Equine Palmar Angle: 5 Warning Signs All Owners Must Know

To truly appreciate the nuances of equine well-being and prevent long-term issues, it’s essential to delve into the fundamental principles that govern a horse’s physical stability and comfort.

The Unseen Foundation: Decoding the Palmar Angle and Securing Your Horse’s Soundness

Every horse owner understands the critical importance of a sound horse – one free from pain or lameness that impacts their ability to move and perform. However, achieving and maintaining this soundness is often a complex endeavor, beginning deep within the hoof itself. This introductory section will illuminate a foundational, yet often overlooked, indicator of hoof balance and health: the equine palmar angle. Understanding this crucial measurement is the first step in a proactive approach to preventing common and debilitating lameness issues.

The Equine Palmar Angle: A Blueprint for Hoof Health

At the very core of your horse’s hoof is the coffin bone (P3), the lowest bone in the limb, encased within the hoof capsule. The equine palmar angle is a specific measurement that defines the orientation of this coffin bone relative to the ground surface. More precisely, it refers to the angle formed by the solar (bottom) surface of the coffin bone and the ground.

Why is this angle so critical? A correctly aligned palmar angle ensures optimal distribution of forces throughout the entire hoof structure and lower limb. It dictates how weight is transferred through the limb, influences the tension on vital soft tissue structures, and plays a direct role in the biomechanics of every stride. When the palmar angle is ideal, the hoof functions efficiently, absorbing shock and propelling the horse forward with minimal stress. When it deviates, the intricate balance is disrupted, setting the stage for significant problems.

The Silent Connection: Palmar Angle, P3, and Lameness Risk

There is a profound and direct link between the palmar angle of the coffin bone (P3) and the risk of lameness. An incorrect palmar angle, whether too high (positive) or too low/negative, can lead to chronic stress and strain on various structures within and surrounding the hoof.

• Low or Negative Palmar Angle: This occurs when the heel of the coffin bone is lower than its toe relative to the ground. This orientation significantly increases the load and tension on the Deep Digital Flexor Tendon (DDFT), especially as it passes over the navicular bone. Chronic excessive tension on the DDFT can lead to inflammation (tendinitis), fraying, and eventually tears. Simultaneously, the navicular bone and its associated bursa experience increased compression and stress, which is a common precursor to navicular syndrome – a debilitating condition causing chronic heel pain. Furthermore, a low palmar angle can lead to increased pressure on the caudal (back) part of the hoof, causing bruising and discomfort.
• High (Excessive Positive) Palmar Angle: While less common, an excessively high palmar angle can shift weight predominantly to the toe, potentially increasing stress on other structures like the laminae and contributing to issues like club foot over time.

In essence, the palmar angle is a biomechanical fulcrum; even slight deviations can dramatically alter the forces acting on the intricate structures of the lower limb, leading to pain and chronic lameness.

A United Front: The Farrier-Veterinarian Partnership

Managing hoof health to ensure correct palmar angle and overall soundness is a collaborative effort that absolutely requires the partnership of a skilled Farrier and an experienced Veterinarian. Each professional brings distinct, yet complementary, expertise to the table:

• The Veterinarian’s Role: The veterinarian offers a diagnostic and medical perspective. They can utilize advanced imaging techniques such as X-rays (radiographs) to accurately measure the palmar angle and assess the internal structures of the hoof, including the coffin bone, navicular bone, and the relationship of the DDFT. They diagnose underlying issues, provide medical treatments for inflammation or injury, and offer guidance on therapeutic shoeing strategies based on their clinical findings.
• The Farrier’s Role: The farrier is the artisan and technician responsible for the practical application of hoof care. They trim the hoof and apply shoes (or barefoot trimming techniques) to achieve and maintain the optimal palmar angle as guided by veterinary diagnostics and their own keen eye for hoof balance. Their skill directly influences load distribution, breakover, and the overall mechanics of the hoof, playing a crucial role in supporting the DDFT and navicular bone.

Effective communication and teamwork between your farrier and veterinarian are paramount. They should consult together, especially when a horse presents with lameness or requires corrective hoof balance adjustments, to ensure a cohesive and effective treatment plan.

