LEAN MANUFACTURING, HUMAN RESOURCE MANAGEMENT AND WORKER HEALTH: ARE THERE SMART BUNDLES OF PRACTICES ALONG THE ADOPTION PROCESS? LEAN MANUFACTURING, MANAGEMENT DES RESSOURCES HUMAINES ET SANTE AU TRAVAIL : QUELLES COMBINAISONS DE PRATIQUES AU COURS DU PROCESSUS D'ADOPTION?

Keywords: Pratiques lean, santé au travail, pratiques de management des ressources humaines, combinaisons de pratiques, processus d'adoption Lean practices, Worker health, Human resource management practices, Bundles of practices, Adoption process

Les effets du lean manufacturing sur la santé au travail restent peu étudiés. Si des travaux récents montrent le rôle modérateur des pratiques de management des ressources humaines (MRH) sur cette relation, ils se focalisent le plus souvent sur quelques pratiques spécifiques et n'appréhendent pas leurs effets aux différentes étapes du processus d'adoption. En considérant le lean comme une innovation managériale, l'objectif de cet article est d'explorer la relation entre les pratiques lean, MRH et la santé au travail en prenant en compte explicitement la maturité lean de l'entreprise (i.e. intensité d'usage des pratiques et stade d'adoption). Les résultats, basés sur trois études de cas d'entreprises industrielles françaises, montrent que les effets du lean sur la santé au travail sont à évaluer à la lumière de combinaisons de pratiques lean et MRH qui diffèrent selon la phase du processus d'adoption.

INTRODUCTION

Lean management, whose foundation is the Toyota Production System is one of the most important management innovation (MI) of the twentieth century [START_REF] Birkinshaw | Management innovation[END_REF]. It has been positively linked to multiple dimensions of economic and operational performance (e.g. productivity, cost, quality and time) in the operations and supply chain management literature [START_REF] Jasti | [END_REF][START_REF] Shah | !!! INVALID CITATION !!! (Guerrero and Barraud-Didier[END_REF][START_REF] Souza | Lean-integrated management system: A model for sustainability improvement[END_REF]. However, its effects on employee health at work 1 (or similarly worker health) are less explored and remain contradictory [START_REF] Bouville | The effects of lean organizational practices on employees' attitudes and workers' health: evidence from France[END_REF][START_REF] Erdil | Embedding sustainability in lean six sigma efforts[END_REF]. These contradictory results may be due to the conception of lean adoption which is too often restricted to a static perspective, that does not take into account the different phases of the lean adoption and tends to exclude human resources management (HRM) practices from investigation [START_REF] Bouville | The effects of lean organizational practices on employees' attitudes and workers' health: evidence from France[END_REF][START_REF] Chanegrih | The Effect of Internal and External Lean Practices on Performance: A Firm-Centered Approach. El efecto del Lean interno y externo sobre el desempeño: un enfoque orientado sobre las empresas[END_REF][START_REF] Cua | Relationships between implementation of TQM, JIT, and TPM and manufacturing performance[END_REF][START_REF] Longoni | When does lean hurt? -an exploration of lean practices and worker health and safety outcomes[END_REF]. Indeed, recent works in innovation management and human resource management highlight that the integration of specific HRM practices can significantly moderate the effects of lean on health at work [START_REF] Bertrand | Voyage en pays de lean management[END_REF][START_REF] Longoni | When does lean hurt? -an exploration of lean practices and worker health and safety outcomes[END_REF][START_REF] Stimec | Le Lean Management est-il responsable?[END_REF]. These studies provide some critical insight into the relation between lean and worker outcomes. However, exploring how lean and HRM practices are adopted remains a critical issue [START_REF] Longoni | When does lean hurt? -an exploration of lean practices and worker health and safety outcomes[END_REF] since the combined use of HRM practices might not be always beneficial for employee [START_REF] Ogbonnaya | Integrated and isolated impact of high-performance work practices on employee health and well-being: A comparative study[END_REF]. The current study addresses these limitations in two ways. First, it examines a full list of lean and HRM practices in line with research that shows that considering bundles of practices can provide a more accurate understanding of lean effects [START_REF] Bowen | UNDERSTANDING HRM-FIRM PERFORMANCE LINKAGES: THE ROLE OF THE "STRENGTH" OF THE HRM SYSTEM[END_REF][START_REF] Macduffie | Human resource bundles and manufacturing performance: Organization logic and flexible production systems in the world auto industry[END_REF][START_REF] Milgrom | Complementarities and fit strategy, structure and organizational change in manufacturing[END_REF][START_REF] Ogbonnaya | Integrated and isolated impact of high-performance work practices on employee health and well-being: A comparative study[END_REF]. Second, it proposes a processual approach considering that the different stages of lean adoption can be critical because various factors may differ according to the stage [START_REF] Damanpour | Phases of the Adoption of Innovation in Organizations: Effects of Environment, Organization and Top Managers[END_REF]. To the best of our knowledge, no extant research investigates the relationship between lean and health at work integrating a full list of lean and HRM practices in various stages of the adoption process. The current study addresses this research gap pertaining to the complex relationship between lean maturity (in terms of practices and adoption phases), HRM practices and employee health at work. Empirically, this research is based on a multi-actor qualitative methodology through three case studies of French industrial companies that have adopted lean using the same regional lean program. A stabilized 2-D lean maturity matrix enables precise identification of the lean practices each firm has adopted [START_REF] Shah | !!! INVALID CITATION !!! (Guerrero and Barraud-Didier[END_REF] as well as their stage of adoption [START_REF] Damanpour | Phases of the Adoption of Innovation in Organizations: Effects of Environment, Organization and Top Managers[END_REF]. Moreover, the comparison uses a well-accepted list of HRM practices through high involvement practices (HIPs) (Guerrero & Barraud-Didier, 2004, 1 We focus on the concept of employee health at work or worker health [START_REF] Bäckström | Is there a relationship between Lean Leaders and healthy coworkers? Quality Innovation Prosperity[END_REF], 2016;[START_REF] Bäckström | Change of the quality management culture through health-promotion activities?[END_REF][START_REF] Bouville | The effects of lean organizational practices on employees' attitudes and workers' health: evidence from France[END_REF][START_REF] Longoni | When does lean hurt? -an exploration of lean practices and worker health and safety outcomes[END_REF]) that is commonly used in the literature suggesting that the relationship between lean and worker outcomes (job satisfaction, health at work, employees' intention to stay) is related to the manner in which lean is implemented [START_REF] Bertrand | Voyage en pays de lean management[END_REF][START_REF] Bouville | The effects of lean organizational practices on employees' attitudes and workers' health: evidence from France[END_REF][START_REF] Longoni | When does lean hurt? -an exploration of lean practices and worker health and safety outcomes[END_REF]. This conception of employee health at work is in line with the World Health Organization's definition (1946, p100) as "a state of complete physical, mental and social well-being and not merely the absence of disease or infirmity." This conception has the advantage of addressing health at work in both its positive and negative connotations. [START_REF] Lawler | High involvement management: San Francisco[END_REF]. Finally, objective measures of worker health control for potential biases inherent to respondents' subjective scores. [START_REF] Bäckström | Is there a relationship between Lean Leaders and healthy coworkers? Quality Innovation Prosperity[END_REF][START_REF] Pasmore | Designing effective organizations: The sociotechnical systems perspective[END_REF] Results confirm the moderating role of HRM practices on the relationship between lean and employee health at work. They also show that the effect of lean practices on health depends not on the intensity of lean and HRM practices firms adopt but rather on the combination thereof. Interestingly, the bundles of practices differ according to the stage of lean adoption. In the early stages of the adoption process, a purely theoretical and technical approach of lean still prevails with negative consequences for worker health. After this theoretical stage, companies are able to make adaptations [START_REF] Ansari | How are Practices Made to Vary? Managing Practice Adaptation in a Multinational Corporation[END_REF] using HRM practices in conjunction with lean practices. These adaptations are rather made during the advanced stages of the adoption process (i.e implementation and the routinization phases). They lead to an integrated system, which is more respectful of worker health. Overall, this research advances literature with two points. First, using a processual and multidimensional approach of lean, it provides a better understanding of the effects of lean practices on worker health throughout the adoption process. Second, it contributes to the literature on MI by considering the link between this specific type of innovation and an understudied dimension of firm performance, namely, social performance.

