The Symbiosis between Beaufre’s Fencing and Network Saturation

Analytical Summary

This study establishes a new paradigm for Security and Defence doctrine, demonstrating the mathematical and tactical exhaustion of linear warfare based on high-cost kinetic platforms. Contemporary conflict has irrevocably shifted to a thermodynamic model of systemic saturation and fractal action. However, in the face of the vulnerability of the electromagnetic spectrum and the logistical collapse seen in recent theatres of operations, the work decrees that blind dependence on information networks (Informational Vanguard, Vanguarda Informacional) is fatal if dissociated from classic industrial and metal-mechanical capacity (Kinetic Rearguard, Retaguarda Cinética).

To avoid what is defined as the Abismo do Rigor (Abyss of Rigour) — the endogenous implosion generated when the political and strategic leadership designs operations founded on pure will, ignoring the immutable laws of communications engineering and the physics of materials —, the thesis proposes the institution of Verticalidade (Verticality). This doctrine requires the transition from static infrastructure to a Dynamic Hybrid Matrix (Matriz Híbrida Dinâmica), capable of jumping autonomously between optical fibre, free-space optical communications (FSOC) and the radio spectrum, cannibalising the entropy generated by the adversary’s Electronic Warfare in order to become antifragile.

In parallel, the work formalises the New Human Engineering (Nova Engenharia Humana) to mitigate the cognitive suicide imposed by the speeds of hyperwar. By raising the biological operator from micro-executor on the trigger to macroscopic Scenario Architect (human-on-the-loop), the system frees the algorithm to operate at the limit of lethal latency (closing the OODA Loop in milliseconds), while the human intellect works as the supreme heuristic filter against the brittleness of artificial intelligence and cognitive spoofing.

In short, it is concluded that the strategist of the twenty-first century is primarily a master of the Engineering of Controlled Chaos (Engenharia do Caos Controlado). The thesis proves that the classic imposition of will and psychological shock (Beaufre’s fencing) only crush the adversary when the State’s directive is fully anchored in a systems-integration architecture immune to friction, subjecting the politics of conflict to the non-negotiable rigour of engineering.

1. Introduction: The Collapse of Surface Topology and Structural Symbiosis

For more than two centuries, military doctrine was founded on the paradigm of kinematic penetration and tactical fencing. As grounded in Carl von Clausewitz’s mechanical friction and in André Beaufre’s classic “dialectic of wills”, strategy required geographic vastness to absorb attrition.

Today, that surface topology has collapsed. The omnipresence of uncrewed vectors and mesh networks has disintegrated the metric of linear space-time. We are witnessing the materialisation of “netwar” (Arquilla and Ronfeldt), in which heavy hierarchies succumb to decentralised webs. The threat springs simultaneously from multiple nodes in a fractal environment (Kilcullen). Linear geography has been inverted: the centre of gravity now lies in submerged infrastructure, commercial ports and submarine cables (Lind; van Creveld).

Operational Evidence:

• Russia and Ukraine: The apparent trench war is an illusion. The front is fractal: small groups use low-orbit satellites to operate FPV swarms that destroy logistics tens of kilometres away, cancelling the tactical depth of traditional tube artillery.
• USA/Israel and Iran: Iran projected the “Axis of Resistance” as a fractal network. Israel does not defend a trench, but manages the saturation of an omnidirectional airspace, where the port of Eilat is paralysed by a network node 2,000 km away (the Houthis).

2. The Physics and Mathematics of Conflicts: From Static Anchoring to the Dynamic Hybrid Matrix

Survival in a decentralised theatre of operations is dictated by three non-negotiable vectors: massive bandwidth, near-zero algorithmic latency and supremacy in the electromagnetic spectrum. The classic industrial model has collapsed in the face of the new thermodynamics of conflict. The “mathematics of attrition”, exhaustively detailed by Justin Bronk, proves the financial and logistical unsustainability of intercepting disposable threats (weaponised commercial drones) with premium air-defence systems. We are thus witnessing the empirical confirmation of T.X. Hammes’s thesis: the asymmetric lethality of small, smart and massed vectors condemns large centralised platforms to exhaustion.

However, this informational swarm is an absolute slave to the Physical Layer (telecommunications, processing and energy infrastructure). As the Electronic Warfare analyses of Jack Watling and the scrutiny of signal processing by Thomas Withington warn, lethal resilience requires a surgical escape from broadband jamming. To guarantee that survival and not fall into the “tactical prison” of an immutable physical cable, the Command and Control system (C4I) requires the transition to a Dynamic Hybrid Matrix, capable of materialising Nassim Nicholas Taleb’s concept of antifragility.

The End of the “Cable Fetish” and Electromagnetic Agility

Terrestrial optical fibre guarantees total immunity to interference (EMI/RFI), but imposes an unacceptable sacrifice: immobility. The “cable fetish” anchors the force to the static, returning conflict to the lethargy of the trenches.

The evolution of tactical communications engineering involves the adoption of Free-Space Optical Communications (FSOC) and ultra-short directional burst emissions. This architecture allows mechanised forces and drone swarms to recover two- and three-dimensional manoeuvre, maintaining bandwidths in the order of gigabits per second, while remaining invisible to Radio Frequency (RF) interception.

Operational Evidence and Implementation of the Hybrid Matrix

To substantiate this transition, three theatres of operations are analysed in which network engineering dictates the boundary between tactical success and systemic collapse:

I. The Ukrainian Theatre: From Static Silica to Autonomous Multipath Routing When Moscow applies massive jamming to GNSS/UHF signals, Ukraine initially responds by overcoming the electromagnetic barrier through anchoring in the classic Physical Layer, guiding ground drones via optical-fibre cables unwound in real time. However, in order to scale up the offensive and regain the capacity for mechanised breakthrough, this physical anchoring has evolved.

• The Application of the Matrix: The new Ukrainian C2 systems operate with resilient multipath routing. The data link jumps autonomously, in fractions of a second, between directional optical terminals (immune to jamming), radio bursts on atypical frequencies and low-orbit satellite constellations (Starlink).
• Scientific Grounding: This adaptation is the lethal proof of the warnings of Jack Watling (RUSI: Electronic Warfare and UAVs in Ukraine). Watling shows that the network only survives if it is capable of constant mutation in the spectrum. By cannibalising Russian entropy to force frequency jumps, the Ukrainian mesh becomes, in Taleb’s definition, truly antifragile.