Empowering Owners: Proactive Monitoring for Long-Term Soundness

For Horse Owners, an understanding of the palmar angle and its implications is not merely academic; it’s crucial for proactive monitoring and preventing long-term issues related to the Deep Digital Flexor Tendon (DDFT) and navicular bone. You are on the front lines, observing your horse daily.

Proactive monitoring involves:

• Regular Veterinary and Farrier Check-ups: Adhere to a consistent schedule for both, especially ensuring regular X-rays if recommended by your vet to monitor internal hoof structures and palmar angle changes.
• Observing Gait and Behavior: Pay close attention to any subtle changes in your horse’s movement, stride length, willingness to work, or general demeanor. Early signs of discomfort often manifest as slight lameness or reluctance to move.
• Familiarizing Yourself with Your Horse’s Hooves: Learn what a healthy hoof looks like and feels like. While you won’t be performing technical measurements, an awareness of hoof growth patterns and shape can be insightful.
• Understanding the Signs: Being aware of symptoms associated with DDFT strain or navicular syndrome (e.g., heel pain, pointing, stumbling, shortened stride) can prompt earlier intervention.

By understanding these foundational principles and engaging actively with your equine care team, Horse Owners can play a vital role in safeguarding their horse’s soundness for years to come.

As we begin to understand these foundational principles, it’s equally important to recognize the early indicators that something might be amiss, starting with the outward appearance of the hoof.

As we delve into the core elements of equine soundness, one of the most immediate and telling indicators of potential underlying issues can be found in the very architecture of your horse’s hooves.

The Hoof’s Urgent Message: Decoding Visible Warning Signs

The old adage, "no foot, no horse," holds profound truth, as the hoof acts as the primary interface between the horse and the ground, bearing immense weight and absorbing shock. Any deviation from ideal hoof shape and conformation can be a critical warning sign, signaling underlying stress and potential lameness. Recognizing these external indicators is paramount for proactive management and maintaining your horse’s long-term soundness. These visible cues are not merely cosmetic; they are often direct reflections of internal forces and pressures acting upon the delicate structures within.

Identifying a ‘Broken-Back’ Hoof-Pastern Axis

A fundamental principle of proper equine biomechanics is the harmonious alignment of the hoof and pastern. When observing your horse from the side, an ideal configuration presents a straight line extending from the coronary band down through the pastern and hoof wall. A ‘broken-back’ hoof-pastern axis is identified when the angle of the hoof wall is noticeably steeper than that of the pastern. This creates a visually ‘broken’ or kinked line, where the pastern appears to slope more gently than the hoof capsule it sits upon. This misalignment places abnormal stress on several crucial structures:

• Deep Digital Flexor Tendon (DDFT): The DDFT is placed under increased tension.
• Navicular Apparatus: The deep digital flexor tendon’s attachment and the surrounding structures of the navicular bone and bursa experience undue pressure.
• Pastern Joint: Abnormal loading can lead to strain and degenerative changes in the pastern joint itself.

This conformation fault often predisposes horses to issues ranging from soft tissue injuries to degenerative joint disease within the lower limb.

Recognizing a ‘Bull-Nosed’ Appearance

Another significant visual anomaly is the ‘bull-nosed’ appearance of the hoof. This term describes a condition where the front of the hoof wall exhibits a distinct convex or bulging shape, rather than the ideal straight or slightly dished profile. This bulging is typically most pronounced in the toe region. A bull-nosed hoof often indicates:

• Excessive Toe Length: The hoof wall is allowed to grow too long, causing the natural breakover point to be delayed.
• Chronic Laminitis or Founder: In some cases, a bull-nosed appearance can be a lingering sign of past or chronic laminitic episodes, where changes in the lamellar attachment alter the hoof wall’s growth pattern.
• Underlying Bony Remodeling: It can also be associated with bone remodeling of the distal phalanx (coffin bone) due to chronic stress.

This shape significantly impairs the horse’s natural breakover, forcing the limb to remain on the ground for too long, thus increasing the strain on tendons and ligaments further up the leg.

Observing Crushed, Underrun Heels

Perhaps one of the most common and detrimental conformational faults observed in the equine hoof is the presence of crushed, underrun heels. This condition is characterized by heels that migrate forward beneath the palmar (back) aspect of the hoof, failing to provide adequate support to the back of the hoof capsule and the structures within. Key indicators include:

• Heel Bulbs: The heel bulbs appear to be positioned significantly forward, often nearly under the hairline.
• Heel Angle: The angle of the heel wall is often much lower than the toe, appearing to ‘run under’ the foot.
• Frog Recess: The frog often appears recessed and unhealthy due to lack of ground contact.