LITERATURE REVIEW

Lean is a noteworthy managerial innovation (MI) [START_REF] Birkinshaw | Management innovation[END_REF], OECD, 2005) whose foundation is the Toyota Production System [START_REF] Shah | !!! INVALID CITATION !!! (Guerrero and Barraud-Didier[END_REF]. [START_REF] Mol | The sources of management innovation: When firms introduce new management practices[END_REF] define MI as the adoption of management practices, process, structures or techniques new to the firm that are intended to further organisational goals. This innovation is composed of three building blocks, called the 3Ps [START_REF] Mamman | From management innovation to management practice[END_REF]: philosophy, principles and practices/techniques. It is generally defined from a philosophical perspective, related to guiding principles and overarching goals [START_REF] Womack | Lean Thinking: Banish Waste And Create Wealth In Your Corporation[END_REF], or from a practical perspective, describing a set of management practices, tools or techniques that can be observed directly [START_REF] Shah | !!! INVALID CITATION !!! (Guerrero and Barraud-Didier[END_REF]. The philosophy of lean focuses on avoiding cardinal waste, continuous improvement processes and respecting customers, employees and suppliers. Thus, waste elimination, continuous improvement and customer focus constitute its guiding principles [START_REF] Shah | !!! INVALID CITATION !!! (Guerrero and Barraud-Didier[END_REF]. Although no unified definition of lean is accepted, some authors [START_REF] Cua | Relationships between implementation of TQM, JIT, and TPM and manufacturing performance[END_REF][START_REF] Jasti | [END_REF][START_REF] Pettersen | Defining lean production: some conceptual and practical issues[END_REF][START_REF] Shah | !!! INVALID CITATION !!! (Guerrero and Barraud-Didier[END_REF][START_REF] Shah | !!! INVALID CITATION !!! (Guerrero and Barraud-Didier[END_REF] have compiled a comprehensive list of lean practices. [START_REF] Cua | Relationships between implementation of TQM, JIT, and TPM and manufacturing performance[END_REF] identify 29 practices and propose to cluster them in four bundles: total quality management (TQM), just in time (JIT), total productive maintenance (TPM), common practices linked to leadership and strategic management practices. Table 1 summarizes the 3Ps of lean.

Identifying lean practices that organisations already use is an effective initial step to assess the level of integration of the lean approach in organisations. Some authors go further by evaluating the level of maturity regarding actual use of lean practices. For each practice, [START_REF] Lyonnet | Lean manufacturing in the screw cutting sector : assessment of maturity level[END_REF] propose evaluating its intensity of use in the organisation using the NEMSE method: the practice is scored as Non-existent or Existent, implemented with a method likely to be generalized (Method), handled methodically, effectively and systematically (Systematic), or its application is efficient and should be communicated (Exemplary). Beyond the number of practices and their intensity of use, the literature on MI also suggests retaining its adoption phase to evaluate the level of MI maturity. The process of MI adoption has been divided into a variety of phases that can be grouped into three more general phases: (1) Decision, which involves becoming aware of a problem, searching for existing innovation, seizing and evaluating opportunities, benefits and suitability, choosing the best ones and allocating the necessary resources; (2) Implementation, which consists of activities, events and tactics that pertain to the internal actors' acceptance of MI, being skilful and committed in its use and adapting it; (3) until it becomes an organisational routine (Routinization) [START_REF] Damanpour | Phases of the Adoption of Innovation in Organizations: Effects of Environment, Organization and Top Managers[END_REF]. The MI adoption is thus conceptualized as a rational and linear process. However, some authors propose to nuance this rational view incorporating the possibility of recursions, intertwined and repeated cycles throughout this process [START_REF] Zbaracki | The Rhetoric and Reality of Total Quality Management[END_REF]. Here, we take this approach and consider that lean maturity can be evaluated along its intensity of use as well as its phases of adoption.

Lean and worker health

Findings are still contradictory regarding the effects of lean on workers [START_REF] Bruère | Les liens entre le système de production lean manufacturing et la santé au travail : une recension de la littérature[END_REF][START_REF] Longoni | When does lean hurt? -an exploration of lean practices and worker health and safety outcomes[END_REF]. A considerable body of research addresses the negative effects. Some studies underscore its impact on work-related musculoskeletal disorders [START_REF] Brännmark | Lean production and work-related musculoskeletal disorders: overviews of international and Swedish studies[END_REF][START_REF] Landsbergis | The impact of lean production and related new systems of work organization on worker health[END_REF][START_REF] Treville | Could lean production job design be intrinsically motivating? Contextual, configurational, and levels-of-analysis issues[END_REF]. Lean is also linked with increased injuries and job depression [START_REF] Conti | The effects of lean production on l worker job stress[END_REF], pain, discomfort [START_REF] Saurin | The impacts of lean production on working conditions: A case study of a harvester assembly line in Brazil[END_REF], high blood pressure, hypertension, cardiovascular disease, psychological strain and distress [START_REF] Sprigg | Call Centers as Lean Service Environments: Job-Related Strain and the Mediating Role of Work Design[END_REF]. Other authors examine the effects of lean on health at work through job satisfaction, showing a significant association with psychosomatic health complaints, stress-related ill-health symptoms and depression. These negative effects result from the continuous need to develop new capabilities and to improve productivity [START_REF] Askenazy | Innovative Workplace Practices and Occupational Injuries and Illnesses in the United States[END_REF][START_REF] Brenner | Flexible" Work Practices and Occupational Safety and Health: Exploring the Relationship Between Cumulative Trauma Disorders and Workplace Transformation[END_REF]. Reducing time cycles increases work intensity, repetitive movements, worker effort and work-related stress [START_REF] Kaminski | Unintended consequences: Organizational practices and their impact on workplace safety and productivity[END_REF][START_REF] Landsbergis | The impact of lean production and related new systems of work organization on worker health[END_REF]. Furthermore, the combination of increased task variation and lack of competence increases physical stress, risk for disorders and difficulties in filling the production goals [START_REF] Christmansson | Task design, psycho-social work climate and upper extremity pain disorders -Effects of an organisational redesign on manual repetitive assembly jobs[END_REF]. These ill health complaints also pertain to white-collar work, traditionally considered 'safe' jobs [START_REF] Carter | Stressed out of my box': employee experience of lean working and occupational ill-health in clerical work in the UK public sector[END_REF]. By contrast, some studies have shown some positive effects. Well-being outcomes and beneficial effects of lean include job satisfaction, team working, collaboration and employee involvement, opportunity to develop multiple skills with job rotation, greater autonomy of responsibility, innovation, intrinsic motivation, organisational citizenship, promotion of ergonomic and secure workplace design [START_REF] Brenner | Flexible" Work Practices and Occupational Safety and Health: Exploring the Relationship Between Cumulative Trauma Disorders and Workplace Transformation[END_REF][START_REF] Conti | The effects of lean production on l worker job stress[END_REF][START_REF] Hasle | Lean and the working environment: a review of the literature[END_REF][START_REF] Kaminski | Unintended consequences: Organizational practices and their impact on workplace safety and productivity[END_REF][START_REF] Perez Toralla | Participatory design in lean production: which contribution from employees? for what end?[END_REF][START_REF] Seppälä | How do employees perceive their organization and job when companies adopt principles of lean production?[END_REF][START_REF] Souza | Lean-integrated management system: A model for sustainability improvement[END_REF][START_REF] Womack | Lean job design and musculoskeletal disorder risk: A two plant comparison[END_REF]. According to [START_REF] Longoni | When does lean hurt? -an exploration of lean practices and worker health and safety outcomes[END_REF], the adoption of lean practices has a positive effect on operational and health performance. [START_REF] Jackson | Lean production teams and health in garment manufacture[END_REF] and [START_REF] Seppälä | How do employees perceive their organization and job when companies adopt principles of lean production?[END_REF] show increased breadth of employees' role, cognitive demands, better skill utilization and relations that are more social.

Still other studies show both negative and positive effects [START_REF] Conti | The effects of lean production on l worker job stress[END_REF][START_REF] Jackson | Lean production teams and health in garment manufacture[END_REF]. [START_REF] Conti | The effects of lean production on l worker job stress[END_REF] show that lean practices increase work intensity, resulting in a negative effect for employees, but those that increase employees' influence and support have a positive effect. [START_REF] Jackson | Lean production teams and health in garment manufacture[END_REF] also identify both effects in terms of autonomy, physical demands and social climate. Using a French national database, [START_REF] Bouville | The effects of lean organizational practices on employees' attitudes and workers' health: evidence from France[END_REF] show that some lean practices (e.g., delegation of responsibilities, problem-solving demand, standardization, job rotation) have negative consequences on job satisfaction, employees' intention to stay and health at work, while others (quality management) are positively linked to these social outcomes. The literature gives three main explanations for these inconsistent findings. First, lean conceptualizations vary among studies [START_REF] Hasle | Lean and the working environment: a review of the literature[END_REF][START_REF] Parker | Longitudinal Effects of Lean Production on Employee Outcomes and the Mediating Role of Work Characteristics[END_REF]. Although consensus on practices associated to lean has emerged, studies rarely take into account a full menu of lean practices or the level of lean maturity [START_REF] Saurin | The impacts of lean production on working conditions: A case study of a harvester assembly line in Brazil[END_REF]. Second, research results are unstable due to methodological inadequacies, which do not control for potential moderators (e.g., organisation's context, culture, management choices, variation in operation of lean systems) [START_REF] Conti | The effects of lean production on l worker job stress[END_REF][START_REF] Parker | Longitudinal Effects of Lean Production on Employee Outcomes and the Mediating Role of Work Characteristics[END_REF][START_REF] Saurin | The impacts of lean production on working conditions: A case study of a harvester assembly line in Brazil[END_REF]. Third, in some cases, ideological bias has been detected [START_REF] Schouteten | Lean Production Assessed by Karasek's Job Demand-Job Control Model[END_REF]. More recently, to understand the lean effects on worker health, some studies have explored the role of HRM practices as significant moderators [START_REF] Longoni | When does lean hurt? -an exploration of lean practices and worker health and safety outcomes[END_REF]. Following this strand of literature, this study embraces the idea that although lean is inherently stressful and worker well-being deterministic; its effects can be balanced with the recognition that HRM practices could play a crucial role.