II. The Iron Dome System and the Thermodynamic Saturation of C4I (Israel/Iran) Israel’s air-defence architecture faces, every day, the absolute test of the mathematics of Justin Bronk (RUSI: The Economics of Air Defence). Iran and Hezbollah use very low-cost Shahed drones to saturate the radars of Israel’s layered defence, forcing the firing of multimillion-dollar Tamir and Arrow-3 missiles, with the aim of financial exhaustion (the financial Abismo do Rigor).

• The Application of the Matrix: To avoid rupture, the Iron Dome dome acts as a supreme hybrid processing node. The algorithm does not intercept everything it detects. It calculates the ballistics in milliseconds and actively ignores vectors that will strike uninhabited areas. The immediate evolution of this matrix is the integration of Iron Beam (Directed Energy Weapons), in which optical fibre is replaced by high-energy lasers powered by ground generators, eliminating the cost of the physical interceptor.
• Scientific Grounding: This is the crystallisation of the antifragility of Nassim Nicholas Taleb (Antifragile). The system is fed by the disorder of the massive attack; the greater the volume of cheap threats, the more aggressive and selective the routing and interception algorithm becomes, safeguarding the energy anchor of the Hebrew State.

III. Naval Silence in the Red Sea: Inter-ship Optical Meshes (USA/Houthis) In the Red Sea, the US Navy faces a militia (the Houthis) that applies the thesis of cheap proliferation theorised by T.X. Hammes (The Evolution of Small, Smart, and Cheap). Using naval and aerial drones, they threaten billion-dollar surface platforms.

• The Application of the Matrix: To coordinate the defence of the squadron without revealing its position, American destroyers cannot constantly emit tactical radio signals (Link 16), as they would be the target of immediate triangulation by the adversary’s signals-intelligence teams. The solution is the implementation of FSOC (Free-Space Optical Communications) through directional lasers between ships.
• Scientific Grounding: This tactic fully endorses the signal scrutiny advocated by Thomas Withington (Armada International: Electronic Warfare Analysis). Withington proves that RF emissions are always, ultimately, interceptable. The naval Hybrid Matrix solves this constraint: it transfers gigabytes of radar telemetry from one ship to another via an invisible beam of light. The squadron maintains operational Verticalidade while operating in total electromagnetic silence.

3. The Abismo do Rigor: The Informational Vanguard and the Kinetic Rearguard

The Abismo do Rigor manifests itself at the exact moment when the political and strategic leadership designs operations founded on pure abstract will, ignoring the immutable laws of network engineering, of electromagnetic propagation and of industrial thermodynamics. “Netwar” and dominance of the spectrum create a dangerous illusion of technological asepsis. However, as contemporary systems engineering postulates, agile networks and algorithms constitute only the Informational Vanguard: their purpose is to saturate the enemy’s defence and create the rupture. But algorithms and drones do not occupy territory, do not clear trenches and do not control populations. The consolidation of that rupture necessarily requires a Kinetic Rearguard based on raw metal-mechanical force and heavy production rates.

The implosion of the State is mathematically certain if strategic decision-making forgets that agile software is supported by heavy hardware infrastructure. Verticalidade requires politics to submit to the industrial metric; failing in this integration is to plunge into the Abyss.

Operational Evidence and the Mathematics of Rupture

To illustrate the collapse generated by the dissociation between political will and physical engineering, three critical operational scenarios are dissected in which the theoretical foundation of these authors materialises on the ground:

I. The Offensive on Kyiv (2022): The Collapse of Telecommunications Engineering The initial Russian operation in Ukraine is the encyclopaedic example of the absolute Abismo do Rigor. The political leadership in Moscow ordered a deep and fast mechanised advance, totally divorced from the laws of logistics and of radio-signal propagation.

• The Integration Failure: The armoured columns advanced beyond the range of their own secure communication nodes (the “Era” cryptographic system, which depended on 3G/4G cellular towers to operate). Without network coverage, the Russian forces reverted to open analogue radios (often for civilian use) of high frequency (VHF/UHF).
• Scientific Grounding: This failure is the tactical manifestation of the warning of Eliot Cohen (Supreme Command). Politics overrode engineering. The Ukrainian signals-intelligence system (SIGINT) triangulated the unencrypted analogue emissions and directed the artillery with geometric precision. Russian strategy did not fail for lack of armour (Kinetic Rearguard); it failed because its Informational Vanguard collapsed owing to crass ignorance of the physical limits of secure data transmission.

II. The War of Attrition in the Donbas: The Thermodynamic Limit of Software Today, the Ukrainian theatre shows the other side of the coin. Ukraine has an undeniable superiority in networked planning, using software-defined C4I systems (such as Delta or GIS Arta) that process the interception cycle at an unmatched speed, distributing targets from drones and satellites directly to the artillery.

• The Integration Failure: Despite this algorithmic superiority, the front line suffers constant setbacks. The reason is strictly mechanical: the excellence of the software cannot compensate for the thermal and material deficit. Ukraine suffers from inferiority in the manufacture of 155 mm shells, in the replacement of artillery barrels worn by thermal attrition and in the replenishment of infantry vehicles.
• Scientific Grounding: This is the empirical confirmation of the thesis of Michael Kofman (Analyses of Industrial Attrition). Kofman proves that “software webs” evaporate if the logistical Physical Layer does not exist. The most sophisticated software in the world becomes irrelevant if, after the algorithm calculates the perfect firing solution, there is no physical artillery shell to be fired. The Western Abismo do Rigor was to believe that the supply of network intelligence would cancel the need for heavy industrial capacity.

III. The Natanz Complex and Hormuz: Geophysics and Global Logistical Collapse In the Middle East, the internal political pressure in Israel (and at times in the USA) to neutralise pre-emptively the Iranian nuclear programme, buried in the mountains of Natanz and Fordow, illustrates the perfect divorce between diplomatic will and the scale of mathematical attrition.

