Network Flow Optimization

Route flow through a capacity-constrained network to maximize throughput, minimize cost, or avoid bottlenecks.

Version

v1 · 2026-08-24 · History

Solution archetype #

676

Problem family

Congestion, Backlog & Flow Breakdown

Problem subfamily

Routing, Distribution & Endpoint Failure

Essence

Network Flow Optimization is the archetype for routing movement through a constrained topology. It applies when the important decision is not simply “who gets how much,” but “which paths should the flow use, given where it starts, where it must end, how much each link can carry, and what costs or constraints each route imposes?”

The archetype turns a vague flow problem into a structured network decision. It defines the moving unit, maps nodes and edges, states source and sink points, attaches capacities and costs, makes conservation or loss assumptions explicit, and selects a feasible allocation of flow across paths.

Compression statement

When materials, information, people, money, work, risk, or demand move through a connected network, represent the nodes, edges, capacities, costs, sources, sinks, and conservation rules so flow can be allocated across paths rather than pushed through locally convenient or historically inherited channels.

Canonical formula: Given a directed or undirected graph G = (V, E), source and sink definitions S/T, link capacities u_e, optional costs c_e, conservation or loss rules K, and objective O, choose flows f_e across edges such that capacity and conservation constraints hold while O is optimized or an acceptable tradeoff is documented.

When This Archetype Applies

Partial catalog groundingSome structural conditions are represented by existing abstractions, but no sufficient condition set is fully represented.

Diagnostic problem

A flow network has constrained paths, bottlenecks, costs, handoff losses, or imbalanced supply and demand, but routing decisions are made locally or heuristically without seeing how the whole topology constrains feasible movement.

What this problem means

The structural problem is end-to-end movement constrained by a network. Local actors may optimize their own handoff, local queue, local route, or local metric while the whole system remains congested, costly, unreliable, or unfair. One team may forward work rapidly into a downstream bottleneck. A logistics node may appear efficient while creating expensive routing elsewhere. A hospital department may be blamed for delay when the true constraint is downstream bed capacity or discharge flow.

The deeper issue is that flow feasibility is shaped by the whole topology. A link that looks adequate in isolation may be unusable because an upstream source cannot reach it, a downstream sink cannot absorb it, or a parallel path has incompatible constraints.

Applicability expression5 distinct conditions

Conserved network flowandHeterogeneous link capacitiesandSeparated imbalanced endpointsandMigrating bottleneckandExplicit routing objective

Algebraic1∧2∧3∧4∧5

3=a∨b∨c∨d∨e∨f∨g∨h∨i∨j∨k∨l∨m∨n∨o∨(p∧p′)

′ context guard? connective not recorded∅ no catalog witness yet

groundedpartly groundedopen

5 conditions, all required.

5Required in every casenumbered 1–5

These hold no matter which pattern applies.

1

Conserved network flow · grounded

A conserved quantity moves through multiple connected paths in a graph. more

primeNetwork Flow Models— Optimize flow across networks.

and — also required

2

Heterogeneous link capacities · grounded

Links or nodes have heterogeneous capacities, costs, risks, or service times. more

primeNetwork Flow Models— Optimize flow across networks.

and — also required

3

Separated imbalanced endpoints · grounded · any one of 16

Sources and sinks are imbalanced or separated across the network. more

a

domainTransfer-Learning Attack— Vulnerabilities, backdoors, or poisoned representations baked into an upstream pretrained model ride intact into every downstream system built on it, because the downstream team's audit boundary encloses only its new layers while the attack surface spans the whole inherited substrate.

or — any one of these establishes this case

b

domainInjection Weakness— The software-security failure in which untrusted data crosses into a control channel and a downstream interpreter executes it as command, query, or instruction — a collapse of the data/control boundary that a legitimate, often credential-free, input channel is enough to exploit.

or — any one of these establishes this case

c

domainImputation Leakage— The model-evaluation failure in which a missing-value repair step is fit across the train/test boundary, so its parameters encode facts about the held-out rows — inflating performance that survives into the test metric, because imputation, mentally filed as data cleaning, is really a model.

or — any one of these establishes this case

d

domainWatershed— Bound the space of contributing sources for any point in a river to the terrain-defined area draining to a common outlet, then exploit the asymmetric upstream-downstream coupling — everything propagates down, nothing back up against gravity — to fix search direction and intervention shape.