The role of HRM practices on the relationship between lean and worker health [START_REF] Conti | The effects of lean production on l worker job stress[END_REF] show that the relationship between lean and worker job stress is not linear, depending on management decisions in designing and operating lean systems. In this vein, other studies have examined the moderating role of several HRM practices, such as spaces for discussion [START_REF] Bertrand | Voyage en pays de lean management[END_REF][START_REF] Detchessahar | L'avènement de l'entreprise communicationnelle[END_REF][START_REF] Stimec | Le Lean Management est-il responsable?[END_REF], practices associated with joint regulation between employer and union [START_REF] Bruère | How Can the Organizing Work Involved in the Joint Regulation of Lean Projects Promote an Enabling Organization and Occupational Health? ¿De qué manera el trabajo de organización requerido por la regulación conjunta de proyectos de racionalización (Lean Projects) puede promover una organización habilitadora y la salud ocupacional?[END_REF], employees' involvement [START_REF] Conti | The effects of lean production on l worker job stress[END_REF][START_REF] Hasle | Lean and the working environment: a review of the literature[END_REF][START_REF] Perez Toralla | Participatory design in lean production: which contribution from employees? for what end?[END_REF] or training [START_REF] Kaminski | Unintended consequences: Organizational practices and their impact on workplace safety and productivity[END_REF]. All these HRM practices are positively linked with increased worker health. Despite their advances, these studies have been criticized for considering HRM practices separately. Indeed, recent studies have shown the ineffectiveness of examining only a single type of HRM practice when studying HRM's influence on system or employee outcomes. For example, comparing the integrated and isolated effects of highperformance work practices on employee health and well-being, [START_REF] Ogbonnaya | Integrated and isolated impact of high-performance work practices on employee health and well-being: A comparative study[END_REF] find evidence that the integrated effects of HRM practices have additional explanatory power on employee outcomes (i.e. employee health and well-being) above their isolated effects. However, their study does not relate specifically to a context of lean adoption. Other studies on lean support this view by providing a careful examination of the relationship between HRM and lean practices [START_REF] Cua | Relationships between implementation of TQM, JIT, and TPM and manufacturing performance[END_REF][START_REF] Macduffie | Human resource bundles and manufacturing performance: Organization logic and flexible production systems in the world auto industry[END_REF]. [START_REF] Macduffie | Human resource bundles and manufacturing performance: Organization logic and flexible production systems in the world auto industry[END_REF] shows that a bundle of 'high-commitment' HRM practices associated with lean practices positively affects plant performance in both productivity and quality. Extending the menu of HRM practices common to TQM, JIT and TPM technically oriented practices, [START_REF] Cua | Relationships between implementation of TQM, JIT, and TPM and manufacturing performance[END_REF] show that different configurations of practices, both socially and technically oriented, can improve organisational performance. Based on similar practices, [START_REF] Longoni | When does lean hurt? -an exploration of lean practices and worker health and safety outcomes[END_REF] provide a nuanced perspective of the effects of lean on both operational and worker health and safety performance when a lean adoption model made of bundles of HRM/lean practices is at work. Together, these studies confirm that HRM practices should be implemented as interrelated elements in a bundle of HRM practices complementary to the lean practice bundle. However, they restrict their investigations to certain high-commitment HRM practices or HRM practices common to lean programs, while a satisfactory study of complementarities between bundles of practices requires a full set of HRM practices [START_REF] Milgrom | Complementarities and fit strategy, structure and organizational change in manufacturing[END_REF]. Therefore, the current study adopts a broader definition of HRM practices to ensure that no practice is omitted. In line with [START_REF] Guerrero | High-involvement practices and performance of French firms[END_REF], the study considers High-Involvement Practices (HIP), which consist in gathering intelligence, ideas and the motivation of all workers. Because HIP are a source of motivation and commitment for employees, they are positively related to performance dimensions [START_REF] Guest | Human resource management: when research confronts theory[END_REF][START_REF] Lawler | High involvement management: San Francisco[END_REF]) such as social performance [START_REF] Guerrero | High-involvement practices and performance of French firms[END_REF]. One of [START_REF] Guest | Human resource management: when research confronts theory[END_REF] key findings is that the impact of HIP on social performance is stronger when they are combined into a bundle rather than taken in isolation. Recently, [START_REF] Ogbonnaya | Integrated and isolated impact of high-performance work practices on employee health and well-being: A comparative study[END_REF] obtain a more nuanced result depending on the coverage of practices associated with employees' experience of work intensification. Concerning HIP, [START_REF] Guerrero | High-involvement practices and performance of French firms[END_REF] identify four categories of core practices widely accepted in the literature: (1) training and skill development practices, (2) motivational incentives and recognition practices, (3) communication and information sharing practices and (4) participation and empowerment practices (see Table 2). We therefore consider this full set of HIP (see Table 2). In sum, there is still neither consensus on the effects of lean on worker health nor on the potential moderating role of HRM practices. Prior studies focus only on some specific HRM practices and consider the transition process to lean as a whole without distinguishing between its different adoption phases [START_REF] Martínez-Jurado | HR management during lean production adoption[END_REF]. Therefore, the aim of this study is to take a first step towards a better understanding of the effects of lean on worker health by taking into account a full set of lean and HIP practices and their potential combinations throughout the different phases of the lean adoption process.

METHODOLOGY

We use a qualitative methodology for several reasons. First, this methodology is well-suited to our exploratory objective [START_REF] Eisenhardt | Building Theories from Case Study Research[END_REF][START_REF] Glaser | The Discovery of Grounded Theory: Strategies for Qualitative Research[END_REF]. Second, lean adoption is treated herein as a complex phenomenon encompassing not only diverse practices but also multiple actors. The richness of the data collected will provide a finer-grained picture of the complexity from different points of view [START_REF] Miles | Qualitative Data Analysis: An Expanded Sourcebook[END_REF]. Third, because human activity can hardly be studied out of its context, a replication strategy using multiple case studies is optimal [START_REF] Yin | Case study research : design and methods[END_REF].

Case selection

Since our objective is to explore the relationship between lean, HRM practices and worker health by considering lean maturity (in terms of practices and adoption phases), we selected three manufacturing companies, which have all adopted lean but at distinct levels of maturity.

All companies adopted Lean with the support of the same regional programme called "industrial excellence". To provide a robust assessment of each company's lean maturity, we proceeded in two ways. First, we drew upon the knowledge of consultants who accompanied the studied companies2 . Second, each managing director completed a self-assessment grid comprising the two dimensions of lean maturity: intensity of lean practices used (number of lean practices adopted among a full menu of 32 practices and their intensity of use, which produces a score) and phases of adoption achieved. We then applied the following criteria to ensure triangulation: cases giving us access to several types of informants (internal and external, from different status) and internal documents. Table 3 gives an overview of the three cases selected, which are presented below.

Brief description of the three cases

Company A: Created in 1909, company A is a world leader in stainless steel long products.

With its recognized business-specific and technological expertise, it has a strong position in an environment that remains challenging and uncertain. It produces and sells a wide range of products such as bars, wire rods and wires, used in particular in automotive and aerospace industries, medical field, oil and gas production. Company A has always been oriented toward profitability and has a long history with lean: TQM, TPM and World Class Manufacturing, renamed as an internal label in 2006. The majority of lean practices was handled methodically, effectively and systematically. Company A has reached the stage of routinization and a high level of maturity in terms of lean practices from the self-assessment (2.87/5) while this score is clearly under-estimated in the consultant's view. "This was the first time I accompanied a company with such a maturity, much better than XX [another emblematic company with regard to lean adoption] that set standards" (Consultant A). The consultant reinforces this idea explaining: "in spite of its successive buyouts, the fundamentals are there and the lean adoption has never been called into question (Consultant A).