• The Integration Failure: Politics demands rapid neutralisation. Civil engineering and the physics of penetration dynamics stand in the way. The Iranian facilities are buried at depths that reach 80 metres of solid rock and reinforced concrete. The kinetic energy needed to penetrate such density often exceeds the physical limit of conventional penetrating munitions (heavy bunker busters such as the GBU-57). Moreover, the guaranteed Iranian retaliation would close the Strait of Hormuz.
• Scientific Grounding: This scenario crosses the mechanical planning set out by Lawrence Freedman (Strategy: A History) with the war of logistical networks theorised by William S. Lind (Fourth Generation Warfare). Deciding on an attack while ignoring that the laws of geophysics prevent the total destruction of the facility, and simultaneously ignoring that the asymmetric response would paralyse the circulation of 20% of the world’s oil in an infrastructural choke point (4GW), is the final definition of the Abismo do Rigor. Verticalidade obliges the leadership to recognise that the thermodynamics of the explosive and the fragility of the maritime corridors veto the “genius” of aggressive political manoeuvre.

4. The New Human Engineering: The Scaling of Autonomy

In an era of hyperwar, in which lethal open-source tools and decentralised manufacturing capabilities have democratised access to mass destruction for state and non-state actors, the temporal metric of conflict has collapsed. Biological latency has become the main vulnerability of any Command, Control, Communications and Intelligence (C4I) architecture.

In this environment of saturation, the doctrinal requirement that the human being mechanically and individually validate each interception or target constitutes an unacceptable cognitive suicide. The New Human Engineering does not propose the removal of the human factor from the military equation, but rather its systemic elevation. The aim is to prevent neurological reaction time from compromising the imperative speed of the OODA Loop (Observe, Orient, Decide, Act).

To materialise this evolution, the design of decision interfaces and protocols undergoes a structural mutation:

Scenario Architect vs. Micro-Executor

The classic dialectic of wills moves from the finger on the trigger to the parameter-setting keyboard. The human operator acts as a “Scenario Architect”, defining the Kill Box (the three-dimensional annihilation box, bounded by strict geographic, temporal and ethical limits).

Inside that box, artificial intelligence takes autonomous lethal control in milliseconds. By raising the human to macroscopic supervision (human-on-the-loop), the system actively mitigates two pathologies inherent in the pure machine: susceptibility to brittleness (brittle AI) in the face of uncatalogued noise, and vulnerability to the injection of false data (algorithmic spoofing). Morality and the International Law of Armed Conflict come to be coded in the intention of the parameter’s design, and not in the mechanical pressure of firing.

Operational Evidence and the Management of Cognitive Entropy

To substantiate this doctrinal evolution, three highly complex operational architectures are analysed in which survival depends on the perfect calibration between the speed of silicon and neurological intuition:

I. Arrow and David’s Sling Systems: The Financial Entropy Filter (Israel) During multi-vector ballistic saturation attacks, the air-defence leadership faces hundreds of projectiles (ballistic and cruise missiles, and drones) simultaneously, forcing the saturation of the tactical decision channel.

• The Application of Autonomy: The human operator acts exclusively as a macroscopic modulator. The machine calculates, in fractions of a second, the firing solutions and the interceptor ballistics for more than 300 simultaneous threats. The operator does not aim weapons; he applies Verticalidade. He delegates to the algorithm the automatic and autonomous destruction of missiles aimed at critical air bases and dense residential areas, but obliges the system deliberately to ignore projectiles whose calculated trajectory predicts a harmless impact in the Negev desert.
• Scientific Grounding: This architecture is the validation of John Boyd (The OODA Loop) and Paul Scharre (Army of None: Autonomous Weapons). If the human tried to carry out the individual interception (micro-executor), biological latency would shatter the time cycle (Boyd), and the missiles would hit the target. By implementing the human-on-the-loop model (Scharre), the system fuses the thermodynamic speed of the machine with the management of financial entropy (not spending expensive missiles against sand), preserving moral authority without sacrificing mechanical rigour.

II. Distributed C4I Platforms (Delta/GIS Arta): The Mitigation of Algorithmic Brittleness (Ukraine) In the theatres of operations of Eastern Europe, software-defined systems fuse thousands of video feeds from low-cost drones, commercial satellites and mobile-phone data into a single tactical interface to coordinate the artillery.

• The Application of Autonomy: The Machine Learning algorithm automatically analyses the terrain and identifies a column of camouflaged vehicles, immediately proposing the distribution of targets to HIMARS artillery batteries or 155 mm howitzers stationed kilometres away. However, the algorithm does not have the heuristic perception to understand that a group of farmers with modified tractors in an undocumented area may share the same thermal signature as Russian armoured vehicles.
• Scientific Grounding: Here the clinical urgency outlined by Mary “Missy” Cummings (Brittle AI) and Audrey Kurth Cronin (Power to the People) becomes manifest. In a chaotic environment where civilian technology (Cronin’s open-source) mixes with military means, AI becomes dangerously “brittle” (Cummings), collapsing in the face of the unforeseen that is not categorised in its training data. The New Human Engineering places the operator auditing the screen in real time: the human does not calculate the ballistics, but uses his heuristic discernment to cancel the lethal chain in the face of a false positive, avoiding disastrous collateral damage.

III. Aegis Combat System and Naval Cognitive Spoofing (USA) The destroyers integrated into the Aegis system, which form the backbone of naval ballistic-missile defence in theatres such as the Red Sea or the Taiwan Strait, operate in semi-autonomous and fully autonomous lethality modes (such as the Auto-Special mode) for point defence.

• The Application of Autonomy: Faced with a coordinated attack by adversary forces that master advanced Electronic Warfare, the SPY-1/SPY-6 radar system may be the target of phantom injections (ghost tracks). The enemy algorithm injects the mathematical illusion of a massive attack by anti-ship missiles. The Aegis computer, processing data that are logically perfect but factually poisoned, proposes the immediate launch of dozens of interceptor missiles, which would empty the ship’s magazine, leaving it defenceless against the real kinetic attack that would follow.
• Scientific Grounding: This is the scenario of systemic failure described by August Cole and P.W. Singer (Burn-In / Ghost Fleet) and resolved by the technological leadership of Mick Ryan (War Transformed). Cole and Singer show that blindly trusting the processor is to give in to cognitive spoofing. The solution (Verticalidade) is Mick Ryan’s requirement: the naval tactical officer must be a superior cognitive engineer. The human detects anomalies in the logical cadence of the attack that the machine passively accepts. The intuition of the human engineer serves as the ultimate and supreme firewall against algorithmic corruption.

