order accurate in time and space, using Crank–Nicholson time stepping, centered finite differences, a nonlinear multigrid FAS solver, and block-structured adaptive mesh refinement with four levels and finest mesh $z$11. Interface thickness $z$12 is chosen proportional to mesh size, for example $z$13, yielding overall $z$14 accuracy in $z$15 and $z$16 norms.

Parameter sensitivity is central to the protocol. Larger $z$17 increases vertical growth. Increasing $z$18 reduces $z$19 and can suppress $z$20 growth, with simulations noting suppression around $z$21. Larger $z$22 smooths corners and reduces growth rates. Decreasing $z$23 favors vertical growth kinetically, while increasing $z$24 generally feeds $z$25. Kinetic and edge anisotropy are modeled through

$z$26

and

$z$27

with $z$28 for graphene-like and $z$29 for MoS$z$30-like systems. The paper reports that, in 6-fold anisotropy, increasing $z$31 can trigger $z$32 morphological instability, while in 3-fold anisotropy, increasing $z$33 favors $z$34 growth without instability.

The protocol translates directly into CVD guidance: estimate $z$35, $z$36, $z$37, $z$38, and $z$39; evaluate the growth criterion; and, if it fails, reduce substrate flux $z$40, increase temperature to raise $z$41 and $z$42, modify edge passivation to lower $z$43 or raise $z$44, or seed a larger $z$45. The model reproduces star-shaped bilayer graphene, twisted bilayer graphene, vertically stacked MoS$z$46 triangles with negative curvature, and nearly overlapped bilayers. Its principal limitations are the neglect of strain and lattice mismatch, frequent omission of desorption, neglect of anisotropy in $z$47, and a primary focus on two-layer systems despite an $z$48-layer extension.

4. Atmospheric science: variational vertical-slice models and growth experiments

In "A variational formulation of vertical slice models" (Cotter et al., 2012), a vertical slice is a three-dimensional velocity field depending only on $z$49, $z$50, and $z$51. The slice velocity is $z$52 in the $z$53–$z$54 plane and the transverse velocity is $z$55 in the $z$56-direction. The specialized Lagrangian map is

$z$57

and the configuration space is the semidirect product $z$58. Areal density $z$59 is advected within the slice, while potential temperature is decomposed as

$z$60

which yields the slice evolution law

$z$61

For a slice Lagrangian $z$62, the Euler–Poincaré equations lead to a Hamiltonian structure, a Lie–Poisson bracket, and conservation laws. In geometric variables,

$z$63

the Kelvin–Noether circulation theorem is

$z$64

and the corresponding slice potential vorticity is materially conserved: $z$65

The incompressible Eady–Boussinesq slice model is obtained from the Lagrangian

$z$66

which, under $z$67 and $z$68, yields

$z$69

The conserved energy is

$z$70

The paper also introduces a sliced compressible model with Lagrangian

$z$71

which preserves its own energy, Kelvin–Noether circulation, and potential vorticity. It is explicitly stated that this compressible model does not produce solutions that are also solutions of the three-dimensional compressible equations, but it reduces to the Eady–Boussinesq model in the low-Mach-number limit, making it useful for asymptotic limit error testing.

The protocol built on this framework prescribes numerical frontogenesis and baroclinic-instability experiments in a slice domain $z$72, typically periodic in $z$73 and rigid free-slip at top and bottom in $z$74. The summary specifies a uniform $z$75 grid, for example $z$76 for linear stages, and a time step chosen by stability or CFL constraints. The base Eady-type incompressible state uses

$z$77

with small perturbations added through $z$78, a streamfunction-generated incompressible perturbation $z$79, and a compatible $z$80.

Growth is diagnosed numerically rather than through an explicit linear theory supplied by the paper. Perturbation kinetic energy,

$z$81

supports an estimated exponential growth rate

$z$82

Frontogenesis is tracked through $z$83, $z$84, slice PV, Kelvin–Noether circulation integrals, enstrophy, and energy conservation. The protocol places particular emphasis on structure-preserving discretization so that PV and circulation remain numerically compatible with the geometric form of the continuous model.