Company B has been a part of a French pharmaceutical laboratory since 1996. It is organised as an independent profit centre with its own product area. Company C is an industrial manufacturer specializing in automatic assembly. It was created in 1978, following the acquisition of a French company skilled in wood assembly by a German group specializing in metal assembly. Company C provides a service on joining methods used in mass industrial production for several sectors such as automotive, electrics, electronics and telephony. It benefits from very favourable market conditions, in particular due to the growth in the automotive sector. The firm adopted lean in 2012, based on its ISO 9001 quality standard and is still at the beginning of the implementation phase: about half of the lean practices were implemented, exhibiting a low intensity of use. Compared with respondents' and the consultant's statements, the CEO's lean maturity perception seems overvalued (score = 2.45/5). "The functional base from which this company started was too low and very little progress has been made" (Consultant B).

Data collection and interview protocol

We chose a multi-actor approach and selected respondents who were likely to play a significant role in the lean adoption process, regardless of whether they are operating at a strategic or operational level. For each company, six to nine people were engaged in a rigorous protocol of semi-directed interview (see Table 4). The interview grid consisted of the following themes: (1) characteristics of the respondent, (2) organisational and managerial characteristics, (3) presence or absence of HIPs (in relation to the full set described in Table 2) at the organisational and workplace levels, (4) lean maturity in terms of practices and phases of adoption and (5) lean and worker health (perceived effects). All interviews took place in the workplace to shed light on the respondents' direct environment. The 25 completed interviews lasted one hour on average, resulting in 27 hours of recording and 290 pages of transcripts.

To complement primary data, internal and external secondary data were also collected. First, both internal and external sources have proven essential to complete the lean maturity diagnosis given by consultants and respondents in 2015. Second, worker health indicators within a three-year period (2012-2014) were also collected from each company (see Appendix A). These indicators are in line with the concept of employee health at work or similarly worker health we retain in this research [START_REF] Bäckström | Is there a relationship between Lean Leaders and healthy coworkers? Quality Innovation Prosperity[END_REF], 2016[START_REF] Bäckström | Change of the quality management culture through health-promotion activities?[END_REF][START_REF] Bouville | The effects of lean organizational practices on employees' attitudes and workers' health: evidence from France[END_REF][START_REF] Longoni | When does lean hurt? -an exploration of lean practices and worker health and safety outcomes[END_REF]. All these indicators were valuable to corroborate subjective information gathered during the interviews and to make comparisons [START_REF] Yin | Case study research : design and methods[END_REF]. Moreover, each participant responded to a series of seven questions (measuring job satisfaction, health at work, intention to stay) at the end of the interview that were formulated using Bouville and Alis (2014)'s constructs (see Table 5). Finally, secondary external sources (websites, newspapers articles, professional magazines as well as reporting of the consultants' interventions, companies' progress and results made available by the pilot of regional program) were helpful to shed light on the economic environment and results of the companies under study.

Data analysis

Content analysis was performed. To do so, all data collected were double coded according to the aforementioned themes and related sub-themes. Two researchers were involved at each step of coding and their work was checked by a third one. Coding was not considered complete until all three researchers reached consensus.

RESULTS

Consistent with our aim, results on the relationship between lean, HIP practices and worker health are presented according to the different phases of lean adoption (decision, implementation and routinization).

Decision Phase

The three companies justified their decision to adopt lean on the grounds that they expected to achieve better operational results, even if firm B was also preoccupied by its growing problems of musculoskeletal disorders. "Our objective was to link continuous improvement to versatility because employees' versatility avoids doing things too redundant and is a solution to the growing problems of musculoskeletal disorders' (B -CEO). Among the intended operational results, "ongoing improvements of processes and products", "an increase of the overall equipment's effectiveness", "waste reduction" (including the reduction of useless steps in the workshops at company B), "improvements in the quality of service" (service rate) and "customers' satisfaction" were the most cited by the three companies. The financial return objective remained the most frequently cited ground by the three firms. For company B, the firm's profitability was perceived as a necessity for survival in the context of requirements imposed by its group. To deal with these needs, lean appears to be a ready-made solution all the more so because external consultants can help them in their actions. "Our primary focus was the economic aspect of the company, in particular costs reduction. This is what I call an indisputable truth in such an economic world. A business is legitimate and justified only if it makes profitable. So, at the decision stage, costs were a strong axis. The second strong point, that is partly related to costs, but not only, was the satisfaction of our customers, which is the quality aspect." (A -Industrial director 1) "The fact to be able to do this with external assistance, through training, using lean tools, in a more progressive way was important in our decision." (C -Quality manager) At this stage of decision, with the exception of a few internal actors, all companies discover the lean principles and practices through the regional program. The directors and some managers said that they read press articles or media reports on lean manufacturing success stories and best practices. As a result, the decision to adopt lean followed a top-down approach, which remained very theoretical. The lean philosophy was productive, mainly focused on tools and technical practices without any idea of issues related to managerial aspects. "The approach was initially instituted by the steering committee, accompanied by black belts. They give us a list of tools, with things that may have been directive at first; our more general concern was to develop the involvement, to disseminate the tools. So, we pushed people to use the tools: 'do a SMED, do a Kaizen, do a 5 why'." (A-Industrial director 2) Then, at this stage, lean was perceived as an instrumental system to solve operational difficulties and financial challenges without any managerial foundation. The ignorance of most internal actors led companies to hold simplistic and theoretical expectations about lean.

Implementation Phase

The decision phase had undoubtedly consequences on the implementation one, which could not be considered as a whole process. Our results show different steps of maturity within this phase with specific effects on worker health.

Step 1: Lean as an instrumental and technical system with negative effects on worker health Because of the decision's turn of events, the first step of the implementation phase was designed on lean theory based on a methodology that adhered to key lean principles, scrupulously modelled on what had been done elsewhere, and involving carefully imitated, 'formatted' practices. In Company A, the first step of implementation has been source of tensions among employees as well as managers: 'At the beginning, we first experienced phases that were somewhat summary, poorly prepared, poorly accompanied, which resulted in semblances of things, failures that ultimately destabilize the employees of the company' (A -HR manager). The focus was clearly on the technical lean tools, and the human side was overlooked. This focus had a negative effect on employee well-being: stress for the managers who had to follow indicators for which they were not particularly familiar; Unease of the operators and technicians who had to use tools and methods that did not make sense to them; employee difficulties in or even resistance to adopting unilaterally imposed methods; disinclination on the part of the workers and an unrelaxed work atmosphere between the workers who used the lean methods and tools and the ones who were reluctant to use them. In company B, when lean was first put in place, no more than 10 people were involved, mainly employees in charge of production lines, technicians and top managers. All of them attended training sessions led by external consultants. The implementation was difficult given the limited amount of managerial resources allocated. The lean manager, also responsible for purchasing, admits to becoming overwhelmed by the amount of work: 'Many improvements could be resolved through brainstorming and other lean tools. Unfortunately, I had a little bit of trouble following because of my heavy workload in purchasing tasks' (B-Lean Manager). This difficulty was reinforced by the structure of the company, which has no middle management, and by values more declared than shared. Shared philosophy and principles of lean were not established within the company in particular because of the top down decision of lean adoption. While some people associated lean with good manufacturing practices oriented towards customer satisfaction, others associated it with principles oriented towards productivity, quality or waste reduction. For some operators, lean represented something external to their workplace: 'I don't see lean in my work' (B -Technician). A respondent noted that practices related to continuous improvement, JIT or quality are not systematic: 'I do not have the time to do preventive maintenance. It is a black spot' (B -Technician). Company B also considers lean as a solution to its growing problems of musculoskeletal disorders but without really thinking about the necessity to include HIP practices. It only places strong emphasis on versatility, job rotation and autonomy to facilitate fast changeover and make jobs less difficult. Lean has no effect on schedules, but changeover times have been greatly optimized as well as working pace. This is one of the lean positive effect on worker health but it was low because company B has not thereby realized the consequences of the just-in-time phenomenon, through ignorance. "It may be a little more tense. Because in fact, the flow is more tense, so necessarily ..

. "(B -HRM).