5. Conclusion: A Fundação da Verticalidade (The Foundation of Verticality) and the Engineering of Controlled Chaos

Survival in contemporary decentralised conflict is not achieved by rejecting brute force, nor by blind subordination to software. It invariably requires the building of a Hybrid Architecture. The strategist must use the informational swarm (the cyber, electronic and autonomous-vector Vanguard) to saturate the sensors and blind the enemy’s Command and Control (C2). This saturation does not win the war on its own, but it creates the exact temporal and cognitive breach for the heavy kinetic force (the physical and mechanised Rearguard) to advance, anchor itself and irrevocably occupy the space.

In this final synthesis, the modern strategist acts primarily as a master of the Engineering of Controlled Chaos. In an environment where linear topology has been disintegrated, the decision-maker uses the absolute rigour of systems and network engineering not to create a predictable, static and mechanised plan, but to set the parameters of risk. Verticalidade is the triumph of rigour: it ensures that the State’s political directive (the will) submits to the immutable laws of physics (engineering). The dialectic of wills only crushes the adversary when supported by an inter-arm communications architecture that proves immune to systemic friction.

Operational Evidence and the Systemic Synthesis

To demonstrate the absolute effectiveness of Verticalidade in subjugating the enemy, three operational archetypes are analysed that enshrine the fusion between network engineering and the violent imposition of will:

I. The Hybrid Breakthrough Manoeuvre: Saturation as Breacher (Territorial Occupation) In an offensive against a modern fortified line (crossing minefields and pre-registered artillery), classic doctrine would dictate a massive artillery barrage followed by an armoured advance. The Hybrid Architecture inverts the energy paradigm.

• The Application of Controlled Chaos: The attack begins in the invisible spectrum. Swarms of disposable drones and Electronic Warfare (EW) emitters are launched to flood the adversary’s radars with false echoes (spoofing) and exhaust the front line’s air-defence interceptors. At the exact millisecond when the enemy’s screens go white from thermodynamic saturation, heavy armoured columns, communicating internally by optical beams (FSOC) and in total radio silence, tear through the enemy line, occupying the trench before the adversary recovers situational awareness.
• Scientific Grounding: This is the perfect symbiosis between the massed and cheap lethality of T.X. Hammes (Sling and the Stone) and the brutal need for heavy industrial massing of Michael Kofman. The swarm (Hammes) creates the blindness; the steel (Kofman) capitalises on the paralysis. The engineer designs the network so that the cognitive shock precedes the mechanical shock.

II. Parametrised Audacity: The Non-Linear Assault and Friction Deep decapitation operations (Special Forces or deep air interdiction) often look like suicidal manoeuvres in the light of classic planning, given the level of isolation of the troops and the foreseeable break in communications.

• The Application of Controlled Chaos: An infiltration force is inserted beyond the range of its conventional support networks. For the adversary, this is an exploitable tactical error. However, what looks like an irrational risk was previously validated by engineering. The force does not depend on a central command, but carries with it acoustic mesh terminals and small LEO (Low Earth Orbit) relay satellites. They withstand the break in communication because the C4I algorithm has already pre-calculated autonomous decision matrices in case the link drops.
• Scientific Grounding: Here, the scientific rigour of complexity theorised by Antoine Bousquet (The Scientific Way of Warfare) crosses with the “Genius” and audacity of Carl von Clausewitz (On War). The engineer (Bousquet) did not try to eliminate “Friction” (Clausewitz) by keeping a cable connected to the soldier; he modelled the system to survive within that friction. Absolute rigour does not castrate the violent audacity of the tactical manoeuvre; rather, it guarantees its physical feasibility, proving that the apparent irrationality was, in fact, superior mathematical calculation.

III. The Paralysis of the “System of Systems”: The Collapse of the Will without Symmetric Attrition Imposing defeat on a modern nation-state does not necessarily require the physical annihilation of all its brigades or the carpet bombing of its cities, but rather the structural rupture of its nerve nodes.

• The Application of Controlled Chaos: In an escalation of regional tension (e.g. blockade simulations in the South China Sea or the Persian Gulf), the attacking force does not target the enemy fleet directly. Instead, it uses surgical cyberattacks against the commercial data centres that process naval logistics and employs uncrewed submarines (UUVs) to threaten (or sever) the submarine optical-fibre cables at their landing points. At the same time, it compromises the energy synchronism (the inertia of the electricity grid) of the target country.
• Scientific Grounding: This operation materialises the trinitarian collapse foreseen by Martin van Creveld (The Transformation of War), fused with the final objective of the “dialectic of wills” of General André Beaufre (Introduction à la Stratégie). The primary target was not the opposing army, but the civil-military matrix that sustains its cognitive and economic capacity. Beaufre is executed in masterly fashion: the psychological shock and political surrender are achieved because the adversary’s engineering collapsed. The attacker’s Verticalidade crushed the defender’s Abismo do Rigor, dictating victory through the strangulation of its physical and digital infrastructure.

Conclusion: The Paradigmatic Synthesis

1. The Change in Time: From Reaction to Prediction

• The Previous Paradigm (The Reactive): It was characterised by the culture of corrective intervention (“wait to repair”). Human action was subordinate to the occurrence of the incident: one waited for the failure of the mechanical asset, the frequency collapse of the electricity grid or the symptomatic manifestation of the illness in order, reactively, to mobilise the technical or clinical resources for repair.
• The Current Paradigm (The Predictive): It consists in the absolute anticipation of error (“mitigate the anomaly at its origin”). Through the convergence between sensor networks and Artificial Intelligence at the periphery (edge computing), the “silent pain” of the system is mapped. The predictive model intercepts the kinematic or electromagnetic deviation in real time, carrying out the autonomous correction before the failure materialises in the physical world.