5. 5G network slicing: per-vertical, per-use-case life-cycle growth

In "How Should Network Slice Instances be Provided to Multiple Use Cases of a Single Vertical Industry?" (Habibi et al., 2021), a Vertical-Slice Growth Protocol refers to the provisioning and evolution of per-vertical, per-use-case network slices in a 5G system. A vertical industry consists of multiple use cases with differing service, network, and connectivity requirements. The central objects are the end-to-end Network Slice Instance (NSI), the Use-case Specific NSI (US-NSI), and the Generic NSI (GN-NSI) built from Sub-network Slice Instances (S-NSIs).

A US-NSI is one end-to-end NSI per use case. The number of US-NSIs equals the number of use cases, each with its own SLA, templates, life-cycle, and isolation. Sub Network Slicing introduces S-NSIs dedicated to single use cases; a GN-NSI is a per-vertical cluster of S-NSIs offered as a single business product. GN-NSIs are either standard, with predefined templates registered in the network slice catalog, or non-standard, co-designed by operator and tenant and then inserted into the catalog. The protocol distinguishes the two models operationally: US-NSI maximizes isolation and independent life-cycle control, whereas GN-NSI supports modular reusability, coordinated governance, and selected sharing of common functions.

The architecture combines 3GPP and ETSI components. Tenant-facing exposure occurs through SCEF/NEF northbound APIs over T8, using SCS/AS; GN-NSI introduces a Master-SCS/AS coordinating multiple Slave-SCS/ASs. Admission and dynamic resource leasing are performed by a Network Slice Broker in the operator’s NMS. Management functions include CSMF for service-to-slice translation, NSMF for NSI life-cycle orchestration, NSSMF for subnetwork management, NFMF for FCAPS at network-function level, and ETSI NFV-MANO components NFVO, VNFM, and VIM. A delegated tenant-MANO is exposed through a Management Level Agreement to give tenants autonomy over selected management functions while central administrative control remains with the operator.

Each end-to-end slice is composed of 5GC, NG-RAN, and TN subnetworks. The paper explicitly notes that UEs can be served by up to eight NSIs concurrently over a single NG-RAN, and that a common AMF may be shared while SMFs remain separate per slice. In GN-NSI clustering, this concurrency bound constrains the number of S-NSIs per UE, and the protocol therefore recommends defining the cluster with up to eight S-NSIs.

The life-cycle is organized into ten steps. Step 0 captures the vertical’s portfolio of use cases, business and technical requirements, regulatory constraints, and existing catalog entries, then designs and catalogs US-NSITs or GN-NSIT plus S-NSITs. Step 1 translates tenant service requests and SLA intents into slice requirements through CSMF and, for GN-NSI, establishes Master/Slave control hierarchy. Step 2 decides among US-NSI, GN-NSI, or a hybrid. US-NSI is preferred when stringent independent isolation, different life-cycles, or different administrative ownership dominate; GN-NSI is preferred when commonalities, shared resources, and single-product governance dominate. Step 3 derives 5GC, NG-RAN, and TN subnetworks and determines what is shared or dedicated, such as shared AMF, dedicated SMF, shared gNB CU, DU partitions, and dedicated TN QoS pipes. Step 4 performs admission and instantiation through NSB, NSMF, NSSMF, MANO, and NFMF. Step 5 handles vertical and horizontal scaling. Step 6 coordinates sharing and reuse within GN-NSI. Step 7 extends to multi-domain federation where necessary. Step 8 enforces SLA assurance and run-time admission control. Step 9 implements monitoring and closed-loop automation. Step 10 adds new use cases either by instantiating new US-NSIs or extending a GN-NSI cluster with new S-NSIs.

