Actors and Patrons in the Yemen Conflict

A complex web of local factions, regional powers, and international actors

Conflict Overview

The Yemen conflict involves a complex mix of local warring factions, regional powers backing different sides, and influential international actors. The situation is fluid, with recent military actions in late 2025 shifting control in southern Yemen.

Main Yemeni Factions & Their Patrons

The Houthis (Ansar Allah)

Primary Patron: Iran

Support: Weapons, training, ideological support (since ~2009)

Control: Northern Yemen (Capital Sana'a and northwest)

Presidential Leadership Council (PLC)

Primary Patron: Saudi Arabia

Role: Internationally recognized government; formed in 2022 to unify anti-Houthi forces

Control: Fragmented territories, including Marib and Taiz

Southern Transitional Council (STC)

Primary Patron: United Arab Emirates (UAE)

Role: Separatist group aiming to restore an independent southern state

Control: Southern Yemen (including Aden and 8 governorates)

Al-Qaeda & Islamic State

Primary Patron: Largely Autonomous

Role: Terrorist groups exploiting the conflict

Control: Hinterlands and some coastal areas

Key Regional & International Actors

Saudi Arabia

Primary Role

Leads military coalition against Houthis since 2015; primary patron of the PLC

United Arab Emirates (UAE)

Primary Role

Key coalition partner; shifted to backing the STC and local militias

Iran

Primary Role

Primary backer of the Houthis, providing weapons, training, and ideological guidance

United States & United Kingdom

Primary Role

Provided support to the Saudi coalition; US has scaled back some support

United Nations

Primary Role

Brokers ceasefires and humanitarian efforts; passed key resolutions like the arms embargo

Key Points to Understand the Conflict's Nature

• Multilayered Conflict: The Yemen war is not a simple two-sided fight but involves multiple groups with shifting alliances.
• Temporary Alliances: Groups frequently unite based on a "common adversary" rather than shared goals, leading to unstable coalitions.
• Patron-Client Complexities: External patrons like Iran or the UAE provide support, but their Yemeni allies fiercely guard their autonomy.
• Internal Divisions: The anti-Houthi bloc (PLC and STC) are allies against the Houthis but have fought each other for control of the south.

Note: The situation in Yemen is highly fluid, with control of territories and alliances subject to change. The information above represents a snapshot of the main actors based on recent reporting up to early 2025. For the very latest developments, consult current news sources and official UN reports.

Sturm's Principle in Projective Geometry

1. Core Concept

Sturm's principle (named after Charles-François Sturm, 1803–1855) provides a method for solving geometric construction problems by using projective transformations to simplify configurations.

The fundamental idea: Many problems in Euclidean geometry become easier if we first transform the figure projectively so that some elements assume a more convenient special position (e.g., a conic becomes a circle, a line becomes the line at infinity), solve the simpler problem, and then reverse the transformation. This works because incidence, collinearity, tangency, and cross-ratio are preserved under projective transformations.

A specific formulation states: If a problem is expressed entirely in terms of points, lines, conics, incidences, and tangencies (without metric properties like distances or angles), then one may projectively transform the figure so that a given conic becomes a circle, or given lines become parallel or perpendicular, to simplify construction or proof.

2. Methodological Example

Consider proving: Given two triangles ABC and A'B'C' inscribed in the same conic, their sides intersect in six points that lie on a conic.

Transformation Approach

Project the given conic into a circle. In circle geometry, we can apply Pascal’s or Brianchon’s theorems more easily, then observe that the property "six points lie on a conic" is projective, so it holds in the original figure as well.

This transformation trick exemplifies Sturm’s principle in practice.

3. Step-by-Step Demonstration

Step 1 — Transform conic to circle

Apply a projective transformation sending conic \(K\) to a circle. Since the desired property is projective, proving it for the circle suffices for all conics.

Step 2 — Choose convenient projection

After making \(K\) a circle, apply another projective transformation to send specific points to infinity to create parallel lines, if helpful for the proof.

Step 3 — Solve special case

For instance, send line \(EF\) to the line at infinity, making corresponding sides parallel. Solve the simplified configuration using basic properties of parallelograms or rectangles inscribed in a conic.