Crushed, underrun heels are a classic manifestation of a low or negative palmar angle. The palmar angle refers to the angle of the distal phalanx (coffin bone) relative to the ground surface. A low or negative palmar angle means the back of the coffin bone is lower than the front, placing immense crushing forces on the sensitive structures in the back of the foot, including the digital cushion, navicular bursa, and deep digital flexor tendon. This dramatically reduces the hoof’s natural shock-absorbing capabilities and is a leading cause of caudal heel pain.

How These External Signs Suggest Internal Stress on the Distal Phalanx

Each of these visible changes—the broken-back axis, bull-nosed appearance, and especially crushed, underrun heels—serves as a critical diagnostic clue, pointing directly to internal stress and compromised biomechanics affecting the distal phalanx (coffin bone) and its surrounding soft tissues.

• Distal Phalanx Position: The distal phalanx is the primary skeletal structure within the hoof capsule. Its proper alignment and articulation with the other bones of the lower limb are crucial. Visible external deviations directly reflect abnormal forces acting on this bone. For instance, a low palmar angle, indicated by underrun heels, means the coffin bone is tilting backward, predisposing it and the soft tissues (ligaments, tendons, digital cushion) to compression and trauma.
• Soft Tissue Impingement: These conformational faults lead to the impingement or excessive stretching of vital soft tissues. The deep digital flexor tendon, for example, is excessively loaded in both broken-back axes and low palmar angles. The digital cushion, a critical shock absorber, becomes compressed and loses its elasticity with underrun heels.
• Inflammation and Degeneration: Over time, these chronic stresses lead to inflammation, micro-trauma, and ultimately, degenerative changes in bone, cartilage, and soft tissues, manifesting as conditions like navicular syndrome, sole bruising, and laminitis.

Recognizing these external warning signs enables early intervention through professional farriery and veterinary care, potentially preventing minor imbalances from escalating into debilitating lameness.

While visible hoof changes offer crucial insights, it is equally important to observe how these structural imbalances might subtly influence your horse’s movement and posture.

While visible changes in hoof shape and conformation provide crucial early warnings, sometimes the most telling signs of underlying discomfort are more subtly expressed through a horse’s movement.

More Than Meets the Eye: Decoding Subtle Shifts in Your Horse’s Stride and Stance

Beyond the visual assessment of the hoof itself, astute observers can often discern early indicators of pain or imbalance by carefully watching how a horse moves and stands. These subtle shifts in gait and posture are not always immediately obvious but can be highly informative for identifying developing hoof issues before they escalate into more severe problems. Recognizing these nuanced changes requires a keen eye and a thorough understanding of normal equine biomechanics.

A Shortened Stride: A Quiet Cry of Forelimb Discomfort

One of the primary indicators of discomfort in the forelimbs, particularly heel pain, is a noticeable shortening of the stride. A healthy horse typically exhibits a long, fluid stride. When a horse experiences pain in the heels of its front hooves, it will unconsciously attempt to minimize the time its painful heel spends on the ground. This often manifests as a reluctance to fully extend the limb forward, resulting in a ‘choppy’ or abbreviated stride. Pay close attention to the arc and reach of the forelimbs – any decrease in their natural extension warrants further investigation as it can be a clear sign of impending or existing hoof issues.

The ‘Toe-First’ Landing: A Strategy to Evade Heel Pressure

Under normal circumstances, a horse should land either flat-footed or slightly heel-first, distributing impact forces evenly across the hoof. However, when heel pain is present, horses often alter their landing pattern to avoid placing pressure on the sensitive caudal (rear) aspect of the hoof. This compensatory mechanism results in a ‘toe-first’ landing. The horse essentially attempts to protect the back of its hoof by striking the ground with the front of the hoof wall or sole first. This unnatural landing significantly changes the biomechanics of impact absorption, placing undue stress on other structures within the hoof and limb over time.