In company C, the first steps of the lean implementation were marked by dissonances and misunderstanding about lean. For the CEO, 'lean' is just a word to name a global process of continuous improvement or 'only a theory' not achieved in the field. He underscores the disconnection between the quality approach supported by the quality manager, and lean supported by a line manager. Lean philosophy is not shared in Company C. The CEO still considers that experts (here, the quality manager) must think about the work while others execute. This lack of experience about lean has led to oversimplification, reducing it to technical lean practices implemented through instrumental and theoretical approaches. This in turn has led to the production and consumption of lean without an in-depth grasp of its underlying foundation. Few HIP practices are in place and they are not considered as necessary for the lean implementation. Furthermore, the CEO "had not a delegating style" (Consultant B) and there were some difficulties within the executive committee. "To be brief, it was a can of old crabs" (Consultant B). About HIP practices, training and skill development are limited, disconnected from the lean process: ('Training about lean? There isn't'" (C -Middle manager) The CFO denounced the mismatch between firm needs and training, noting the latter was 'made to please everyone'. Concerning HIP practices, company C had just begun to set up individual interviews initiated by the CFO: 'We try to ask them questions, to target, with open questions, to make them talk'. This initiative has surprised some operators, not used to talk about their work. Motivational incentives and recognition practices remain limited and widely non-formal. The line manager tries to increase daily team recognition. 'The recognition? It is made every day by being present and available' and by promoting some employees 'in relation to what guys have done ... but the board has declined unfortunately all my demands' ( C -Middle Manager). Third, communication and information sharing in Company C are largely informal: billboards near the coffee machine communicate training and 'a mini corporate network on which everyone access and can publish some interesting news' (CEO). The CFO reported a lack of management and several organisational dysfunctions. He denounced the poor distribution of tasks, useless people and the fact that lean is led by a line manager and not by the quality manager. In addition, the staff manager has tried to offset organisational dysfunctions by staying close to his team: 'I wished my office was in the production workshop, to be always closer to the ground' to play his role of 'fuse', 'buffer' and 'intermediary' (C -Middle Manager).

Step 2: First difficulties related to the addition of HIP practices to lean

As noted above, all three companies reported difficulties and negative effects on employees well-being in the preliminary stages of implementation: stress; unease of the operators and technicians; resistance to adopting unilaterally imposed methods; feeling overwhelmed especially from managers; feeling helpless; work intensification because of the just-in-time production; dissonances and misunderstanding about lean; lack of management support. These first steps led two of the three companies to re-examine the way that they managed its adoption. Therefore, HIP have been integrated step by step to lean practices and methods in a more or less integrated way depending on the companies. Company A has adopted several HIP that have been increasingly incorporated into the lean approach. Amongst these HIP, Company A firstly adopted participative practices such as workshops to involve all employees in the new work procedures' definition. 'When you are in a working group, you can be consulted. And, lastly, we can influence decision making.' (A -Operator 1). Second, the firm renamed lean to use an internal label: Atlas. 'I think that the change of name is an element that nevertheless participates in the appropriation of the approach. Lean, doesn't sound French, it was indeed necessary to give a connotation from our universe' (A -Middle manager 1). Formal communication practices were developed, with meetings at several levels and time scales. The workshops organised around Atlas projects are also opportunities for discussions and for sharing information, achievements, shortfalls and emerging issues. 'The working groups around the Atlas pillars are motivating for them [operators]. They are meeting points, places of exchanges. They are keen on that. And that, I think it is really positive' ((A -Middle manager 2). The employees value the 'bottom-up' and participatory orientation of these workshops: 'It's basically top down, we're not going to hide it … except the workshops. That is why they are so important for them [employees]' (A-Industrial Director). Company A has also developed a dynamic ad hoc training program focused on the Atlas approach. In 2014, 2.9% of the wage bill was devoting to training compared with 2.8% in 2013 and 2% in 2012. Some specific training are also developed for managers to help them to deal with the Atlas practices, methods, indicators and lead working groups. Last, the degree of maturity both in terms of lean and HIP of company A is reflected by a growing awareness of the importance to include a grasp of health and safety issues. A specific pillar of the Atlas approach was developed on this focus, which became a central element of Company A's strategy. Specific indicators of health and safety are communicated and analysed daily. Regular safety audits, effort studies and stress enquiries are performed. 'In the Atlas program there are 12 pillars. The health and safety pillar is now the first one. Therefore, yes, it is totally integrated' (A -Operator 3). Company B put in use some lean practices, while maintaining a work organization in which the degree of employees' autonomy remains limited, due to the precise standards, highly standardized procedures and strict quality control system. Indeed, Company B can be considered as a hybrid system since it includes lean practices that coexist with a Taylorian philosophy and principles. Employees noted thresholds above which they have no decisionmaking power: 'When serious problems arise, the decision is no longer in my hands' (B -Operator 2). The managerial maturity of Company B appears to be weak. The lack of managerial practices is partly offset by a managerial proximity with top managers. First, training and skill development were mainly based on a peer training support system. Trained technicians provided the basic tasks and procedures to operators in charge of production lines, who in turn provided their know-how and interpersonal skills to other operators. If trainers regarded this system as beneficial to their own work, trainees were more critical, considering that 'training could include other aspects than [technical] manufacturing operations; it is something we know how to do very well!' (B -Operator 1). Social data confirmed that efforts in terms of continuous training did not increase during the 2012-2014 period. Company B has no annual individual interviews, motivational incentives or recognition practices because 'the company's management doesn't want that' (B -Quality Manager). Employees expressed frustration and demotivation: 'It's really a lack of symbolic gestures. I would say that it can discourage me' (B -Operator 2). By contrast, other employees see increased responsibility as a benefit despite low wages. Furthermore, apart from billboards in the shop area, communication remains informal. A consequence is the saturation of certain top managers or committees. In the absence of team or workshop managers, the chief human resources officer must deal with all the types of problems on the work floor. Moreover, the lean manager admits that the works council as well as the hygiene, safety and working conditions committee (HSWCC) had become 'catch-all' bodies because employees did not know from whom or where to get information.

Concerning worker health, practices such as versatility, job rotation and teamwork made work less difficult. However, all the issues about health and security have been entirely delegated to the HSWCC. Its annual budget amounts to 250 000€ for 2014 (compared with 150 000€ for 2012). In this context, quarterly meetings with occupational physicians and ergonomists are organised and seem to product positive effects: 'I would say that about half the requests led to something.' (B -Lean Manager). Employees are more critical as the focus is rather on safety with the diffusion of information (gestures that should be done), the acquisition of new machinery and equipment that make work less difficult but that are not often used. However, 'what has really changed is the comfort of machinery and the workplace environment as it gets warmer'. (B -Operator 1). The approach is still reactive and do not allow implementing proactive solutions. 'It must be said there are reactions when the accident occurs. I myself will tell you, there is a lack of prevention' (B -Operator 2). Social data confirm employees' perceptions, specifying that the cases treated by the HSWCC over the period 2012-2014 focussed exclusively on safety and workstation ergonomics. Health and safety issues delegated to this committee appear to be completely disconnected from the lean approach. Concerning health issues, working in Company B appears to be physically tiresome for operators (5/5) and stressful for managers (3/4). Absenteeism due to accident at work has increased substantially from 65 in 2012 to 197 in 2014, despite the increase in budget allocated to improving working conditions. Employees perceive that efforts have been made about safety to comply with legislation, but little progress has been made on health: 'There is no overall improvement on this issue' (B -Technician). Moreover, the lack of HIPs has not helped the integration of this issue in the lean context even if 'people [have] become more involved' (B -Human Resources Manager). The report of the consultant states that they "failed to anchor the lean and managerial routines" and that company B tended to "upgrade the bride when they self-assess their lean maturity level" (Consultant B). Company C was still at the beginning of the implementation phase five years after the decision to adopt lean. There was no shared representation or philosophy of lean between the CEO, the chief financial officer (CFO), the quality manager, the line manager and operators. For the consultant, who accompanied the company, "The real job was at the board level. It was necessary to encouraging people to evolve in terms of management." He called on another consultant in order to bring more cohesion within the board but "things did not function well." (Consultant B). First, training and skill development remain limited, disconnected from the lean process: 'Training about lean? There isn't' (C -Quality Manager). Second, company C had just begun to set up individual interviews initiated by the CFO: 'We try to ask them questions, to target, with open questions, to make them talk'. Some operators were very surprised by this initiative because they were not used to talk about their work. Motivational incentives and recognition practices are limited and widely non-formal. Third, communication and information sharing in Company C are largely informal: billboards near the coffee machine communicate training and 'a mini corporate network on which everyone access and can publish some interesting news' (C-CEO). This network is not limited to corporate discussions but also contains current discussions. A survey on communication modalities indicated 'a poor communication between departments "top-down" and "down-top"' (C-Quality Manager). A weekly planning meeting was organized but "sometimes cancelled for three weeks", and 'people come without preparation' (C -Quality Manager), making any progress difficult. Working in Company C appears tiresome and stressful for top managers (2/3) and stressful for other respondents. Faced with these difficult working conditions, one top manager planned to change his place of work. CEO considers that 'working conditions are awesome in our firm!', underscoring that the transition from a historical directive management to a participative one is still in progress. At the same time, the quality manager seems less convinced: 'I don't know if it is linked with lean... Why not? lean and our own management!'. This shows that the combination of incompatible, even contradictory, practices destabilize all the company staff except the CEO. Concerning occupational health and safety indicators in the period 2012-2014, Company C reported no accidents at work or occupational diseases. Absenteeism due to illness increased from 18 days in 2013 to 26 in 2014. Expenditures for improving working conditions and preventing risks in terms of health and safety were not disclosed.

