OPEN PUBLICATION | PUBLIC CATALOG RECORD
DOC AE-2026.III | EDITION 01
Authority&Architecture
Imprint of Record · Est. 2026
 Acquire
Book I The Authority Equation Three volumes Book II Autonomous Authority Three volumes Book III The Authority Discipline Four volumes
AE / III.II.I · THREE VOLUMES · 2026 · RECORD 01

The Authority Equation. Governing the Migration of Lethal
Decision-Making from Human to Machine

A three-volume work on the architecture, validation, and synthesis of human-machine authority under conditions of temporal compression, system confidence collapse, and escalation coupling.

Master Equation α = β · (C / τ) · e−γE
Examine the Trilogy The HMAA Framework
TIER 0 TIER 1 TIER 2 TIER 3 TIER 4 N S W E 000° 090° 180° 270° α = β · (C / τ) · e −γE FIG·01 HMAA · 5T
Title
The Authority Equation
Author
Burak Oktenli
Imprint
Authority & Architecture
Volumes
I · II · III
Edition
First · 2026
Catalog Status
Open Publication
3
Volumes · One Framework
VOL. I · II · III
8,415
Simulation Runs
REF·AE-II / RESULTS
101
Battle Reports Analyzed
Public sources · CENTCOM, JINSA, ISW
5-Tier
Authority Spectrum
FIG·01 / HMAA
§ 01 / THE TRILOGY DOC AE-2026.I/II/III

Three volumes.
One framework.

The architecture, the test, the synthesis. The Authority Equation is published in three sequential volumes, theoretical, empirical, and discursive. Each is independently rigorous; collectively they form a single argument about how lethal authority must be governed when it migrates from human to machine.

FILE I · FOUNDATIONS
VOL. I § Theoretical

Foundations The architecture, before the test.

What if the question of when a machine may decide for itself could be written as an equation? Volume I formalizes that equation, derives the Authority Migration Function, establishes the boundary conditions and exponential damping properties under which authority must transition, and introduces the Five-Tier Human-Machine Authority Spectrum that classifies every level of machine decision-making from human-held to machine-held.

Part I · The Master Equation
  • The Authority Equation α = β · (C / τ) · e−γE
  • Decision Compression and the Migration Boundary
  • Confidence (C) and the Trust Variable
  • Time-to-Kill (τ) and Temporal Compression
  • Erosion (E) and Exponential Damping
Part II · The Authority Migration Function
  • Boundary Conditions for Authority Transfer
  • Reversibility and Recovery Conditions
  • Damping Properties and Stability Regions
  • The Migration Threshold αcap
Part III · The Five-Tier Authority Spectrum
  • T0 · Human-Held Authority
  • T1 · Human-Approved Action
  • T2 · Human-Reviewed Authority
  • T3 · Human-Supervised Authority
  • T4 · Machine-Held Authority
ISBN 979-8-9958757-0-3 Print · Ebook Buy on Amazon →
FILE II · EMPIRICAL
VOL. II § Empirical

Governance & Results Where governance meets the kill chain.

What happens when the equation meets the real world? Volume II tests the framework against the empirical record: the Vertical Alignment Principle, the Five-Layer Stack of doctrine through architecture, Cross-Theatre Propagation, and the simulation methodology, evaluated event by event against the most complex multi-domain conflict of the algorithmic age. 8,415 simulation runs and 101 publicly reported battle accounts inform the findings.

Part I · The Governance Stack
  • The Vertical Alignment Principle
  • The Five-Layer Stack: Doctrine, Procedure, Protocol, Policy, Architecture
  • Stack Integrity Under Compression
  • Cross-Layer Failure Modes
Part II · Multi-Domain Validation
  • The Simulation Architecture
  • Single-Theatre Validation Cases
  • Cross-Theatre Propagation
  • Stack Failure Modes Observed
Part III · Empirical Results
  • 8,415 Simulation Runs: Method and Findings
  • 101 Operational Battle Reports (CENTCOM, JINSA, ISW)
  • Cross-Spectrum Findings Across the Five Tiers
  • Authority Migration Under Sustained Stress
ISBN 979-8-9958757-2-7 Print · Ebook Buy on Amazon →
FILE III · SYNTHESIS
VOL. III § Synthesis

Discussion & Synthesis The framework, after the test.

What does the framework become after it survives the test? The Human-Machine Authority Architecture emerges from validation transformed: an adaptive meta-architecture that redefines authority migration under temporal compression, confidence collapse, and escalation coupling far beyond the cases the framework was originally written to address. Volume III reconstructs the framework, names the open problems, and points to the operational continuation in Autonomous Authority.

Part I · What the Framework Survived
  • The Test as Designed
  • What Failed and What Held
  • Edge Cases and the Boundary Question
Part II · What the Framework Revealed
  • Temporal Compression Beyond Forecast
  • Confidence Collapse as a System Property
  • Escalation Coupling Across Domains
  • New Variables Required by the Test
Part III · The Framework, Reconstructed
  • HMAA as Adaptive Meta-Architecture
  • Authority Migration Generalized
  • Open Problems and Research Frontier
  • Toward the Operational Continuation
ISBN 979-8-9958757-4-1 Print · Ebook Buy on Amazon →
§ 02 / THE FRAMEWORK REF HMAA-001

An equation that makes lethal autonomy governable.

The Human-Machine Authority Architecture parameterizes the migration of lethal authority through three core variables and a governance ceiling anchored in international humanitarian law. The framework defines three variables, one equation, and five tiers of authority.