The protocol includes explicit run-time checks. A per-use-case SLA indicator is defined as

$z$85

and availability for a path set $z$86 is

$z$87

The resource-allocation model minimizes domain costs and penalties subject to latency, reliability, throughput, jitter, availability, mobility, bandwidth, compute, isolation, cluster assignment, UE concurrency, and template-compliance constraints.

Domain examples illustrate how the framework is meant to grow in practice. For automobile/V2X, autonomous driving is mapped to uRLLC with latency $z$88–$z$89 ms, reliability $z$90, and availability $z$91; infotainment is mapped to eMBB with latency $z$92 ms and up to $z$93 Mbps; remote diagnostics is mapped to mMTC with latency $z$94 ms. Manufacturing and power-grid examples similarly combine uRLLC, eMBB, and mMTC use cases under either US-NSI or GN-NSI. The principal limitations stated are the single-operator assumption, the challenge of clustered NG-RAN slicing, central MANO bottlenecks, the need for robust MLA governance in t-MANO, the eight-slice concurrency bound, and the lack of a detailed quantitative comparison between US-NSI and GN-NSI.

6. 3D semantic occupancy: height-aware multimodal representation and staged training

In "SliceSemOcc: Vertical Slice Based Multimodal 3D Semantic Occupancy Representation" (Huang et al., 4 Sep 2025), the protocol defines a vertical-slice-based multimodal framework for 3D semantic occupancy. The task is to predict a semantic label for each voxel in a fixed 3D grid from synchronized multi-view RGB images and LiDAR. The voxel feature tensor is

$z$95

and semantic logits are

$z$96

The benchmark settings are explicit: on nuScenes-SurroundOcc the spatial range is $z$97 m in $z$98 and $z$99, $u_i = [T_i, D_i, R_i]^\mathsf{T},$00 m in $u_i = [T_i, D_i, R_i]^\mathsf{T},$01, with grid $u_i = [T_i, D_i, R_i]^\mathsf{T},$02; on nuScenes-OpenOccupancy the range is $u_i = [T_i, D_i, R_i]^\mathsf{T},$03 m in $u_i = [T_i, D_i, R_i]^\mathsf{T},$04 and $u_i = [T_i, D_i, R_i]^\mathsf{T},$05, $u_i = [T_i, D_i, R_i]^\mathsf{T},$06 m in $u_i = [T_i, D_i, R_i]^\mathsf{T},$07, with grid $u_i = [T_i, D_i, R_i]^\mathsf{T},$08.

Image features are extracted by ResNet-50 or ResNet-101 with FPN. Visual features are lifted to the voxel grid by projecting each voxel center into each camera with camera intrinsics and extrinsics and bilinearly sampling the corresponding image feature. LiDAR uses 10 sweeps voxelized into the same grid and encoded by a VoxelNet or 3D sparse-convolution backbone to obtain a geometric feature volume $u_i = [T_i, D_i, R_i]^\mathsf{T},$09.

The protocol’s central innovation is explicit extraction of height-axis slices. Global vertical slices are obtained by pooling over $u_i = [T_i, D_i, R_i]^\mathsf{T},$10 and $u_i = [T_i, D_i, R_i]^\mathsf{T},$11 at each height layer: $u_i = [T_i, D_i, R_i]^\mathsf{T},$12 forming $u_i = [T_i, D_i, R_i]^\mathsf{T},$13, followed by a height-preserving 1D convolution along $u_i = [T_i, D_i, R_i]^\mathsf{T},$14, implemented as a $u_i = [T_i, D_i, R_i]^\mathsf{T},$15D convolution with kernel $u_i = [T_i, D_i, R_i]^\mathsf{T},$16. Local vertical slices are extracted per $u_i = [T_i, D_i, R_i]^\mathsf{T},$17 column and convolved along $u_i = [T_i, D_i, R_i]^\mathsf{T},$18, then restricted to predefined height bands. For nuScenes-SurroundOcc, the data-driven bands are

$u_i = [T_i, D_i, R_i]^\mathsf{T},$19

All slice operations preserve height indexing.