Routinization Phase

Only company A really reached the phase of routinization. While the continuous improvement approach has taken years to be implemented and generalized, at the time of the interviews, the lean maturity diagnosis showed that 23 of 32 lean practices had been implemented, and a majority of them (17) were handled methodically, effectively and systematically. "It took three, four years to initiate an approach that begins to live and to be appropriated by employees." (A -Industrial Director). Lean practices are integrated into all tasks and missions and are part of the company's everyday language and routines. 'Today, Atlas is in everything in A and used lavishly in our work and in speeches.' (A -Operator 3). Furthermore, if lean was considered through a theoretical way at the beginning of the process, its philosophy and its system moved forward since then. Its philosophy was based on instrumental and productive foundations and evolves towards managerial foundations including health and safety management. "At the beginning of the whole process, we had some steps that were a little sketchy, badly prepared, badly accompanied, that led to semblances of things, to failures and that destabilized employees. It was necessary to go through this methodological axis, which was a little painful for people. Today, I think that we have gained in maturity. We pilot a process of continuous improvement, while keeping a methodological base that is part of our know-how and using it more wisely. We have incorporated new pillars centered on well-being through lean practices and health and safety. For us, all this, is Atlas." (A -Industrial Director). "Atlas, for me, I would say improving a process, in the sense of quality, safety and productivity." (A -Operator 2). Unfortunately, the results about health issues, are not so clear, but interviewees provide further evidence of significant improvements in working conditions. The majority of the respondents (5/8) stated that they are more satisfied today with working conditions. However, top managers (2/2) indicated that working in Company A remains physically very tiresome and stressful, and 6 other respondents rated it as stressful as well. The respondents noted that the lean approach increases requirements and challenges, which can be source of stress because many indicators are watched closely. 'What can be scary, this is the number of pillars and the number of indicators you have to manage. […] it has caused, and I am sure it still causes situations of stress for people who are piloting pillars" (A -Industrial Director). Regarding worker health indicators along a three-year period, the expenditures for improving working conditions and preventing risks in terms of health and safety have indeed increased by 177% during the between 2012 and 2014. Then, the number of occupational illnesses has decreased by 32 % between 2012 and 2014. However, the number of days lost due to accidents at work and the number of days absent due to illness increased by 49% and 17%, respectively, in the same period.

DISCUSSION AND CONCLUSION

This study extends the conceptualization of lean as a system composed of highly integrated elements [START_REF] Shah | !!! INVALID CITATION !!! (Guerrero and Barraud-Didier[END_REF]. A novel contribution of this study is that HRM practices (from the perspective of HIP), when taken in combination with lean practices, can moderate their damaging effect on worker health and safety along the different phases of the adoption process (i.e. decision, implementation, routinization). The study follows [START_REF] Jasti | Lean production: literature review and trends[END_REF] recommendations that 'researchers should propose various frameworks along with implementation steps to adapt the particular framework in organisations ' (p.880). This study reveals several ways in which lean effects on health might be mitigated, depending on how the firm integrates its HIP and lean practices along the adoption process. This link between bundles of lean, HRM practices and worker outcomes has been poorly investigated. Using a full list of HIP and lean practices, consideration of lean philosophy as well as lean maturity (both in terms of practices and adoption phases), the results confirm that the relationship between lean and worker outcomes depends on firms' ability to combine bundles of technical and managerial practices [START_REF] Longoni | When does lean hurt? -an exploration of lean practices and worker health and safety outcomes[END_REF][START_REF] Treville | Could lean production job design be intrinsically motivating? Contextual, configurational, and levels-of-analysis issues[END_REF]. This study extends Longoni et al.'s (2013) statement that 'the adoption of lean without the human component is not only mean, it is bad for operational outcomes as well ' (p. 3314). However, the current study's findings significantly nuance this. Lean is not a simple, one-way process. Lean is a 'double-edged sword' [START_REF] Adler | Lean Production and Worker Health: A Discussion[END_REF], which depends on how HIP are combined with lean practices, the phase of their adoption and the way of thinking lean. Depending on these elements, lean can degrade or improve health outcomes.

Revisiting the relationship between lean, HRM practices and worker health in light of the adoption process: the role of bundles of practices

In the cases studied, the issue of the effects of lean on employees' health was deferred until the end of the implementation phase. It was common for the human side to be forgotten during the decision phase and the first steps of the implementation process. Furthermore, the decision to adopt lean was always justified by operational performance without considering the lean philosophy and its compatibility with the Taylorian culture already rooted. Consequently, in the first steps of implementation, lean was put into use by opening a toolbox without giving much thought to its compatibility with company's culture or technical systems. The adoption process appears to be mainly top-down, driven by a desire to implement lean methodology and tools learned from external consultants, which can be difficult for managers to master due to temporal and material constraints. At this stage, executives did not perceive the difficulties managers and employees faced. Lean without the support of HIP appears to be a difficult process to implement, with a negative effect on employee well-being. This confirms that lean is primarily a management philosophy, which requires the involvement and commitment of everyone [START_REF] Moyano-Fuentes | Learning on lean: a review of thinking and research[END_REF][START_REF] Womack | Lean Thinking: Banish Waste And Create Wealth In Your Corporation[END_REF]. Lean adoption entails significant organisational change; therefore, organisations should manage people at the beginning of the process [START_REF] Treville | Could lean production job design be intrinsically motivating? Contextual, configurational, and levels-of-analysis issues[END_REF]. Realizing the need to connect philosophy, HIP and lean practices often occurs after a long delay. [START_REF] Mamman | From management innovation to management practice[END_REF] explains that lean philosophy interpretations are diverse: some are poorly developed, oversimplified or inherently contrary to lean principles. The companies that succeed in reaching the routinization phase, have faced difficulties and are often humbler about their lean expertise. They have integrated HIP in the lean system, and specific indicators about worker health complement the previous menu of lean indicators more oriented on wasps, productivity gain, reject rate and so on. At this stage, lean becomes more an integrated system with both technical and HIP, including preventive health practices. In this study, we are sufficiently removed from the beginning of the adoption process ( 2012) to be able to observe its effects on worker health. In line with de Koeijer, Paauwe and Huijsman (2014), we consider that changes in work processes resulting from the implementation of lean can lead to improved performance within 6-18 months. In the light of social data collected in 2015, three years later, results look encouraging, but they are not yet entirely satisfactory. The adoption process is not yet complete and continued efforts will be needed to reduce the number of days lost due to work accidents and occupational illnesses.