The Distinct ‘Sawhorse’ Stance: Alleviating Deep Digital Flexor Tendon Strain

A distinct postural change that signals significant heel pain or issues involving the deep digital flexor tendon (DDFT) is the ‘sawhorse’ stance. In this position, the horse stands with its front feet positioned further forward than normal, ‘camped out’ ahead of its body. This posture is an adaptive response designed to shift the horse’s weight backward, away from the painful heels and the DDFT which attaches to the coffin bone within the hoof. By moving its front limbs out, the horse reduces the load on the caudal aspect of the hoof and lessens the tension on the DDFT, effectively creating a more comfortable, albeit unnatural, resting position. This stance is a strong indicator that the horse is experiencing considerable discomfort.

Increased Stumbling and Tripping: A Consequence of Imbalance

While occasional stumbling can occur in any horse, an increase in frequency or a change in the nature of stumbling and tripping can be a critical warning sign. Poor hoof balance, whether due to overgrown hooves, improper trimming, or underlying pain that causes altered movement, can directly lead to an uneven or uncoordinated gait. If the hooves are not balanced correctly, the horse may struggle to place its feet securely, leading to a loss of equilibrium. Discomfort itself can also distract the horse or cause it to move guardedly, further contributing to a higher incidence of stumbling. This loss of sure-footedness is a clear signal that something is amiss with the horse’s foundational support system, particularly its hoof balance.

Recognizing these physical signs of discomfort is paramount, as they often precede more overt declarations of pain in a horse’s demeanor and willingness to perform.

While observing subtle changes in how a horse moves provides crucial insights, equally telling are the behavioral patterns that emerge when discomfort takes hold.

Beyond the Gait: Unmasking Discomfort Through Your Horse’s Actions

Beyond the purely physical manifestations of lameness, horses often communicate their pain and discomfort through a range of behavioral cues and resistances. These signals, though sometimes subtle, are critical warning signs that should prompt careful investigation. Recognizing these behaviors requires keen observation and an understanding of the horse’s natural responses to pain.

Pain Response During Hoof Examination

One of the most direct indicators of foot pain is an increased sensitivity to diagnostic tools, particularly hoof testers.

• Increased Sensitivity to Hoof Testers: Hoof testers are an invaluable tool for pinpointing areas of tenderness within the hoof. When a horse exhibits marked sensitivity, especially over the frog and heel region, it strongly suggests pain in the caudal (back) part of the foot. This area is common for issues like navicular syndrome, heel bruising, or abscesses. A sharp, consistent reaction to pressure in these specific zones, where a healthy hoof would show minimal response, is a clear red flag.

Resistance During Farriery Work

The routine process of farriery work, which involves lifting, trimming, and potentially shoeing the hooves, can become a significant source of distress for a horse experiencing foot pain.

• Fidgeting and Pulling Away: Horses that are typically cooperative during farriery may begin to resist or fidget excessively. This can manifest as repeatedly pulling the foot away from the farrier, shifting weight uncomfortably, or showing an unwillingness to bear weight on the opposite limb. Such resistance is not merely a behavioral quirk but often a direct avoidance of pain caused by prolonged weight-bearing or manipulation of the painful foot. A skilled farrier is often the first to notice these changes, as they are intimately familiar with the horse’s typical demeanor and tolerance.

Environmental Aversions

A horse’s preference for certain surfaces over others can also signal underlying foot issues.

• Reluctance on Hard or Uneven Surfaces: Horses with foot pain, particularly in the heel or sole, will often show a marked reluctance to move on hard, stony, or uneven ground. These surfaces increase concussion and pressure on the sensitive structures within the hoof, exacerbating discomfort. Conversely, they may actively seek out and prefer softer ground, which provides more cushioning and reduces impact. This change in preference can be a consistent indicator of chronic, low-grade foot pain that is aggravated by less forgiving terrain.

General Changes in Temperament

Chronic pain, even if not immediately obvious in gait, can significantly impact a horse’s overall well-being and disposition.

• Irritability and Sour Attitude: A horse experiencing persistent pain may exhibit general changes in temperament. This can range from subtle irritability, such as pinning ears or swishing the tail more frequently, to a more pronounced sour or withdrawn attitude. These behavioral shifts are often the horse’s way of communicating chronic discomfort and should not be dismissed as simply a change in personality. They are often linked to a reduced tolerance for handling, training, or social interaction, signaling that something is fundamentally amiss.

These behavioral indicators are often the first alert, paving the way for more definitive diagnostic tools like radiographs.