Master Equation · HMAA
α = β · (C / τ) · e−γE
Authority Migration Function
REF · AE-VOL-I § 3.2
τ
Temporal Compression
The collapse of decision time toward zero. As τ decreases, machine authority α rises. The kill chain compels migration from the human node when biological reaction time exceeds engagement windows.
C
System Confidence
Measured reliability of the autonomous decision stack. Authority scales linearly with C: as confidence falls, authority must regress to the human tier. Confidence collapse is itself a governance event.
E
Escalation Coupling
The damping coefficient e−γE exponentially restricts machine authority as engagements couple to strategic escalation. The higher the coupling, the closer authority returns to human command.
αcap
Governance Ceiling
The legally-anchored upper bound on machine authority, derived from international humanitarian law. The ceiling is enforced even when β·(C/τ)·e−γE would otherwise permit higher migration.

The Five-Tier Authority Spectrum.

Vertical Alignment Principle
TIER 0α ≈ 0
Human-Operated
Full human control. Machine acts only as a sensor or actuator extension. Decision authority rests entirely with the human operator.
TIER 1α < .25
Human-Decided
Machine recommends, human decides. Authority remains with the human; the machine optimizes presentation and reduces cognitive load.
TIER 2α ≈ .50
Human-Supervised
Machine acts within rule envelopes. Human supervises and may intervene. Authority is shared; reversion to human is preserved.
TIER 3α > .75
Machine-Authorized
Machine executes within pre-authorized rules of engagement. Human is on-the-loop. Reversion is delayed; oversight is post-hoc.
TIER 4α → αcap
Machine-Autonomous
Machine acts under engagement compulsion. Authority is at the governance ceiling. Human reversion is structural, not interactional.
§ 03 / VALIDATION CASE AE-II / RESULTS

The framework survived the test.
What it revealed transformed it.

Volume II tests the Human-Machine Authority Architecture against Operation Epic Fury, the most complex multi-domain conflict of the algorithmic age, across four conflict archetypes simultaneously.

CASE FILE · AE-VOL-II PRIMARY-SOURCED

Operation Epic Fury.

Eight thousand four hundred and fifteen simulation runs. One hundred and one operational battle reports. Primary-source documentation walked event by event against the master equation and the five-tier spectrum.

The framework survived the test, but only after extending from three core variables to a family of new governance concepts that Volume III's discussion makes explicit. The HMAA emerges as an adaptive meta-architecture, not merely a governance scheme.

Sources: CENTCOM · JINSA · ISW
Conflict Archetypes · Tested Simultaneously
01
Counterterrorism
Discrete-target authority migration under positive identification constraints.
02
Gray-Zone Operations
Sub-threshold engagement under attribution ambiguity and escalation coupling.
03
Asymmetric Conflict
Defensive authority compression against missile and drone arsenals at saturation.
04
High-End Engagement
Peer-conflict envelopes including autonomous swarm warfare and contested kill chains.
§ 04 / THE AUTHOR FILE AE-PR/01

Burak Oktenli.

Independent autonomous systems governance researcher. Architect of the Human-Machine Authority Architecture and the AUTHREX research program comprising seven governance architectures across defense, automotive, maritime, and critical infrastructure domains.

Burak Oktenli is an independent researcher working at the intersection of autonomous systems engineering, decision theory, and military doctrine. The Authority Equation is the first three-volume work in the catalog, followed by Autonomous Authority and The Authority Discipline. The 2026 catalog represents work undertaken from 2024 forward, brought to publication concurrently as a single coherent argument across ten volumes.

The work formalizes the conditions under which lethal decision authority must transition between human and machine, and the governance machinery required to keep that transition lawful, auditable, and reversible.

The AUTHREX program comprises seven governance architectures: SATA, HMAA, CARA, MAIVA, FLAME, ADARA, and ERAM. Each addresses a distinct failure mode in autonomous systems governance, including authority migration, integrity verification, deception resistance, latency-coupled escalation, and adversarial deception under temporal compression.

“The framework survived the test. What it revealed transformed the framework itself.”
Volume III · Discussion & Synthesis

The research is validated across six cross-domain prototype platforms spanning defense, automotive, maritime, and critical infrastructure. The body of work is published across twenty-four open-access deposits on Zenodo and SSRN, supported by four U.S. provisional patents and verifiable through ORCID 0009-0001-8573-1667.

Authority
& Architecture
Imprint of Record · Established 2026
§ 05 / THE IMPRINT

Authority & Architecture is the publishing imprint dedicated to the formal governance of autonomous systems: the books, monographs, and technical records that define how lethal authority is parameterized, migrated, and bounded.

Our publications target the readership that operates at the intersection of policy and engineering: defense planners, doctrine writers, AI governance researchers, acquisitions program offices, and the legal infrastructure that bounds them. Our standard is institutional. The rigor of a defense research center, the clarity of a technical manual.

All titles distributed via the IngramSpark global network. Print and ebook formats. ISBNs registered through Bowker.

§ 06 / ACQUIRE

The trilogy.
Now available.

The Authority Equation is published in three volumes through Authority & Architecture, distributed via Amazon and IngramSpark to global trade and institutional channels. All three volumes are available now in print and ebook formats. Review copies are available to qualified academic, defense, and policy reviewers writing for publication.

Trade · Vol I Vol I on Amazon →

Foundations. Print and ebook on Amazon, available globally.

 Trade · Vol II Vol II on Amazon →

Empirical Governance & Results. Print and ebook on Amazon, available globally.

 Trade · Vol III Vol III on Amazon →

Discussion & Synthesis. Print and ebook on Amazon, available globally.

 Academic · Press · Policy Request review copy →

Review copies for qualified academic, defense, and policy reviewers writing for publication.

 Library · Institution Library & institutional order →

Library acquisitions, institutional standing orders, course adoption, and bulk-purchase inquiries.

 Catalog · Citation View catalog & citation record →

Full verification record: ISBNs, DOIs, patent filings, prototype platforms, third-party citations.