Lean as a managerial innovation: a more fine-grained assessment of organization-level practices related to adoption and adaptation The findings also nuance the lean adoption framework stemmed from the rational perspective of MI adoption, implying a simple sequence of rational activities that occur relatively automatically. Rather, it involves a complex, systemic, long process, with uncertain phases [START_REF] Damanpour | Managerial Innovation: Conceptions, Processes, and Antecedents[END_REF][START_REF] Damanpour | The dynamics of product and process innovations in organizations[END_REF][START_REF] Gondo | Variations in practice adoption: the roles of conscious reflection and discourse[END_REF][START_REF] Hamel | The Why, What, and How of Management Innovation[END_REF][START_REF] Walker | Management innovation and firm performance: An integration of research findings[END_REF][START_REF] Zbaracki | The Rhetoric and Reality of Total Quality Management[END_REF]. In line with the cultural perspective of MI adoption [START_REF] Akrich | The Key to Success in Innovation Part II: The Art of Choosing Good Spokespersons[END_REF][START_REF] Ansari | How are Practices Made to Vary? Managing Practice Adaptation in a Multinational Corporation[END_REF][START_REF] Birkinshaw | Management innovation[END_REF][START_REF] Zbaracki | The Rhetoric and Reality of Total Quality Management[END_REF], our results show that lean as a MI cannot be implemented and routinized without adaptation. We contribute to this perspective showing the crucial role that HIP practices can play for this adaptation at the different stages of the process. We showed contrasting situations in terms of HIP throughout the adoption process. In Company B, they were mainly informal and gave rise to misunderstanding or frustration when some employees were insufficiently recognized and rewarded. This lack of practices oriented toward employees' participation and empowerment hindered the firm form fully appropriating lean practices. Employees' responsibility remained limited when they faced difficulties. Thus, the solution to each problem depends on top managers' reaction, the only ones in a position to answer. This reactive approach is also observed for the health issues delegated to the HSWCC. By contrast, Company A has become so aware of the risks of an instrumental adoption of lean (because it has experienced considerable obstacles in the first and too much theoretical steps of lean implementation), specifically in terms of health, that health issues were used to upgrade existing lean routines with a proactive approach, seeking to transform constraints into opportunities. Participative practices, formal communication and a dynamic training program on the lean approach, and health allow all actors involved to better appropriate lean. In line with [START_REF] Mamman | From management innovation to management practice[END_REF], our results show the importance to consider MI modification that refers to "changes made to the innovation itself so that it can fit the organizational settings" (p.27). For this author, there does not exist a unique type of MI alteration. Some elements can be omitted (i.e omission) or added (i.e. addition) from the 3Ps of the MI "to attain make it workable or to meet the organizational or individual goals for adopting the idea in the first place" (Mamman, 2009:41). These two forms of alteration echo what we call a defensive approach, which is observed in the first stages of the lean adoption process. Worker health issues remain largely exogenous and some solutions are proposed in responses to shocks such as injuries, diseases, etc. By contrast, some elements of the 3Ps can be replaced with "new elements" (i.e. substitution) or mixed with elements of 3Ps of another MI (i.e. hybridization) in order to achieve specific objectives. In the light of our results, these types of alteration are a sign of a more proactive and mature approach that allows employees become agents of change. Following [START_REF] Souza | Lean-integrated management system: A model for sustainability improvement[END_REF], our result also show that the transition from a technical and instrumental version of lean to a lean integrated socio-technical system requires to pass difficult steps that can have negative effects on worker-health. Organizations face difficulties in operating multiple managerial systems simultaneously to achieve an integrated managerial innovation, which will better respect worker health and render organizations more sustainable.

In summary, such an approach of lean adaptation shows the relationship between lean, HIP and health in a new light that can reconcile previous contradictory results (see Figure 1).

Figure 1 -The relationship between lean and worker health along the adoption process

Contributions, limitations and research avenues

In addition to proposing a method to evaluate firms' lean maturity, this study offers two main new insights for a better understanding of the relationship between lean and worker health. First, previous studies on the effects of lean on health explain the instability of results by the incomplete or inadequate way to operationalize lean [START_REF] Longoni | When does lean hurt? -an exploration of lean practices and worker health and safety outcomes[END_REF][START_REF] Parker | Longitudinal Effects of Lean Production on Employee Outcomes and the Mediating Role of Work Characteristics[END_REF]. In particular, a critical issue emerged concerning the non-inclusion of the multi-dimensional nature of lean [START_REF] Longoni | When does lean hurt? -an exploration of lean practices and worker health and safety outcomes[END_REF]. We go beyond this critique by proposing at last a threedimensional identification of lean maturity: (1) maturity in terms of the technical lean practices adopted by the firm according to its level of expertise; (2) maturity in terms of phases of adoption (decision, first step of implementation, implementation and routinizing);

(3) maturity in terms of HIP and the way they are integrated into the lean system. Considering these dimensions, the very nature of lean becomes clear, as well as the differentiated responses to operational health throughout the adoption process (see figure 1). Up to now, HIP are rarely considered as a valuable dimension of lean. Some previous studies have shown their moderator role in the relationship between lean and occupational health (Bamber et al., 2014;[START_REF] Bruère | Les liens entre le système de production lean manufacturing et la santé au travail : une recension de la littérature[END_REF][START_REF] Longoni | When does lean hurt? -an exploration of lean practices and worker health and safety outcomes[END_REF]. Our results indicate something similar with one important difference. It is not sufficient to adopt HIP concomitantly with technical lean practices if they are not fully integrated in the lean system and if they are limited to few disconnected human practices. As observed in company A, continuous improvement practices and health preventive human practices must be combined with common lean indicators. Following some rare authors (Combs, Liu, Hall, and Ketchen, 2006;Macky and Boxall, 2007;Wood and De Menezes, 2008), this suggests, beyond the traditional HIP identified in the literature, the necessity to consider prevention practices as an important bundle of HIP. In that sense, workers' health does not mean 'more of everything' but depends on their combination in a same 'lean system'. We extend here previous results on the crucial role of configurations [START_REF] Cua | Relationships between implementation of TQM, JIT, and TPM and manufacturing performance[END_REF] or bundles of practices (MacDuffie, 1995) by extending the range of both socially and technically oriented practices and by establishing their link with worker health. Furthermore, our results show the crucial explanatory role of the adoption phases on the Second, this research also contributes to a better understanding of the link between MI adoption and social performance, which is still understudied (Damanpour, 2014). First, results emphasise the complexity and non-linear nature of this link. Workers' health needs the lean process to be adapted, allowing the latitude to employees to make these issues become theirs, but this takes time. We here propose to extend Mamman's typologies of MI modification by considering the different phases of lean adoption. This study has important managerial contributions. First, the research points to the necessity for top managers to make a diagnostic of their lean maturity including their HIP. Except for one firm that reached the most advanced phase, top managers tended to overestimate their degree of maturity in terms of lean practices and adoption phases. Similarly, the managerial practices they declared as effective in their organisation are non-existent in reality. Reducing this discrepancy between discourse and reality is of primary importance. Too often, firms perceive lean first from a technical point of view while ignoring its potential negative effects on health. Both top managers and consultants should be aware of the crucial role of HIP to adapt lean to organisational culture and anticipate employees and managers' tensions and stress throughout the adoption process. This requires not only the mobilization of new HIP, but their effective integration into the lean system. Finally, the results provide a recommendation for consultants in charge of accompanying firms in a lean approach: they should rethink their role, which is too often limited to the adoption of technical practices. Important preliminary work must be carried out on the managerial philosophy and "how" lean can be adopted. Similarly, consultants facilitating the adoption of a lean source of operational performance should not overlook social performance.

Considering this type of performance should be at the heart of their programme and mission. This study is not exempt from limitations, which also represent future research opportunities.

First, the research is based on three case studies of French industrial companies that have adopted the same regional lean program during their adoption process. A larger sample that includes both companies that used external consultants and those that did not would improve its external validity. Second, this study is based on a cross-sectional design, which does not allow for closely tracking social data throughout the process. Incorporating a longitudinal design could help capture changes in practices and their effects on worker health. Third, the study is focused on internal actors; however, external stakeholders might, for example, favour the diffusion of sustainable practices. Thus, studies could be undertaken to identify the role of the stakeholders in the supply chain. Fourth, a growing body of literature addresses the environmental dimension of lean practices, which results in the new concept of 'green lean'; however, the social aspects of this dimension remain largely unknown. Further work is needed to investigate lean social performance and its antecedents.

Table 1 -

 1 Lean manufacturing: philosophy, principles and practices

	PHILOSOPHY	PRINCIPLES	PRACTICES
	To avoid cardinal wastes and	• Waste elimination	• TQM practices
	respect customers, employees	• Continuous	• JIT practices
	and suppliers	improvement	• TPM practices
		• Customer focus	• Leadership and strategic practices

Table 2 -

 2

A full set of HIP HIP DEFINITION • Training and skill development Practices aimed at acquiring new skills, developing collective competences and organisational learning • Motivational incentives and recognition Practices aimed at rewarding group and employee efforts, including monetary compensation and nonmonetary compensation • Communication and information sharing Practices aimed at improving communication between groups of employees in terms of content of information or information management, from the top down or from the bottom up • Employee participation and empowerment Practices aimed at sharing power and promoting employees' autonomy through task enrichment and work organisation

Table 3 -

 3 Sample characteristics

	Firms	Industry		Employees	Turnover	Net	Total	Financial rate	Lean Maturity 2014
					(K€)	profit(k€)	equity (k€)	of return	Intensity	Phase (1)
			2017	1500	597700	17750	237316	7,5
	A	Metallurgy							2.87	R	R
			2015	1500	602950	5970	202370	3
			2017	295	62938	233	18016	1,3	I
	B	Chemical industry							3.54	I	advan-ced
			2015	289	45102	1053	17488	6	stage
		Equipment and	2017	30	7936	984	5597	17,6	I
	C	machinery							2.45	I	first
		manufacturing	2015	28	5645	413	4060	10,2	stage
	Phase (1

) : Classification from the respondents' responses in the left column; classification from the consultants' responses in the right column.