Before slice extraction, the feature volume is reweighted by SEAttention3D, a height-aware alternative to SENet. Instead of pooling over all spatial dimensions, SEAttention3D squeezes over $u_i = [T_i, D_i, R_i]^\mathsf{T},$20 only: $u_i = [T_i, D_i, R_i]^\mathsf{T},$21 then applies a per-height MLP

$u_i = [T_i, D_i, R_i]^\mathsf{T},$22

and broadcasts back: $u_i = [T_i, D_i, R_i]^\mathsf{T},$23 The parameter count is $u_i = [T_i, D_i, R_i]^\mathsf{T},$24 per block, and the FLOPs are $u_i = [T_i, D_i, R_i]^\mathsf{T},$25 for the MLP plus $u_i = [T_i, D_i, R_i]^\mathsf{T},$26 for pooling and scaling.

Global and local slice features are aligned by compact $u_i = [T_i, D_i, R_i]^\mathsf{T},$27D convolutions, converted to saliency maps,

$u_i = [T_i, D_i, R_i]^\mathsf{T},$28

$u_i = [T_i, D_i, R_i]^\mathsf{T},$29

and fused bidirectionally through

$u_i = [T_i, D_i, R_i]^\mathsf{T},$30

The concatenated result is projected back to $u_i = [T_i, D_i, R_i]^\mathsf{T},$31 channels and passed again through SEAttention3D. The full multimodal pipeline processes camera and LiDAR branches separately through this Vertical Slice Fusion, concatenates the outputs, and decodes them to per-voxel class logits.

Training is staged. Stage 0 warms up the image and LiDAR encoders for 5–10 epochs without VSF. Stage 1 enables SEAttention3D and the global slice path for 5 epochs while freezing the local branch. Stage 2 adds local slices for 10 epochs without cross-attention. Stage 3 enables bidirectional cross-attention for 10–20 epochs and trains the full model. The loss is

$u_i = [T_i, D_i, R_i]^\mathsf{T},$32

with softmax focal loss, Lovász-Softmax loss, and MonoScene-style affinity losses. The optimizer is Adam or AdamW with learning rate $u_i = [T_i, D_i, R_i]^\mathsf{T},$33, cosine decay, weight decay $u_i = [T_i, D_i, R_i]^\mathsf{T},$34, and batch size typically $u_i = [T_i, D_i, R_i]^\mathsf{T},$35–$u_i = [T_i, D_i, R_i]^\mathsf{T},$36. Modality dropout with probability $u_i = [T_i, D_i, R_i]^\mathsf{T},$37 is used for robustness.

On nuScenes-SurroundOcc validation, the protocol reports $u_i = [T_i, D_i, R_i]^\mathsf{T},$38 mIoU. On nuScenes-OpenOccupancy validation, it reports $u_i = [T_i, D_i, R_i]^\mathsf{T},$39 mIoU. The ablation trajectory on nuScenes-SurroundOcc is explicit: baseline without slices $u_i = [T_i, D_i, R_i]^\mathsf{T},$40; local slices only $u_i = [T_i, D_i, R_i]^\mathsf{T},$41; global slice only $u_i = [T_i, D_i, R_i]^\mathsf{T},$42; both without cross-attention $u_i = [T_i, D_i, R_i]^\mathsf{T},$43; both with global–local cross-attention $u_i = [T_i, D_i, R_i]^\mathsf{T},$44; and SENet versus SEAttention3D improves from $u_i = [T_i, D_i, R_i]^\mathsf{T},$45 to $u_i = [T_i, D_i, R_i]^\mathsf{T},$46. Uniform 8 bands of 1 m yield $u_i = [T_i, D_i, R_i]^\mathsf{T},$47, coarser 4 bands yield $u_i = [T_i, D_i, R_i]^\mathsf{T},$48, and the data-driven 6-band strategy is best at $u_i = [T_i, D_i, R_i]^\mathsf{T},$49. The paper attributes gains especially to small-object categories such as barrier, bicycle, motorcycle, pedestrian, and traffic cone.