While resistance and subtle behavioral shifts offer critical early insights into equine discomfort, sometimes the underlying issue demands a definitive, internal confirmation that only advanced diagnostics can provide.

Peering Within: The Radiographic Revelation of the Equine Palmar Angle

When behavioral cues and movement abnormalities hint at deep-seated hoof issues, radiographs, commonly known as X-rays, emerge as the gold standard for precise diagnosis. These diagnostic images move beyond surface observation, offering an invaluable window into the intricate skeletal structures within the hoof capsule, particularly for accurately assessing the Equine Palmar Angle.

The Definitive Diagnostic Tool

Understanding the Equine Palmar Angle is paramount for evaluating hoof health and biomechanics. It refers to the angle formed by the solar (bottom) surface of the coffin bone (P3) relative to the ground. Radiographs are the definitive and most accurate tool for measurement of this crucial angle, providing objective data that is indispensable for effective veterinary and farriery interventions. Without this precise measurement, corrective strategies are largely based on estimation, carrying a higher risk of suboptimal outcomes.

Capturing the Hoof’s Inner Geometry

To accurately determine the palmar angle, Veterinary Care professionals employ a specific technique. They take a precisely positioned lateral (side) view of the hoof, ensuring the X-ray beam is perfectly aligned to capture the true profile of the coffin bone (P3)—the innermost bone within the hoof capsule. Specialized markers and careful positioning are used to establish a reliable ground reference line, allowing for the precise measurement of the angle formed by the solar margin of P3 against this ground plane. This detailed imaging provides the foundational data necessary for a comprehensive assessment.

Interpreting the Palmar Angle: Ideal Ranges and Critical Deviations

Once the radiographic images are captured and measured, the veterinary team can interpret the findings against established norms. Understanding these Ideal Ranges and their deviations is critical for anticipating and addressing potential soundness issues.

Palmar Angle Range	Classification	Implication for Soundness
3 to 5 degrees	Ideal	Promotes optimal hoof biomechanics, reduces strain on soft tissues, and supports long-term soundness.
0 to <3 degrees	Low Positive Angle	Suboptimal; increases risk of strain on the deep digital flexor tendon (DDFT) and heel pain.
0 to -5 degrees	Negative Angle	Critical; significantly elevates the risk for navicular syndrome, DDFT lesions, sole bruising, and chronic caudal heel pain.
>5 degrees	Excessively High Angle	Compromised; can lead to a toe-first landing, increased lamellar strain, and potential for coffin joint compression and arthritic changes.

Deviations from the ideal 3-5 degrees, whether a low positive angle, a negative angle, or an excessively high angle, signify biomechanical imbalances that can predispose the horse to specific lameness conditions. A negative palmar angle, for instance, places undue stress on the deep digital flexor tendon (DDFT) and the navicular apparatus, often leading to chronic pain and unsoundness. Conversely, an excessively high palmar angle can increase concussive forces on the toe region and contribute to laminitis or coffin joint issues.

Guiding Corrective Strategies

The objective data provided by these diagnostic images is invaluable for guiding corrective shoeing and trimming strategies. Farriers, working in conjunction with veterinarians, utilize the precise palmar angle measurements to formulate a targeted plan designed to restore the hoof’s natural balance and mitigate biomechanical stress. Adjustments may include specific shoe modifications, such as wedges or pads, or strategic trimming techniques aimed at altering the breakover, caudal support, or overall hoof-pastern axis. This evidence-based approach ensures that interventions are tailored to the horse’s individual needs, maximizing the potential for improved soundness and athletic longevity.

While diagnostic imaging offers irrefutable evidence, consistent, successful management also hinges on the response to ongoing treatment.

While radiographs provide invaluable diagnostic confirmation of internal hoof structures, a more apparent, daily warning sign often emerges in the consistent failure of standard farriery to maintain your horse’s hoof health.

When Standard Farriery Falls Short: Decoding Persistent Hoof Issues

One of the most undeniable indicators that something is fundamentally amiss with your horse’s hooves is their poor response to standard farriery practices. This isn’t about blaming the farrier; rather, it highlights an underlying issue that even the most skilled hoof care professional cannot resolve with conventional methods alone. When basic, routine care consistently fails to deliver sound, healthy hooves, it’s a significant red flag signaling a deeper biomechanical problem requiring urgent attention.