Step 4 — Reverse transformation

Since the proven statement concerns only projective invariants, it remains true when transforming back to the original figure.

4. Formal Statement

One standard formulation:

If a construction problem or a theorem is projective (stated in terms of incidence and tangency, independent of metric properties), then it is sufficient to prove it in a specially chosen projective position (e.g., a conic as a circle, or a given quadrilateral as a parallelogram). This follows because any two non-degenerate conics are projectively equivalent, and any two quadrilaterals (with no three collinear vertices) are projectively equivalent.

5. Important Limitations

Caution: Sturm’s principle does not apply to metric properties such as distances, angles, or ratios of non-collinear segments. It preserves only projective properties. Many Euclidean geometry problems contain metric conditions, so projective distortion cannot be freely applied unless the property in question is invariant under projective transformations.

6. Summary of the Approach

Sturm’s principle is essentially the projective equivalence principle used strategically:

1. Identify that the problem’s conclusion is projective (depends only on incidence, tangency, cross-ratio).

2. Transform part of the figure to a more convenient position via a projective transformation.

3. Solve the simpler special case.

4. Conclude the general case by reversibility of projective maps.

// This principle is implemented conceptually rather than computationally // In computational geometry, one might represent it as: function applySturmPrinciple(problem) { const transformed = projectiveTransform(problem, 'specialPosition'); const solution = solveSimplified(transformed); return inverseProjectiveTransform(solution); }

Vedic Cosmology in Contrast to Mechanistic Science

These explanations address your questions about the internal mechanics of the Vedic cosmological model, particularly as analyzed by scholars like Richard L. Thompson. The model describes a geocentric, flat-disk universe (Bhu-mandala) that operates on specific principles distinct from modern astronomy.

The Multi-Layered Cosmos: Why the Moon is "Above" the Sun

In the Puranic planosphere model (e.g., from the Srimad Bhagavatam), the universe is structured as a vertical hierarchy of planes, or Lokas. "Above" refers to a higher plane in this spiritual and metaphysical hierarchy, not merely greater linear altitude.

Cosmic Level	Vedic Realm (Loka)	Key Characteristics
Upper Planes	Satyaloka, Tapoloka, etc.	Realms of sages, advanced beings, and liberation, far above the celestial realms.
Middle Celestial Plane	Svargaloka (Heavenly Planets)	Abode of Chandra (the moon deity) and other celestial beings. This is the plane higher than the sun.
Solar Plane	The Sun (Surya)	The pivotal plane where the sun's chariot orbits, regulating time, light, and seasons for the earthly plane below.
Earthly Plane	Bhu-mandala	The vast, central horizontal disk. Our known Earth (Bhu-gola) is described as one small part of this larger plane.
Subterranean Planes	Bila-svarga & Lower Lokas	Realms below the surface, such as Atala and Vitala, inhabited by asuras and nagas.

Key Explanation: Hierarchical Placement

The moon (Chandra) is described as being situated on a celestial plane (Svargaloka) that is metaphysically higher than the plane on which the sun's chariot travels. This placement relates to its nature, presiding deity, and function within the cosmic order, not solely to a measurable distance.

Mechanics of Sunlight on a Flat Earth (Bhu-mandala)

The model provides an integrated explanation for how a single sun illuminates a flat, expansive disk, avoiding the "flashlight" problem.

[Schematic Diagram: A top-down view of Bhu-mandala with a central Mount Meru, concentric rings of islands, and the circular orbital path of the sun around it.]

Conceptual diagram of the Sun's orbit around Mount Meru, illuminating half of Bhu-mandala at a time.

1. The Sun's Divine Function

The sun (Surya) is not considered a ball of gas but a divine luminary and planet (graha). Its primary function is to measure time and distribute light, heat, and seasonal influence across the Bhu-mandala.

2. Circular Orbit & Sphere of Influence

The sun's chariot orbits in a fixed circular path around the central axis, Mount Meru, on a plane parallel to the Earth-disk. It is described as having a localized sphere of radiant influence. As it circles, it illuminates the region of the disk directly facing it, creating day. Night falls where its light does not reach or is blocked.