or — any one of these establishes this case

e

domainQuote Laundering— A provisional but accurate statement is cited across successive venues that each strip its caveats and scope, until it circulates as authoritative settled fact — a channel failure, not a false source, so it resists source correction and needs traceability instead.

or — any one of these establishes this case

f

domainDeposit Concentration Risk— Judge a bank's funding fragility by the correlation-adjusted effective depositor count rather than the headline number — coupled depositors collapse toward one bet, voiding the law-of-large-numbers smoothing a large base seems to guarantee.

or — any one of these establishes this case

g

domainAI Supply-Chain Attack— The compromise of an upstream AI-pipeline component — training data, weights, packages, eval sets — by an adversary who exploits the deployer's trust in the producer's channel rather than breaching the perimeter, so the poisoned artefact is imported voluntarily.

or — any one of these establishes this case

h

domainException Management— Run high-volume normal items on a streamlined standard path and deliberately divert off-plan items onto a separate specialist channel, while feeding the diversion rate back upstream to fix the normal flow when it climbs.

or — any one of these establishes this case

i

domainBiogeochemical Cycling— Model the circulation of a conserved Earth-system element through compartmental reservoirs — each with a stock and residence time — linked by canonical transformations and governed by a rate-limiting bottleneck, with mass balance forced to close.

or — any one of these establishes this case

j

domainConvergence Failure— The disaster-management pathology in which uncoordinated pro-social inflows — volunteers, donations, inquiries — arrive faster than incident command can absorb, consuming the same coordination bandwidth the primary hazard needs and triggering a second disaster.

or — any one of these establishes this case

k

domainCircular Flow— Represent the whole economy as two loops running opposite ways between households and firms, then track every off-loop flow as a leakage or an injection whose sums must balance when the loop closes in steady state.

or — any one of these establishes this case

l

domainOutbreak Underascertainment— The surveillance failure in which recorded case counts fall systematically below the true count because a multi-stage detection pipeline — symptom expression, care-seeking, testing, confirmation, reporting — filters cases with biased attenuation at each layer.

or — any one of these establishes this case

m

domainReturns Friction— Diagnose why returns, recalls, and repairs move badly: the reverse flow is an irregular trickle of heterogeneous, quality-uncertain units forced through a network designed and optimized for one-directional forward flow, sharing its rails as an afterthought.

or — any one of these establishes this case

n

domainSupplier Concentration Risk— Exposure that arises when a buyer's dependency for a critical input rests on so few suppliers that one node's disruption propagates downstream faster than alternatives can be qualified — a shape property of the dependency distribution, not of any supplier's performance.

or — any one of these establishes this case

o

domainKarst— Diagnose a landscape where acidic groundwater has dissolved soluble bedrock into a self-reinforcing hidden conduit network, so the surface no longer maps the subsurface drainage and porous-media terrain rules are suspended.

or — any one of these establishes this case

p

domainSediment Budget— Account for sediment as a mass-balance ledger of sources and sinks over a bounded coastal or fluvial cell, so the running balance — not the last storm — tells whether the shoreline is accreting, stable, or eroding.

AND both parts required

context guardThe sediment budget's running balance is nonzero.

suppliesThe sources and sinks are imbalanced in supply, capacity, or demand.

How this was matched — 1 shared + 4 branches

flow-network sources and sinks have a listed imbalance or separation

All of

• roleA flow network has source and sink roles.

…and any one of

• branchThe sources and sinks are imbalanced in supply, capacity, or demand.
• branchThe sources and sinks are geographically separated.
• branchThe sources and sinks are institutionally separated.
• branchThe sources and sinks are logically separated.

and — also required

4

Migrating bottleneck · open

Relieving one bottleneck causes the bottleneck to migrate elsewhere. more

and — also required

5

Explicit routing objective · grounded

Routing is judged by an explicit objective such as throughput, cost, reliability, fairness, latency, or loss. more

primeNetwork Flow Models— Optimize flow across networks.

Coverage

4 of 5 conditions grounded · 1 open.

Read the methodology · Download the trigger-logic data

When to Use This Archetype

Use this archetype when goods, people, patients, money, information, requests, cases, energy, risk, or work move through a connected network and the topology changes what is feasible. The pattern is especially useful when local routing creates congestion somewhere else, when improving one segment fails to improve final throughput, or when several paths exist but differ in capacity, cost, delay, reliability, or fairness.