Efficiency costs are also explicit. Memory scales as $u_i = [T_i, D_i, R_i]^\mathsf{T},$50; for SurroundOcc with $u_i = [T_i, D_i, R_i]^\mathsf{T},$51, $u_i = [T_i, D_i, R_i]^\mathsf{T},$52, $u_i = [T_i, D_i, R_i]^\mathsf{T},$53, and $u_i = [T_i, D_i, R_i]^\mathsf{T},$54, a single tensor is about $u_i = [T_i, D_i, R_i]^\mathsf{T},$55 million floats, or about $u_i = [T_i, D_i, R_i]^\mathsf{T},$56 MB in fp32. VSF adds about $u_i = [T_i, D_i, R_i]^\mathsf{T},$57 GB GPU memory. The paper recommends mixed precision, BatchNorm3d or GroupNorm with synchronized statistics, reflective padding along $u_i = [T_i, D_i, R_i]^\mathsf{T},$58, and careful extrinsics synchronization when temporal fusion is used. The main stated limitations are confusion among flat-ground classes and the linear growth of memory and runtime with increasing $u_i = [T_i, D_i, R_i]^\mathsf{T},$59.

7. Comparative structure, misconceptions, and limitations

Taken together, these sources suggest that Vertical-Slice Growth Protocol is not a discipline-specific theorem but a recurring methodological pattern (Daniels et al., 2023, Guo et al., 2019, Cotter et al., 2012, Habibi et al., 2021, Huang et al., 4 Sep 2025). In every case, the protocol serves as a translation layer between a compact formal representation and an executable workflow. In indoor farming, the compact representation is a three-state crop model and three daily controls. In CVD growth, it is a free-boundary layer system coupled through attachment kinetics. In atmospheric science, it is an $u_i = [T_i, D_i, R_i]^\mathsf{T},$60–$u_i = [T_i, D_i, R_i]^\mathsf{T},$61 slice with semidirect-product structure and conserved PV. In 5G slicing, it is a catalog-and-life-cycle abstraction for US-NSIs, GN-NSIs, and S-NSIs. In semantic occupancy, it is a height-resolved voxel tensor with explicit vertical feature extraction.

A common misconception would be to treat all uses of vertical slice as geometrically identical. The surveyed literature does not support that. In four of the five cases, vertical refers to a spatial height or stacking coordinate; in the 5G case, it refers to a vertical industry. Another misconception would be to interpret the protocols as purely theoretical. Each source instead pushes toward implementation: indoor farming maps SRAD to DLI and PPFD practice; the vdW model maps $u_i = [T_i, D_i, R_i]^\mathsf{T},$62, $u_i = [T_i, D_i, R_i]^\mathsf{T},$63, and $u_i = [T_i, D_i, R_i]^\mathsf{T},$64 to CVD knobs; atmospheric slice theory is turned into a numerical experiment design; 5G slicing is mapped to NSMF, NSSMF, MANO, and NEF flows; and SliceSemOcc specifies pseudocode, training stages, and memory costs.

Their limitations are strongly domain-specific. The indoor farming protocol omits nutrients, vernalization, explicit HVAC, and realistic wheat economics. The vdW growth model neglects strain and mismatch, often sets desorption to zero, and primarily studies two layers. The compressible atmospheric slice model preserves energy and PV but is not a restriction of the full three-dimensional compressible equations. The 5G slicing framework assumes a single operator and leaves clustered NG-RAN slicing and comparative business quantification for future work. SliceSemOcc remains computationally heavy and still struggles on flat-ground classes. A plausible implication is that the term is most useful when understood operationally: it identifies a staged, vertically organized control or representation scheme whose value depends less on nomenclature than on how successfully it links model structure to measurable execution.