3. Mount Meru as the Central Axis & Obstructor

Mount Meru, at the center of the disk, is described as being of immense height. It acts as a permanent, colossal gnomon that casts the shadow of night upon the regions on the opposite side of the disk from the sun's current position.

In Summary: Within its own premises, the Vedic planosphere model is self-consistent. The moon occupies a higher celestial stratum. Sunlight is not from a distant point source but from a localized, orbiting luminary whose defined sphere of illumination systematically traverses the flat, geographical complex of Bhu-mandala, with day and night governed by this orbital mechanics and the central mountain.

Explanation based on analysis of Puranic cosmography, including references from the Srimad Bhagavatam and scholarly works such as Richard L. Thompson's Vedic Cosmography and Astronomy.

This presentation aims to clarify the internal logic of the traditional model.

The Relationship Between M-theory and the Hubble Constant

Core Answer: No, M-theory does not have to prove the value of the Hubble Constant (H₀). Instead, precise measurements of H₀—particularly the unresolved tension between different methods—are used to test and constrain theories like M-theory.

The Role of the Hubble Constant

The Hubble Constant is the present-day expansion rate of the universe. It is a cornerstone observational parameter for testing cosmological models, not a value that a fundamental theory like M-theory must derive from first principles.

The current "Hubble tension"—a significant disagreement between high-precision measurements of H₀ from the early universe and the local universe—suggests there might be new physics beyond the standard cosmological model (ΛCDM).

How M-theory Interacts with Cosmology

M-theory, as a candidate for a "Theory of Everything," aims to unify quantum mechanics and general relativity. Its connection to cosmology involves several key aspects:

Providing a Theoretical Framework

It offers a framework (e.g., through string cosmology) to model the universe's earliest moments, such as inflation or the nature of dark energy.

Making Testable Predictions

Models inspired by string/M-theory can make specific predictions about the universe's composition and evolution, which in turn affect the inferred value of H₀.

Being Constrained by Empirical Data

The precise, conflicting measurements of H₀ act as a critical empirical test. If an M-theory model claims to resolve the Hubble tension (e.g., by proposing a new form of early dark energy or altering the number of relativistic species), it must produce an H₀ value consistent with all observations.

The Current Hubble Tension: A Critical Conflict

The following table contrasts the two primary measurement methods whose disagreement forms the core of the Hubble tension:

Aspect	Early Universe Measurement (Planck Satellite)	Local Universe Measurement (SH0ES Team)
Primary Method	Analysis of the Cosmic Microwave Background (CMB) within the ΛCDM model.	Direct cosmic distance ladder using Cepheid stars and Type Ia supernovae.
Value for H₀	Approximately 67.4 km/s/Mpc.	Approximately 73.0 km/s/Mpc.
Foundational Assumption	The standard model of cosmology (ΛCDM) is complete and correct from the Big Bang to today.	The calibration of nearby astronomical "standard candles" is accurate and can be extended across cosmic distances.
Statistical Significance of Discrepancy	Over 5σ — a very strong conflict indicating a likely need for new physics.

Conclusion

The Hubble Constant is a key observational benchmark, not a mathematical proof for M-theory. The ongoing Hubble tension serves as a powerful empirical clue that our current model of the universe may be incomplete. Therefore, M-theory and string cosmology are motivated to provide viable models that can explain or resolve this tension, thereby proving their relevance and predictive power for describing our actual universe.

The information presented here is based on the current state of cosmological research and theoretical physics.

The Concept of Kāfir (Disbeliever) in Islam

Core Definition and Etymology

The term kāfir (plural: kuffār) originates from the Arabic root K-F-R, which means "to cover" or "to conceal." In an Islamic context, it fundamentally refers to a person who covers or rejects the truth of God's oneness (Tawhid) and the message of Islam after it has been made clear to them. The common English translation is "disbeliever" or "unbeliever."

Primary Theological Classifications

Islamic scholars have historically distinguished between two main categories of non-believers, with significant legal and social implications:

1. Al-Mushrikūn (The Polytheists / Idolaters)

Those who associate partners with God (Shirk). This is considered the gravest and most unequivocal form of disbelief. Historically, this referred to the pre-Islamic Arab pagans.