It is less appropriate when there is no meaningful path structure. If the problem is simply distributing a finite resource among competing uses, Constrained Resource Allocation is probably cleaner. If the problem is deciding service order inside one queue, Queue Discipline Design is cleaner. If the problem is only a one-time detour around a known blockage, Flow Diversion or Rerouting may be enough.

Structural Problem

The structural problem is end-to-end movement constrained by a network. Local actors may optimize their own handoff, local queue, local route, or local metric while the whole system remains congested, costly, unreliable, or unfair. One team may forward work rapidly into a downstream bottleneck. A logistics node may appear efficient while creating expensive routing elsewhere. A hospital department may be blamed for delay when the true constraint is downstream bed capacity or discharge flow.

The deeper issue is that flow feasibility is shaped by the whole topology. A link that looks adequate in isolation may be unusable because an upstream source cannot reach it, a downstream sink cannot absorb it, or a parallel path has incompatible constraints.

Intervention Logic

The intervention starts by defining the flow unit. A network cannot be optimized until the unit of movement is clear: shipment, vehicle, passenger, patient, case, dollar, request, compute job, packet, referral, or another unit.

Next, the topology is represented as nodes and edges. Nodes are the places where flow enters, exits, pauses, transforms, splits, merges, or changes ownership. Edges are the feasible connections between those nodes. Directionality matters: a path that works in one direction may not work in reverse.

Then the intervention adds capacities, costs, and conservation assumptions. A route is not feasible merely because it exists on a diagram. It has limits, risks, delays, costs, eligibility constraints, staffing requirements, legal rules, or loss rates. Finally, the archetype chooses a flow allocation that advances the objective while respecting constraints and preserving visibility into bottleneck migration.

Key Components

Network Flow Optimization turns a vague routing problem into a structured network decision: not just who gets how much, but which paths the flow should use given where it starts, where it must end, and what each link can carry. The Flow Unit Definition anchors the analysis by naming what is moving — shipments, vehicles, patients, cases, packets, dollars, or referrals — along with the time basis and whether units can split, merge, transform, or be lost. The Node Set identifies the places where flow enters, exits, pauses, transforms, splits, merges, or changes ownership, and the Edge or Arc Set specifies which movements between those nodes are actually feasible, including directionality and which classes of flow may use which edges. The Source and Sink Definition names where flow enters the network and where it must be absorbed or resolved — a step many systems skip, then improve intermediate movement while neglecting sink capacity, which only relocates backlog rather than reducing it.

The remaining components convert the topology into a decidable problem and a defensible answer. Edge Capacity states how much flow each link can carry under real conditions — measured in usable units rather than nominal promises, since capacity may be physical, staffing-based, computational, financial, legal, temporal, or quality-limited. The Flow Conservation Rule declares whether inflow and outflow balance at intermediate nodes, or whether the system must account for abandonment, leakage, spoilage, attrition, duplication, transformation, rework, or storage; without this, models acquire false precision. The Cost or Throughput Objective determines how feasible flows are compared — maximizing throughput, minimizing cost, reducing delay, preserving fairness, or balancing several at once — and must remain reviewable because different objectives select different routes. Finally, the Flow Allocation Solution records the chosen distribution of flow across paths along with its assumptions, constraints, expected consequences, and monitoring hooks, so a solver output becomes a decision the organization can inspect, defend, and revisit when bottlenecks migrate.

Component	Description
Flow Unit Definition ↗	This component defines what is moving through the network. A flow unit may be a product, passenger, patient, task, application, packet, dollar, truck, case, request, or other unit. The definition should include the time basis and whether units can be split, merged, transformed, delayed, or lost.
Node Set ↗	The node set identifies the points where flow can originate, terminate, pause, transform, split, merge, or be handed off. Nodes can be warehouses, routers, departments, teams, stations, offices, queues, care units, funding intermediaries, or decision stages.
Edge or Arc Set ↗	Edges define the feasible paths between nodes. They specify which movements are possible, whether they are directional, and whether certain classes of flow may use them. The edge set determines whether a proposed allocation is physically, institutionally, legally, or operationally feasible.
Source and Sink Definition ↗	Sources are where flow enters the network; sinks are where it must be absorbed, completed, served, consumed, paid out, discharged, or otherwise resolved. Many systems improve intermediate movement while neglecting sink capacity, which only relocates backlog.
Edge Capacity ↗	Edge capacity states how much flow a link can carry under relevant conditions. Capacity may be physical, staffing-based, computational, financial, legal, temporal, political, or quality-limited. It should be measured in usable units rather than nominal promises.
Flow Conservation Rule ↗	This component defines whether inflow and outflow balance at intermediate nodes. Formal flow models often assume conservation, but real systems may include abandonment, leakage, spoilage, attrition, delay, duplication, transformation, rework, or storage. The rule prevents false precision.
Cost or Throughput Objective ↗	The objective determines how feasible flows are compared. The system might maximize throughput, minimize cost, reduce delay, increase reliability, preserve fairness, protect priority groups, or balance multiple objectives. The objective must be reviewable because different objectives produce different routes.
Flow Allocation Solution ↗	The solution records the selected distribution of flow over paths, channels, or edges. A good solution is not just a solver output; it includes assumptions, constraints, expected consequences, and monitoring hooks.