2. The Change in Work: From Effort to Scale (The 1:N Ratio)

• The Previous Paradigm (Linear Operation): It rested on the direct and isolated allocation of the human factor. A technician monitoring screens, a clinician’s individual consultation or a trainer’s face-to-face teaching operated at a strict ratio of 1:1. The maximum ceiling of efficiency and quality was rigidly limited by the specialist’s time saturation and fatigue.
• The Current Paradigm (Systemic Multiplication): Algorithmic automation takes over all the mechanical, routine and continuous data-processing tasks. The human specialist is raised to the role of “conductor” of the ecosystem. Freed from the repetitive operational load, the professional comes to exercise analytical supervision and high-level auditing over hundreds of processes, assets or trainees simultaneously (1:N ratio).

3. The Change in Decision: From Intention to Rigour

• The Previous Paradigm (The “Abismo do Rigor”): The design of macro-systems and critical infrastructure — energy grids, transport networks or communications axes — often suffered the intrusion of discretionary criteria, empirical assumptions or budgetary convenience, subordinating the physical integrity of the asset to mere probability.
• The Current Paradigm (“Verticalidade”): It is defined by absolute intolerance of systemic failure. Decision-making is shielded by mathematical models, geometric simulations and phasor data that prove the resilience and integrity of the infrastructure before any allocation of capital (CAPEX). Governance ceases to be a projection of intentions and becomes a well-founded scientific certainty.

In short:

Before, technology operated as a support tool to mitigate the collapse of what had already broken; today, data intelligence acts as the mathematical foundation that guarantees, a priori, the stability and permanent continuity of systems.

Bibliographic Matrix and Cross-References

To consolidate the architecture of this treatise by Gaspar do Amaral with the utmost technical and scientific rigour, the doctrine of Verticalidade and of the Abismo do Rigor rests on these 22 fundamental works.

1. Nassim Nicholas Taleb — Antifragile: Things That Gain from Disorder

Taleb’s work establishes the mathematical and epistemological basis for transcending the mere robustness of Command and Control (C2) systems. Taleb shows that robustness only withstands mechanical shock up to its breaking point, at which moment it fails catastrophically. For the thesis, this concept is vital to design the Dynamic Hybrid Matrix: a tactical telecommunications system that does not merely withstand electromagnetic interference, but uses the adversary’s jamming as a trigger to reorganise its routing (jumping from RF to optical fibre or FSOC), becoming paradoxically more lethal and efficient when exposed to chaos.

Gaspar do Amaral appropriates the concept of antifragility to ground the decentralised shield. From the perspective of communications engineering, a destroyed network node should not represent a degradation of the signal, but rather force the mesh to recalculate lower-latency paths. Antifragility is the academic proof that tactical topology only survives if the entropy imposed by the adversary is cannibalised to feed the constant change of state of our own communications system.

2. John Arquilla & David Ronfeldt — Networks and Netwars: The Future of Terror, Crime, and Militancy

The RAND Corporation researchers were pioneers in modelling the collapse of hierarchies in the face of distributed network topologies. The usefulness of this work lies in its mathematical formulation that “it takes a network to fight a network”. For Gaspar do Amaral, this text is the foundation for decreeing the end of linear surface topology. The thesis uses Arquilla and Ronfeldt to prove that the concentration of processing capacity in static command posts (the classic linear model) constitutes a fatal single point of failure (Single Point of Failure) in the face of swarms of small decentralised vectors.

In the practical application of his thesis, the concept of Netwar justifies the urgency of a truly agnostic joint land-sea-air integration. Amaral extends the authors’ concept to the domain of physical engineering: if the threat acts in a fractal and ubiquitous network, the structural response of the State has to dilute the boundary between civilian infrastructure (data centres, submarine cables, port stations) and the military sensor, fusing them into a single information mesh that makes the decapitation of command impossible.

3. André Beaufre — Introduction à la Stratégie

General Beaufre postulates that the essence of strategy is not the physical annihilation of the enemy, but the “dialectic of wills” operating so as to produce psychological paralysis and the disruption of the opposing command. In Gaspar do Amaral’s thesis, this classic premise acts as the compass that prevents hollow technocracy. Beaufre’s work ensures that all the thermodynamic “Network Saturation” and algorithmic complexity are not ends in themselves, but merely modern vehicles of fencing to break the enemy’s decision-making will.

By crossing Beaufre with contemporary network engineering, Amaral shows that algorithmic saturation and the attack on the electromagnetic spectrum are, in essence, psychological operations. Blinding the adversary’s radar or saturating its processing capacity with cheap threats destroys the mental cohesion of the opposing leadership, forcing it into a state of inaction. Beaufre is the soul of the thesis: he guarantees that the engineer’s rigour is permanently subordinate to the final objective of human strategy.

4. Jack Watling — Work and Reports on Electronic Warfare and the Spectrum (RUSI)

Jack Watling has produced the most rigorous empirical analyses of operational behaviour in the Ukrainian theatre, specifically with regard to Electronic Warfare (EW) and the exhaustion of the radio spectrum. For the thesis, Watling’s technical data work as irrefutable expert proof of the collapse of the unguided channel. Amaral uses Watling’s measurements of Russian attenuation and jamming to validate his demand for Anchoring in the Physical Layer (fibre cables, free-space optical communication).

The RUSI reports ground Amaral’s warning against technological complacency. Watling proves that networks not anchored in physical rigour give way to broadband interference emitters. Amaral takes this tactical evidence and raises it to the strategic level: the Verticalidade of the State can only be maintained if its communications engineers design channels immune to the detection and disruption described by Watling, on pain of the mechanical force being left blind and deaf on the ground.

5. John Boyd — A Discourse on Winning and Losing (The OODA Loop)

Boyd’s Observe, Orient, Decide and Act (OODA) loop provides the exact temporal metric for the doctrine. The usefulness of this concept is central to the chapter on the New Human Engineering. Boyd argues that victory belongs to the one who manages to complete the decision cycle faster and more consistently than the adversary, forcing the adversary to react to a situation that has already changed. Amaral carries this theory over to the environment of automated hyperwar.

In the thesis, the OODA Loop mathematically justifies the Scaling of Autonomy. Amaral argues that if the human being is forced to carry out the “Act” phase in a saturated environment, he will introduce a biological latency that breaks Boyd’s loop in the face of the speed of the machines. Therefore, the rigour of engineering requires that the human be isolated in the “Orient” phase (defining the ethics and the geographic limits), leaving the lethal “Decide and Act” phase to the low latency of the algorithms, maintaining temporal dominance over the enemy.