2. Ahl al-Kitāb (The People of the Book)

Primarily Jews and Christians, who are believed to have received earlier, authentic but altered revelations. They are accorded a distinct, more lenient status within Islamic law (e.g., rules on marriage and food).

Major Types of Disbelief (Kufr al-Akbar)

Classical Islamic theology details several categories of major disbelief that are considered to place a person outside the fold of Islam. These are matters of intent and action, not merely identity.

Type (Arabic)	Meaning and Description
Kufr al-Juhūd (Denial & Rejection)	Rejecting the truth in both heart and tongue, despite knowing it internally.
Kufr al-Kibr (Arrogance & Pride)	Knowing and admitting the truth internally but refusing to submit to it outwardly due to pride, as Iblīs (Satan) did.
Kufr al-Nifāq (Hypocrisy)	Concealing disbelief internally while presenting a false appearance of faith outwardly.
Kufr al-I'rād (Turning Away)	Willfully ignoring the truth, refusing to learn about it, or acting upon it out of arrogance or neglect.
Kufr al-Shakk (Doubt)	Hesitating or being uncertain about the core truths of faith, lacking conviction.
Kufr al-Istihlāl (Making Lawful the Forbidden)	Deeming permissible something that is definitively and categorically prohibited by Islamic law, thereby challenging God's sole right to legislate.

Important Nuances and Modern Perspectives

Judgment is Reserved for God

A central principle in Islam is that ultimate judgment belongs only to God. True disbelief is a matter of internal intent, which only God can know. The Quran (2:62) suggests that sincere believers from other monotheistic faiths may also attain salvation.

The Highly Contentious Act of Takfīr

Takfīr is the act of declaring another professing Muslim a kāfir. This is a grave matter in Islamic law, with strict conditions to prevent its misuse. Historically, it has been exploited for political and sectarian conflict.

Contemporary Debates and Caution

There is significant modern debate about the use of the term. Many scholars and major Islamic organizations urge extreme caution, arguing it should not be used offensively or carelessly to label non-Muslims or other Muslims. For example, the world's largest independent Islamic organization, Nahdlatul Ulama in Indonesia, has called on Muslims to stop using the word kāfir for non-Muslims, describing it as "theologically violent."

Summary and Key Takeaway

The term kāfir is deeply nuanced. It is not a simple, blanket label for all non-Muslims but a theological concept with specific conditions. Its meaning varies between the Quranic text (where it can also mean "ingratitude" or a "farmer"), classical Islamic law (with its detailed categories), and modern discourse (where its application is heavily debated). Understanding this complexity is essential to avoid misinterpretation.

```

The Cosmological Role of Leptons

Leptons, including the stable electron and the elusive neutrino, are fundamental particles that play critical roles in shaping the universe, from the formation of atoms to the large-scale evolution of cosmic structures.

Foundation of Ordinary Matter

The electron is the most familiar lepton and a direct, stable constituent of atoms. Its properties, governed by fundamental laws like the Pauli Exclusion Principle, define atomic structure, chemical bonding, and the existence of all complex matter. This includes the biological molecules that are the building blocks for life in the universe.

Drivers of Stellar Processes

Leptons are essential agents in the life cycles of stars. Within stellar cores, vast numbers of neutrinos are produced through nuclear fusion, carrying away immense energy that influences stellar evolution. In the dramatic finale of massive stars, neutrinos are believed to be crucial in driving the shockwave of a core-collapse supernova, the explosion responsible for dispersing heavy elements throughout space. Furthermore, free electrons within stars scatter photons, creating a slow, random-walk process for energy transport. This explains why the sunlight we see today was generated in the Sun's core thousands to millions of years ago.

Shapers of Cosmic Evolution

Leptons left a definitive imprint on the early universe and continue to influence its structure. In the hot, dense early cosmos, free electrons scattered light relentlessly, rendering the universe opaque. A pivotal transition occurred roughly 379,000 years after the Big Bang.

Hot, Opaque Plasma
(Electrons scatter light)

→

Recombination & Photon Decoupling
(~379,000 years after Big Bang)

→

Transparent Universe & CMB Released
(The "afterglow" we observe)

As the universe cooled, electrons combined with nuclei to form neutral atoms in an event called Recombination. This "cleared the fog," allowing photons to travel freely and creating the Cosmic Microwave Background (CMB) radiation. The number of neutrino flavors also affected the expansion rate during Big Bang Nucleosynthesis, influencing the primordial abundance of light elements like hydrogen and helium. Finally, high-energy electrons and positrons are key components of cosmic rays, acting as messengers from extreme astrophysical environments.

Probes of Fundamental Physics

Leptons serve as unique tools for testing the fundamental laws of the cosmos. The discovery of neutrino oscillations—the phenomenon where neutrinos change from one flavor to another—provided definitive proof that these particles have a small, non-zero mass. This was a major discovery that solved the "solar neutrino problem" and is clear evidence of physics beyond the original Standard Model. The properties and behavior of leptons are integral to the Standard Model of particle physics and the ΛCDM model of cosmology, making them essential for testing and refining our understanding of the universe's origin and fate.

Synthesis: From Micro to Macro

Leptons demonstrate a profound connection between the smallest scales of particle physics and the largest scales of cosmology. The electron ensures the stability of atoms and ordinary matter, while neutrinos act as transformative agents in stellar explosions and relics from the universe's first second. Together, their interactions determined the transparency of the early cosmos and left an observable imprint in the CMB and elemental abundances. Ultimately, studying leptons allows us to probe the most fundamental laws governing the past, present, and future evolution of the entire universe.