Common Mechanisms

8 documented mechanisms across 5 implementation forms.

The grouping reflects forms represented among the mechanisms currently documented for this archetype; an absent form is not necessarily an impossible implementation.

Analysis, Modeling & Optimization · 4 mechanisms

• Max-Flow Analysis — Computes the greatest volume that can move from source to sink under edge capacities, and names the min-cut — the saturated links whose combined limit sets the ceiling.
• Min-Cost Flow Model — Routes a required flow from supplies to demands at least total cost, choosing the cheapest feasible allocation over a capacitated network subject to conservation.
• Multi-Commodity Flow Model — Represents several distinct flow classes over one shared network — each with its own sources and sinks — coupled only where they compete for the same edge capacity.
• Traffic Assignment Model — Predicts how trips spread across a road or transit network by modeling travelers who each choose their own fastest route, until no one can gain by switching — a user equilibrium.

Assessment, Review & Assurance · 1 mechanism

• Patient Flow Pathway Review — A structured multidisciplinary walk-through of the care pathway that traces where patients stall, showing that an upstream jam is usually a downstream sink constraint — and reallocates flow while protecting safety and dignity.

Control, Automation & Runtime · 1 mechanism

• Data Network Routing Policy — A standing rule set that steers packets, requests, and jobs across regions, links, and servers by class, compliance, and failover — deciding routes live as conditions change rather than solving one optimum.

Monitoring, Sensing & Alerting · 1 mechanism

• Network Capacity Dashboard — A live topological view of a flow network that shows where capacity is saturated, where it sits idle, and where the binding bottleneck has moved.

Representation, Specification & Plan · 1 mechanism

• Logistics Routing Plan — The standing plan that decides which front the reserve flows to first and in what feasible sequence, encoding an explicit front-priority ranking against a map of the network's capacities and constraints.

Parameter / Tuning Dimensions

Key tuning dimensions include edge capacity, node capacity, demand level, arrival pattern, source and sink distribution, path cost, latency tolerance, reliability requirement, fairness constraint, priority class rule, loss rate, storage allowance, route switching cost, and slack or redundancy level.

The most important practical tuning choice is often the objective. A network optimized for lowest cost may not be the same as one optimized for fastest completion, most equitable access, highest resilience, or safest service. For this reason, objective choice and constraint governance should be visible.

Invariants to Preserve

The chosen routing pattern should not violate capacity constraints. Source and sink definitions should remain explicit. Conservation, loss, storage, and transformation assumptions should be stated rather than assumed. The objective should remain visible and reviewable. Bottleneck migration should remain observable after implementation.

When people or essential services are the flow units, dignity, safety, consent, equity, and quality of service must be preserved as constraints. A high-throughput network that harms the people moving through it is not a successful application of the archetype.

Target Outcomes

A successful Network Flow Optimization intervention can increase feasible throughput, reduce congestion, lower routing cost, shorten latency, reduce loss, expose hidden bottlenecks, improve coordination across units, and make tradeoffs clearer.

It should also improve the quality of system reasoning. Instead of debating isolated symptoms, participants can discuss how sources, sinks, capacities, and paths interact.

Tradeoffs

Network optimization can trade throughput against fairness, cost against reliability, central control against local judgment, utilization against slack, model precision against maintainability, and efficiency against resilience. These tradeoffs should be documented rather than hidden in the route score.

The archetype is powerful because it makes system-level flow visible. It is risky because it can make locally meaningful constraints disappear if the model is too narrow.