The Persistence of Hoof Problems Despite Regular Care

A healthy hoof, when properly maintained, should not be plagued by recurring issues. Therefore, observing that your horse continues to suffer from a range of persistent hoof problems, even with a regular and appropriate trimming schedule, is a critical warning sign. These issues often include:

• Quarter Cracks: Vertical splits in the hoof wall, particularly in the quarter region, that fail to grow out or reappear after repair. They indicate structural weakness or uneven load distribution.
• Heel Soreness: Chronic tenderness or pain in the caudal (rear) part of the hoof, often leading to a reluctance to land heel-first or a ‘toe-first’ landing pattern.
• Abscesses: Recurrent infections within the hoof capsule that cause acute lameness. Persistent abscesses can indicate underlying structural weaknesses, bruising from incorrect hoof mechanics, or foreign material penetration that isn’t properly addressed.

Such relentless problems suggest that the basic physiological balance and load-bearing mechanics of the hoof are incorrect. The consistent presence of these issues, despite diligent routine care, points to a deeper, unaddressed cause rather than superficial environmental factors or occasional trauma.

When Standard Horseshoes Prove Ineffective

Beyond the challenges of maintaining an unshod hoof, another strong indicator is when standard horseshoes do not seem to improve your horse’s comfort or way of going. Standard shoeing aims to protect the hoof, enhance traction, and provide basic support. If, after several shoeing cycles, your horse continues to exhibit:

• Unexplained or recurring lameness
• A reluctance to move freely or a noticeable change in gait
• A ‘tip-toe’ gait or chronic soreness that doesn’t resolve
• No significant improvement in overall comfort or performance

This suggests that the conventional protection and support offered by standard shoes are insufficient to counteract fundamental issues within the hoof’s structure and function. The very tools designed to aid comfort and performance are failing because the underlying architecture is not conducive to proper function, causing continued stress and discomfort.

The Necessity of Specialized or Corrective Shoeing: A Symptom, Not a Cure

Perhaps the most telling sign of an underlying issue, particularly concerning abnormal palmar angles, is the necessity of specialized or corrective shoeing. While corrective shoeing can be a valuable tool for managing specific conditions, relying on it simply to achieve basic comfort, rather than as a temporary measure towards rehabilitation, raises concerns. This often involves the use of:

• Wedge Pads: Used to elevate the heels, effectively increasing the palmar angle to alleviate strain on the deep digital flexor tendon (DDFT) and coffin joint, often indicating a persistently low palmar angle.
• Shoes with Enhanced Heel Support: Designs that extend support caudally or offer specific heel lift to redistribute weight and protect sore heel structures, again pointing to inadequate heel support or a low palmar angle.

When these interventions become a permanent fixture just to keep a horse comfortable during light work, it’s a major red flag. It indicates that the underlying biomechanics of the hoof are incorrect and cannot function properly without constant artificial compensation. This reliance on specialized shoes suggests that the natural hoof-pastern axis, load distribution, and break-over are severely compromised, demanding more than routine maintenance.

This consistent need for artificial support and the failure of standard approaches to resolve persistent issues are clear indicators that a deeper look is required. It necessitates comprehensive veterinary diagnostics, including detailed radiographic evaluation, to uncover the true extent of the biomechanical imbalance and formulate a targeted, effective long-term solution.

Recognizing these persistent struggles as a significant red flag underscores the necessity of a deeper veterinary investigation, paving the way for the essential team-based approach required to achieve true and lasting soundness.

In conclusion, ensuring your horse’s lasting soundness is a multifaceted commitment, anchored by a deep understanding of the Equine Palmar Angle. We’ve explored the five critical Warning Signs—from visible hoof changes and subtle gait shifts to behavioral cues, the definitive diagnostic power of radiographs, and the red flag of poor response to standard farriery—all designed to alert Horse Owners to potential issues. The journey to optimal hoof health is not a solo endeavor; it demands a collaborative, vigilant team: the observant owner, the skilled Farrier, and the diagnostic Veterinarian. By embracing this proactive approach, incorporating proper trimming, strategic corrective shoeing, and regular evaluation, you can effectively manage the Equine Palmar Angle, mitigating the risk of chronic lameness and safeguarding a long, comfortable, and productive life for your equine partner. Be proactive, be informed, and champion your horse’s soundness.