```

Consolidated Summary: New Cosmic Structures and Cosmological Implications

The Discovery: A "Basin of Attraction" Beyond Laniakea

Research led by R. Brent Tully, published in Nature Astronomy, proposes a gravitational structure that places the Milky Way within a region up to ten times the volume of the Laniakea supercluster. This vast "basin of attraction" is anchored by the Shapley Supercluster and challenges existing models of the universe's large-scale architecture.

The methodology uses the "river and basin" analogy, mapping the peculiar velocities of over 56,000 galaxies to trace gravitational flow lines, revealing a deeper, dynamic web of interconnected matter.

Clarification of Terms: LDCM vs. ΛCDM

A pivotal clarification was made regarding the acronym in question:

LDCM (Landsat Data Continuity Mission): A NASA/USGS Earth-observation satellite (Landsat 8) launched to monitor our planet's surface. The discussed cosmic discovery has no impact on this mission.

ΛCDM (Lambda-Cold Dark Matter): The prevailing standard model of cosmology, which describes a universe with dark energy (Λ) and cold dark matter. This model is directly challenged by the new findings on the scale of cosmic structures.

Impact and Challenge to the ΛCDM Cosmological Model

The identification of a coherent gravitational structure on a scale exceeding one billion light-years creates a significant point of tension with the ΛCDM model.

The core tension lies in the ΛCDM prediction that matter, due to cosmic inflation, should be distributed fairly evenly on the largest scales. While it accounts for structures like clusters and superclusters, the existence of a coherent "basin" of this immense size and gravitational pull pushes at the theoretical upper limit of what the model typically predicts should form.

The central question for cosmology is whether this structure is a rare statistical anomaly within the ΛCDM framework or evidence that requires a refinement of the model, potentially related to our understanding of initial density fluctuations, dark matter, or the Cosmological Principle.

The Path Forward for Cosmology

This discovery does not invalidate ΛCDM but serves as a critical test. The next steps involve:

Confirmation with New Data: Upcoming projects like the Euclid space telescope and the Vera C. Rubin Observatory will provide vastly more precise data on galaxy positions and velocities to confirm and map these large-scale flows.

Advanced Simulations: Cosmologists will run sophisticated N-body simulations within the ΛCDM framework to determine the probability of forming such vast, coherent structures, testing the model's limits.

Potential for Refinement: The outcome may lead to a refinement of cosmological parameters or a deeper understanding of structure formation, ensuring the standard model evolves with our observational reach.