Failure Modes

A common failure mode is false topology: the map omits informal handoffs, blocked paths, real sink constraints, exception routes, or hidden transfers. Another is capacity mismeasurement: nominal capacity is treated as real capacity despite staffing, quality, downtime, regulation, or surge limits.

Bottleneck migration is also common. A change can relieve one link while moving congestion to another part of the network. That is not necessarily failure, but it becomes failure when the team does not monitor the new constraint.

The most serious misuse is solver reification. A formal answer can look objective even when the input topology, objective, capacity data, or fairness constraints are wrong.

Neighbor Distinctions

Network Flow Optimization differs from Constrained Resource Allocation because the decisive structure is connected movement across nodes and edges, not only distribution of resources among uses.

It differs from Load Balancing because load balancing spreads demand among comparable capacity pools, while network flow handles heterogeneous paths, sources, sinks, costs, conservation, and topology.

It differs from Flow Diversion or Rerouting because rerouting can be local and reactive, while this archetype evaluates the whole network and chooses a feasible allocation across paths.

It differs from Bottleneck Identification and Relief because bottleneck relief diagnoses or expands a limiting point, while Network Flow Optimization allocates movement across the network and may reveal bottlenecks as part of that process.

It differs from Queue Discipline Design because queue discipline decides service order, while network flow decides where flow moves across multiple connected paths.

Cross-Domain Examples

In logistics, products move from factories through warehouses and carriers to stores. Network flow reasoning decides which paths carry which volumes under dock, truck, route, inventory, and delivery constraints.

In healthcare, patients move through emergency intake, diagnostics, specialty review, beds, discharge, and referrals. Network flow reasoning can show that an emergency department backlog is really constrained by downstream bed or discharge capacity.

In cloud infrastructure, requests move through regions, queues, services, and compute clusters. Routing policies distribute requests by latency, capacity, cost, reliability, compliance, and failover constraints.

In public benefits delivery, applications and funds move through eligibility checks, document review, local offices, payment channels, and recipients. Network flow reasoning can expose where cases stall or where money leaks before reaching the intended sink.

In transportation, passengers or vehicles move through roads, transit corridors, stations, and transfer points. The archetype can inform route design, detours, station capacity, and congestion management.

Non-Examples

A list of overloaded departments is not Network Flow Optimization unless the connections, capacities, sources, sinks, and flow rules are mapped.

A process diagram is not Network Flow Optimization unless it supports a decision about flow allocation.

A max-flow algorithm by itself is not the archetype; it is one mechanism that may implement the archetype.

A simple budget allocation problem without path structure is Constrained Resource Allocation.

A single queue reordered by urgency is Queue Discipline Design, not Network Flow Optimization.

Related Abstractions

Abstractions this archetype builds on — directly (a source ingredient) or as a related pattern. Links follow the typed catalog namespace.

Built directly on (3)

• Flow: Structured movement of energy, matter, or information.
• Network: Models interactions between components.
• Network Flow Models: Optimize flow across networks.

Also references 13 related abstractions

• Conservation Laws: Quantities remain constant.
• Constraint: Limits possibilities to guide outcomes.
• Controllability: Ability to steer system.
• Coupling: Interdependence among subsystems.
• Feedback: Outputs influence inputs.
• Observability: Infer internal state externally.
• Optimization: Finds best solution under constraints.
• Pipeline: Sequential processing stages.
• Queueing: Organizes tasks into a waiting line based on arrival and service rates.
• Resource Management: Allocation of finite assets.

▸ Show 3 more

Variants

Narrower or domain-specific specializations that share this archetype's core structure. Recognized variants are established; candidate variants are provisional.

Max-Throughput Flow · subtype · recognized

A subtype focused on pushing the greatest feasible volume from source to sink under capacity constraints.

• Distinct from parent: The parent includes cost, reliability, fairness, latency, resilience, and multi-objective flow choices; this variant centers throughput.
• Use when: The dominant objective is feasible throughput; Costs, fairness, and resilience are constraints or secondary checks rather than the main objective.
• Typical domains: transportation, logistics, data networks, hospital throughput
• Common mechanisms: Max Flow Analysis, Capacity Cut Review

Min-Cost Flow Selection · subtype · recognized

A subtype focused on routing feasible flow through the network at the lowest total cost or burden.