6. Paul Scharre — Army of None: Autonomous Weapons and the Future of War

Scharre explores the architecture of autonomous weapon systems and the dichotomy between human-in-the-loop, human-on-the-loop and human-out-of-the-loop. This work is the architecture manual for mitigating the vulnerabilities of artificial intelligence. Gaspar do Amaral uses Scharre to ground his outright rejection of the total removal of the human being from the decision cycle, something that irresponsible doctrine might suggest under the pressure of mechanical saturation.

Amaral crosses Scharre’s vision with the constraints of “Brittle AI” (susceptible to corrupted data or sensor noise). The work proves that the machine does not have the heuristic discernment to operate in situations of extreme chaos that are not in its training data. The thesis appropriates this to define the role of the modern strategist-engineer: a supervising modulator (human-on-the-loop) who holds the millisecond “kill switch” to prevent a runaway algorithm from striking critical civilian infrastructure, precipitating the moral and strategic collapse of the State.

7. Michael Kofman — Analyses of Industrial Attrition, Logistics and Force Structure

Michael Kofman provides the ballistic and industrial anchoring of reality against the excessive fascination with the cyber domain and with software webs. His analysis, focused on the lethality of artillery, industrial production rates of munitions and the need for mechanised mass, is the pillar that supports the Kinetic Rearguard in Amaral’s thesis. Kofman warns that communication technology does not win wars of attrition if there is no metal and gunpowder to sustain physical occupation.

For Gaspar do Amaral’s formulation, Kofman’s usefulness is crystal clear: he is the counterweight that prevents the thesis from falling into the informational Abismo do Rigor. Amaral argues that decentralised networks create the invisible breach in the spectrum, but it is the cold industrial mathematics underlined by Kofman — railway lines, gigawatts of synchronous energy generated in power stations and tonnes of steel — that materialises and consolidates the fracture. It is the academic proof that the New Engineering has not abolished the classic physics of materials; rather, it has redefined how it is projected on the ground.

8. Antoine Bousquet — The Scientific Way of Warfare: Order and Chaos on the Battlefields of Modernity

Bousquet categorises military evolution into four scientific eras: mechanistic, thermodynamic, cybernetic and chaotic (complexity). The colossal usefulness of this work for the thesis is to provide an epistemological framework that justifies the behavioural transition of the military decision-maker. Bousquet proves that trying to resolve contemporary non-linear war (the era of chaos) with tactics of industrial crushing (the thermodynamic era) invariably results in a very serious operational dysfunction.

Gaspar do Amaral absorbs Bousquet to ground the Engineering of Controlled Chaos. The thesis argues that the commander’s Verticalidade no longer comes from his capacity to impose a rigid mechanistic order on the battlefield, but rather from his mastery in navigating complexity. By integrating Bousquet, Amaral decrees that the perfect C4I system is not the one that eliminates chaos (a physical impossibility), but the one that has an architecture fluid enough to exploit the non-linear patterns of friction in its favour.

9. Justin Bronk — Analyses of Financial Attrition and Air Defence (RUSI)

Justin Bronk has relentlessly quantified the asymmetry of contemporary military attrition. His research shows the financial and logistical collapse that occurs when States use very high-precision (and multimillion-cost) air-defence interceptors to neutralise swarms of commercial drones or loitering munitions that cost a tiny fraction of that value. Bronk proves mathematically that the defence model based on premium platforms is unsustainable in a war of saturation, inevitably leading to the depletion of stocks and the economic bankruptcy of the defending force. For Gaspar do Amaral’s thesis, this work provides the thermodynamic demonstration of the structural error of legacy architectures. Bronk’s usefulness lies in justifying the urgency of the “Dynamic Hybrid Matrix”: if mechanical attrition is financially fatal, the system has to transpose defence to network engineering and to denial of the spectrum. Amaral uses these data to prove that the asymmetry is only reversed when low-cost ground tactical vectors, protected by anchoring in the Physical Layer (optical fibre), manage to destroy expensive adversary platforms without needing to emit RF signatures susceptible to interception.

10. Christian Brose — The Kill Chain: Defending America in the Future of High-Tech Warfare

Brose describes the collapse of the traditional “kill chain” (kill chain), criticising military command architectures that are balkanised in slow and bureaucratic institutional silos. The author advocates the construction of agile networks, defined by software and supported by artificial intelligence, in which the process of detection, decision and neutralisation occurs almost instantly, allowing any sensor in the theatre of operations (whether a commercial satellite or a naval radar) to feed directly any effector or firing platform available. Gaspar do Amaral appropriates this concept to materialise the software component of his thesis. To avoid the Abismo do Rigor, Amaral shows that the infrastructure has to operate under real joint integration (land, sea and air). Brose validates the premise that technological Verticalidade obliges the strategist-engineer to eliminate human bottlenecks in the phase of transferring tactical data. The system conceived by Amaral uses Brose’s concept to ensure that the network is a fluid mesh of instantaneous targeting processing, freeing the human operator for the macroscopic echelon of strategy.

11. Eliot Cohen — Supreme Command: Soldiers, Statesmen, and Leadership in Wartime

Analysing the history of great leadership in wartime, Cohen dismantles the myth that politicians should hand over war planning entirely to the military. The author argues that supreme command requires a permanent “unequal dialogue”, in which the statesman relentlessly scrutinises, questions and presses the logic, the logistics and the operational assumptions of his generals, ensuring that brute force fully serves the political purposes of the State. In Gaspar do Amaral’s formulation, Cohen’s work serves as the sociological foundation for avoiding the Abismo do Rigor. The thesis shows that the greatest catastrophes occur precisely when that dialogue fails: when the political leadership designs blind wills and the commands execute without the relentless scrutiny of the laws of engineering and thermodynamics. Amaral uses Cohen to postulate that Verticalidade requires the decision-maker to possess technological rigour, ensuring that the political will (fencing) is only approved if the physics of the transport and communications systems allows it.