• Distinct from parent: The parent can optimize other objectives; this variant focuses on cost or burden minimization while preserving feasibility.
• Use when: Flow must reach sinks, but multiple feasible routes have different costs, delays, burdens, or risks; The cost measure is legitimate and reviewed rather than hidden.
• Typical domains: freight, public benefits delivery, cloud infrastructure, utility networks
• Common mechanisms: Min Cost Flow Model, Route Cost Table, Carrier Cost Planning

Multi-Commodity Flow Allocation · scale variant · candidate

A variant for allocating several types of flow that share edges, nodes, or capacity pools.

• Distinct from parent: The parent can involve a single flow type; this variant stresses shared-capacity interactions among classes.
• Use when: Different flow classes compete for the same links or nodes; Each class has distinct origins, destinations, priorities, constraints, or service requirements.
• Typical domains: telecommunications, transit, hospital triage, supply chains
• Common mechanisms: Multi Commodity Flow Model, Class Based Routing Policy

Resilient Alternate-Path Flow · risk or failure variant · candidate

A variant that reserves or designs alternate paths so flow can continue when a primary path degrades or fails.

• Distinct from parent: The parent optimizes flow generally; this variant accepts inefficiency to preserve alternate route viability.
• Use when: Disruptions are likely or high consequence; The cheapest or fastest route is brittle; Continuity matters more than peak efficiency alone.
• Typical domains: critical infrastructure, cloud infrastructure, emergency logistics, public health supply chains
• Common mechanisms: Failover Routing, Redundant Carrier Plan, Disaster Logistics Routing

Lossy Flow Network Management · subtype · candidate

A variant for networks where flow can decay, leak, be abandoned, spoil, be transformed, or be dropped between source and sink.

• Distinct from parent: The parent may assume conserved flow; this variant emphasizes non-conservative movement as a core modeling and governance issue.
• Use when: Perfect conservation assumptions are false; Loss, attrition, spoilage, abandonment, leakage, or rework materially affect outcomes.
• Typical domains: food distribution, public benefits, patient referrals, information pipelines
• Common mechanisms: Yield Adjusted Routing, Attrition Pathway Review, Leakage Analysis

Merge Parallel Gapped Streams By Monitoring Relative Positions · implementation variant · recognized

Merge parallel gapped streams by monitoring relative positions and inserting items from one stream into available gaps in the other.

• Distinct from parent: Network-Flow Optimization owns routing under capacity constraints; this variant exploits transient item-scale residual capacity through synchronized gap insertion.
• Use when: Two parallel item streams contain usable gaps, but naive merging wastes capacity or creates collisions because relative positions change continuously.
• Evidence (strong independent recurrence confirmed): US9624043B2; Photo-eye and PLC gap-creation merges; Secondary-line products inserted into main-line gaps

Objective Switched Ordered Residual Routing · subtype · recognized

Route a shared resource network by ordered residual allocation, changing path priorities when the operating objective changes.

• Distinct from parent: The candidate's defining object is a flow network whose edge priorities and residual allocation order switch with operating objective. It is therefore a network-flow subtype rather than generic scarce-resource allocation.
• Use when: A site with local generation, storage, load, and grid exchange needs different power priorities under surplus, shortage, and export-assist conditions.
• Evidence (strong independent recurrence confirmed): US9523991B2; Priority-ordered PV, battery, grid, and residual routing modes; Objective-dependent dispatch priorities in energy management

Near names: Capacity-Constrained Routing, Network Routing Optimization, Supply-Chain Flow Optimization, Traffic Flow Optimization, Patient Flow Optimization.

Editorial Notes

Problem Classification

Classification: Congestion, Backlog & Flow Breakdown → Routing, Distribution & Endpoint Failure

Problem kernel: local routing ignores topology-wide feasible flow

Rationale: Earliest causal condition: A flow network has constrained paths, bottlenecks, costs, handoff losses, or imbalanced supply and demand, but routing decisions are made locally or heuristically without seeing how the whole topology constrains feasible movement.

Independent corroboration: The earliest necessary condition in the frozen evidence is: A flow network has constrained paths, bottlenecks, costs, handoff losses, or imbalanced supply and demand, but routing decisions are made locally or heuristically without seeing how the whole topology constrains feasible movement. That is a routing distribution and endpoint failure problem because Flow pools, takes costly paths, misses viable capacity, or breaks at fanout endpoints because access representations, routing, and topology do not distribute it effectively.

Review outcome: Independent reviewer agreement; high confidence.