12. August Cole & P.W. Singer — Ghost Fleet / Burn-In: Realism in Future Conflict

Through Fictional Intelligence (FICINT), Cole and Singer map the complex socio-technical integration of the future battlefield. Their works expose the devastating vulnerabilities that arise from absolute dependence on automated networks and artificial intelligence, illustrating concepts such as cognitive spoofing, the corruption of tactical data packets and the piracy of hardware inserted in global supply chains. The usefulness of this work for Gaspar do Amaral is crucial in consolidating the “New Human Engineering”. Amaral uses Singer and Cole’s scenarios as proof that delegating exclusive lethal command to the machine does not generate efficiency, but rather a colossal systemic fragility. The thesis decrees that the human engineer acts as the irreplaceable filter against this algorithmic spoofing, identifying the disruption in the code that a fully autonomous C2 would process as absolute truth.

13. Audrey Kurth Cronin — Power to the People: How Open Technological Innovation is Arming Tomorrow's Terrorists

Cronin analyses exhaustively the democratisation and proliferation of dual-use technologies (3D printing, open-source software, modified commercial drones). The author stresses that the State has lost its monopoly on technological escalation, allowing non-state actors and irregular armies to access lethal and disruptive capabilities that, historically, would cost billions of euros and decades of research in military-industrial complexes. For the architecture conceived by Gaspar do Amaral, this evidence legitimises the environment of massified entropy (the “cheap gunpowder”). The thesis relies on Cronin to prove that the threat no longer comes only from symmetric powers with classic hierarchies, but from an omnipresent and multidirectional saturation. Amaral demands that the design of defence networks and port infrastructure treat this ubiquitous decentralised threat as the baseline norm, justifying the resilience of the information mesh against attacks that emanate from vectors of irrelevant cost.

14. Mary “Missy” Cummings — Research in Human-Machine Interaction and Autarkic AI

Cummings, a world reference in the study of autonomous systems, studies in detail the limitations of “Brittle AI” (Brittle AI). Her research shows how machine learning algorithms, despite surpassing human reasoning in perfectly controlled and parametrised environments, collapse catastrophically when exposed to untrained external variables, sensor noise or highly entropic operational contexts. This scientific evidence underpins the concept of the “Scaling of Autonomy” in Gaspar do Amaral’s thesis. The usefulness of this evidence is to support mechanically the imperative of human presence in the macroscopic decision cycle. Amaral decrees that, in the face of Clausewitzian Friction (which distorts data), AI disintegrates; it is the rigour of the human — capable of moral and contextual inference — that rescues the operation. The New Human Engineering is the clinical solution to the brittleness diagnosed by Cummings.

15. Lawrence Freedman — Strategy: A History

In this monumental work, Freedman traces the historical evolution of strategic thought, from brute force and political manipulation to modern analytical models. The central argument lies in the fallacy of predictable planning: the mechanistic conviction that perfect planning withstands contact with reality always proves a failure, with mental agility and adaptation being the true engines of victory. Freedman’s macroscopic vision anchors Gaspar do Amaral’s concept of the “Engineering of Controlled Chaos”. The thesis refutes the illusion that a C4I network can foresee and shield itself against all threats. Based on Freedman, Amaral argues that the strategist of the twenty-first century is not a systems bureaucrat who demands absolute certainties in order to operate, but rather a technical leader who designs agile and fluid communication architectures, capable of absorbing disruption and responding organically to the tactical unforeseen.

16. T.X. Hammes — Sling and the Stone and The Proliferation of Small Smart Vectors

Hammes establishes the doctrinal basis for how “technological convergence” annihilated the advantage of large centralised platforms. His theory postulates that “small, smart and cheap” vectors (drones, microsatellites, uncrewed surface vehicles), acting in swarms, have the thermodynamic capacity to saturate and neutralise “few, large and expensive” platforms (such as heavy naval cruisers or armoured divisions). For Gaspar do Amaral, Hammes provides the primordial kinematic justification for the collapse of surface topology. Amaral uses these postulates to argue, from the standpoint of the integration of naval and land systems, that the only way to save heavy infrastructure (such as ports and submarine cables) or armour on the ground is to wrap them in an impenetrable and decentralised electronic shield. The thesis enshrines that betting on heavy military power without a massified antifragile network is a mathematical invitation to the suicide of the force.

17. David Kilcullen — The Dragons and the Snakes / Out of the Mountains

Kilcullen’s research maps the emergence of the “fractal” combat model and the predominance of highly connected littoral and urban environments. The author shows that non-state actors have learnt to circumvent overwhelming Western conventional superiority by operating diluted within the meshes of civilian infrastructure, evaporating the concept of a secure rear and tactical depth. Gaspar do Amaral applies this topological mapping to his network engineering. Kilcullen proves that the threat is, literally, in the street and in the neighbouring server. The thesis uses this to justify that the protection of the State (Verticalidade) is only achieved if defence networks integrate continuously with critical civilian ramifications. Amaral postulates that, in a fractal environment, the engineering of an Internet Exchange Point (IXP) or of a Cable Landing Station becomes as vital for tactical Command as an armoured headquarters.

18. William S. Lind — Fourth Generation Warfare (4GW)

Lind is the central figure in the theorisation of Fourth Generation Warfare, a concept marked by the complete dilution of the boundaries between the state of peace and war, between the formal combatant and the irregular actor, and between civilian and military space. Force comes to reside in psychological manipulation, cyberattacks, the collapse of logistical infrastructure and transnational pressure, subverting the conventional battlefields defined by classic treaties. This premise is absolutely vital to sustain Gaspar do Amaral’s integrated vision in systems engineering. Lind proves politically what Amaral demands structurally: the primary nodes of contemporary war have ceased to be plains and mountain ranges and have become the information domains, the core routers, synchronous energy supply and deep-water ports. The thesis ensures that it is through the technical shielding of these infrastructures that 4GW offensives are contained.

19. Mick Ryan — War Transformed: The Future of Twenty-First-Century Great Power Competition and Conflict

Mick Ryan focuses on the imperative institutional adaptation of the military, arguing that disruptive technologies are useless without the corresponding cognitive evolution of the command leadership. The author argues that the new arms race is, at its origin, a race for the improvement of continuous learning and for the technological literacy of the generals and senior command ranks in the face of open-source tools and AI. Ryan’s analysis unquestionably reinforces the figure of the leader advocated by the thesis: the “New Human Engineering”. Gaspar do Amaral shares the diagnosis and demands that the Verticalidade of the system only operates fully if hierarchies abandon the mechanistic analogue role and take on the function of rigorous auditors of communication systems and algorithmic integration. The supreme decision-maker evolves into a network strategist, capable of reading cryptographic reports and adjusting the assumptions of autonomous loops.

20. Martin van Creveld — The Transformation of War

In this pivotal work, van Creveld foretold the inevitable decline of the purely state-based Clausewitzian universe of war (the trinitarian State). The author argued that the conflicts of the future would be motivated by cross-cutting ideologies, managed by technology corporations, warlords or decentralised networks, acting in scenarios where massive symmetric force becomes irrelevant or politically impracticable to apply effectively. Gaspar do Amaral’s thesis takes up van Creveld’s systemic conclusions to close its architectural paradigm. The field of operations is no longer a board defined by nations, but a holistic mesh of survival. Amaral postulates that in this post-Clausewitzian arena dictated by van Creveld, naval engineers, national cyberspace policies and mechanised brigades act interconnected to defend the “System of Systems”, uniting classic fencing with the thermodynamics of the new information domains.

21. Carl von Clausewitz — On War

The cornerstone of Western military thought. Clausewitz formulates war as the continuation of politics and, more importantly for this thesis, immortalises the concepts of “Friction” (the attrition that turns the simple into something incredibly complex in the reality of combat), audacity as a force-multiplying virtue, and the nebulous fog of war (fog of war). Gaspar do Amaral does not discard Clausewitz, but simulates his exact translation into the era of tactical communications. In the thesis of Verticalidade, classic Friction is rigorously measured by the engineer and translated as signal attenuation in the propagation medium, severe loss of data packets and algorithmic degradation (jitter) in the terminals. The fog of war is the latency of the OODA system. Amaral uses Clausewitz to remind us that, however hybrid or digital the matrix may be, victory always rests on the violent manipulation of that friction against the enemy.

22. Thomas Withington — Technical Analyses in Electronic Warfare and Tactical Radio

Thomas Withington represents a voice of extreme empirical authority in the analysis of air-defence systems, tactical radio and radar processing. His articles scrutinise the false security into which armed forces fall when using software-defined radios (SDR) or frequency-hopping methods (FHSS), proving the mechanical limits of emission in the face of the vast modern receivers and spectrum analysers (Electronic Warfare). In Amaral’s thesis, Withington’s technical essays constitute the insurmountable physical obstacle of the wireless topology. They mechanically justify the central thesis: true camouflage in the electromagnetic spectrum does not exist in operational broadband. To mitigate the Abismo do Rigor in saturated environments, Amaral enshrines Withington’s evidence, stating categorically that the survival of the mechanised force requires the shutting down of traditional radiated emissions, returning to the total silence ensured by the confined layer (optics and cables), supporting lethal resilience in close combat.

The Synthesis for Decision-Makers: The New Cyber-Physical Paradigm

To translate all this complexity of engineering, sensors and algorithms into a universal language that anyone can understand, we can summarise the transition from “What was” to “What is” through three simple and practical changes:

1. The Change in Time: From Reaction to Prediction

• What was (The Reactive): It was the era of “wait and then fix”. We waited for the machine to break down, for the electricity grid to go down, or for the illness to cause pain before, only then, sending a technician or a doctor to repair the damage.
• What is (The Predictive): It is the era of “putting out the spark before the fire”. We use technology (sensors and Artificial Intelligence) to detect the “invisible pain”. The system realises that the machine will fail tomorrow and corrects the problem today, without anyone even noticing that there was any danger.

2. The Change in Work: From Effort to Scale (The 1:N Ratio)

• What was (Manual Labour): A technician looked at a screen, a doctor saw a patient, a teacher taught a class. It was the “1 to 1” model. The limit of our success was the tiredness and the time of each human being.
• What is (Multiplication): The machine has taken over the dull, heavy and repetitive work of looking at the data 24 hours a day. The human specialist becomes a “conductor”. Instead of fixing one thing at a time, they use the computer to watch over and ensure the perfect tuning of hundreds of factories, patients or pupils at the same time.

3. The Change in Decision: From Intention to Rigour

• What was (The “Abismo do Rigor”): It was carrying out large projects — bridges, electricity grids, submarine cables — based on political budgets, opinions or guesswork, keeping our fingers crossed that physical reality would bear out the theory.
• What is (“Verticalidade”): It is intolerance of failure. Mathematics, simulation and data are required to prove that the infrastructure is bulletproof before the money is spent. The decision ceases to be a political promise and becomes a scientific certainty.

In a single summary sentence: Before, we used technology to help us fix what broke; today, we use the intelligence of data to guarantee mathematically that nothing breaks at all.

Methodological note

What this page is. A translation of the article the author published on LinkedIn on 18 May 2026; the full Portuguese version is on this site, and the discussion remains on LinkedIn, in Portuguese.

The author’s concepts. “Abismo do Rigor” (Abyss of Rigour), “Verticalidade” (Verticality) and “A Fundação da Verticalidade” (The Foundation of Verticality, the title of the author’s book) keep their Portuguese names throughout. The other terms coined in the article — Informational Vanguard, Kinetic Rearguard, Dynamic Hybrid Matrix, New Human Engineering and Engineering of Controlled Chaos — are translated, with the Portuguese name in brackets at the first occurrence.

Works cited. The titles of the works are kept as in the original (in English or French). Where the original gives a descriptive label written by the author rather than a title (for example, “Analyses of Industrial Attrition” for Michael Kofman, or “The OODA Loop” for John Boyd), that label is translated. The links to sources are those of the original; the LinkedIn tracking parameter was removed from the link to André Beaufre, which leads to the same page.

Changes of form, not of content. The original illustration is reproduced with its texts in Portuguese and a translated caption. In the Portuguese page the titles of the 22 entries of the bibliographic matrix are bold paragraphs, and in entries 9 to 22 the title and the text share a single paragraph; here every entry has its title as a heading followed by its text. The heading “The Synthesis for Decision-Makers” is set as a section title. Obvious slips of the Portuguese page (“peles teias de software” for “pelas teias de software”, “uma diálogo desigual”, “esta análise tese”) were corrected in the translation only. Numbers, dates and units are those of the original.

Gaspar do Amaral · Original in Portuguese of 18 May 2026, published on this site; translation issued on 27 October 2026 · Figures and tables © Aprecisa.com · AI-assisted