  It is a wipes maker in Europe specialized in cosmetics. In a highly competitive environment, company B focuses on costreduction and quality improvement. It also seeks to reduce musculoskeletal disorders that are closely related to the activity. Using ISO 9001 quality standard as the starting point in 2008, Company B went further by adopting lean (or 'continuous improvement') without any support from its group. Today, Company B is still in the implementation phase with an intermediate degree of use of majority of lean practices. The CEO's score of lean maturity in terms of practices (3.54) appears to be somewhat overvalued in light of the consultant's assessment.

« We're talking about a slow process of adoption in this company" (Consultant B).

Table 4 -

 4 Interviews conducted

	Company	Industry	Number of interviews	Respondents' positions	Additional data
	A	Metallurgy	8	Industrial directors (2); human resource manager (1); middle managers (2); operators (3)
	B	Chemical industry	8	General director (1); human resource manager (1); quality manager (1); lean manager (1); middle managers (2); technicians; operators (2)	Social Balance Sheet Data Lean Self-assessment
	C	Equipment and machinery manufacturing	6	CEO (1); administrative and financial director (CFO) (1); quality manager (1); middle manager (1); operators (2)	Intervention reports

Table 5 -

 5 Constructs operationalization My work is rather harmful to my health' (3) 'My work is rather detrimental to my health' (4) 'I sometimes cannot sleep because of my job'; (5) 'My work is tiring'; (6) 'My work is stressful'. INTENTION TO STAY: (7) Do you intend to change work positions or jobs?'

	Construct		Operationalization			Authors
	LEAN	In terms of	32 lean practices auto-assessed by companies	Cua, et al. (2001);
	MATURITY	practices	through the NEMSE method		Lyonnet, et al.
						(2010); Pettersen
						(2009); Shah and
						Ward (2007);
		In terms of	Phase indication for each lean practice:	Damanpour and Schneider,
		adoption phase	DECISION,	IMPLEMENTATION,	2006;	Damanpour	and
			ROUTINIZATION			Wischnevsky, 2006; Klein
						and Sorra, 1996; Meyer and
						Goes, 1988;
	HIPs		Four bundles: TRAINING AND SKILL	Guerrero	and	Barraud-
			DEVELOPMENT,		MOTIVATIONAL	Didier, 2004; Guest, 2001;
			INCENTIVES	AND	RECOGNITION,	Lawler, 1986;
			COMMUNICATION AND INFORMATION
			SHARING, EMPLOYEES'PARTICIAPTION
	WORKER	Objective	HUMAN RESOURCES INDICATORS (all given	Hurrell et al.,
	HEALTH	measures	over 2011-2013): number of departures depending	1998 Juglaret et
			on the status, turnover (in percentage), number of	al., 2011; O'Brien,
			days lost due to workplace accidents, number of	2000;	Ulrich,
			days lost due to illness, number of occupational	1997
			illnesses; expenditures for continuing education (in
			percentage); Expenditures to improve working
			conditions, number of hygiene and safety
			committee' meetings and main issues addressed
		Subjective	Seven questions administrated at the end of each	Bouville and Alis, 2014
		measures	interview to evaluate:
		(perceptions)	JOB SATISFACTION: (1) 'On the whole, I am
			satisfied with my job'; HEALTH AT WORK: (2)

The two consultants who were called before the start of the study (in 2015) were also interviewed three years later to obtain additional information on the situation of the companies studied (in 2018), in particular on lean effects, both in terms of economic and social performance.


Mesut Kavak
email: kavakmesut@outlook.com.tr

Inequality in the Universe, Imaginary Numbers and a Brief Solution to P=NP? Problem

. In this work, I applied the rules I have been proven to P=NP? problem over impossibility of perpendicularity in the universe. It also brings out extremely interesting results out like imaginary numbers which are known as real numbers currently. Also it seems that Euclidean Geometry is impossible. The actual geometry is Riemann Geometry and complex numbers are real.

Introduction

There exist many exact proofs about the rules of right triangle in abstract math; but what are the actual geometry and mechanism in real physical medium and for real math? What an undertaking can give a triangle about existence to understand it? Actually, it is able to explain everything.

1: This is an Euclidean right triangle. Euclidean geometry is the geometry which areas, angles and lengths are related together by whole and certain numbers and there are no complex, uncertain or irrational numbers, irrational numbers are with a limit. Instead of this right triangle, it can be used a triangle which there is no right angle occurs in it. The shape is random. It does not mean actual geometry. For example, BD length can be longer than AD length in the below stated calculations.

There is a representation of an Euclidean geometry. In this case, being BD and BC are fixed, assume that AB is lengthened to any other AB 2 length. Here A point can be assumed as moving body in free space, B point is a fixed point which its coordinate is known in space and C is an observer.

For the lengthened hypotenuse on Fig. 1, over the inequality and definition of AB 2 > AB, it becomes (1) over the in-

equality of BD 2 2 -BD 2 > AD 2 -AD 2 2 , 1 > AD 2 -AD 2 2 BD 2 2 -BD 2 (1)
where BD 2 + AD 2 = AB 2 and BD 2 2 + AD 2 2 = AB 2 2 are the equations over Pythagorean theorem. In the same manner, it becomes (2),

BD 2 + DC 2 = BD 2 2 + DC 2 2 (2)
where h 2 + t 2 = y 2 and h 2 2 + t 2 2 = y 2 are the equations over Pythagorean theorem.

If (2) is edited, it becomes DC 2 - DC 2 2 = BD 2 2 -BD 2 ; thus if DC 2 -DC 2 2 is used instead of BD 2 2 -BD 2 on (1), also it becomes (3) over DC 2 -DC 2 2 > AD 2 -AD 2 2 inequality. 1 > AD 2 -AD 2 2 DC 2 -DC 2 2 (3)
Now the actual displacement inequalities have been determined. Right this point, assume that there is no displacement, namely there is no lengthening. For this condition, it becomes AB 2 = 0, DC 2 = 0 and AD 2 = 0; thus (3) becomes (4),

DC 2 > AD 2
(4) and (1) becomes (5).

-BD 2 > AD 2

(5)

2 Some results of the inequality The inequality of (5) actually means it is impossible to be AD=DC that means perpendicularity is impossible in universe. This also means that at the same time no lengths can be the same. From physical perspective, it means each point of free space has the same speed and energy magnitude at the end of 1 second but the same time, and emergence is one by one for the total of universe. Each point emerges by order. This also means, for any force-applied, since there is no middle point the natural motion is always circular as there is no alternative. Because of circular displacement, centrifugal force is always together with motion.

The inequality of (5) has another results, and are as the below stated ones.

• Exactly there is no middle point place.

• A right angle cannot emerge. It is only close to right angle due to the energy which area holds. • It cannot be drawn two line segments which have the same length from a point in space to other two points. Namely, 3 or more objects cannot take place in space being the distance between each of them is the same.

There is a time difference between each point of space at the same assumed global time. • For AD DC, it also becomes AB BC, BD DC, BD AD, BD AB and more. Namely, while AB is lengthened, BC or the other lengths cannot protect own actual length. The medium is conservative. This also means, that length and thus 1 dimension do not October 2019) p=NP? Mathematics exist alone; because 2 objects cannot take place at a distance relatively to each other. Namely, length is not absolute since is relative. Length occurs in a limited time interval and gets lost constantly, and cannot be independent on speed. Higher dimension parts of lower dimensions have different size than lower dimensional parts. Namely a 2 dimensional square cannot be used by the same size to create a 3 dimensional cube. • The shortest distance between 2 objects is not a line segment. This distance is an arc so close to a line segment. • Parallel two line segments cannot be drawn beyond drawing line segment. They are exactly intersected, and the intersection point occurs due to area multitude of conservative area. • A closed curve is not possible. Only infinite space closes curve. Limited space is not closed but is conservative.

3 Magic of number world Since in a conservative limited area no two lengths can be equal to each other, the numbers which are defined as x y • z where x, y, z ∈ N + are not real numbers. These are imaginary numbers since are also formed by two the same numbers. Namely, the numbers like 4,8,12,16 and 25 are not real numbers. Even if they can be obtained by addition, multiplication is a process alone as a phenomenon which has different, peculiar and exact properties. You cannot use always addition and subtraction instead of multiplication and division to achieve the same number. Namely, you cannot realize verifying always that this means if a number cannot be obtained by multiplication, then it means also addition will be meaningless. This is very important especially for physics; because in real physical medium it has different meanings. For example fine-tuning problem may occur because of this. While we are using some series to calculate something, we may ignore something important.

Even if we eliminate some numbers from the number line, still there do not exist only prime numbers. If there were only prime numbers, it would mean that the equality is always P=NP since there is no prime factors, and would mean that each length of a polygon or a shape in the universe would get different side lengths as prime numbers that means the universe would be formed only by primes. Even so, still each length of a polygon has different side lengths that some of them are exactly prime numbers.

First solution to the P=NP? problem

Over the above stated information, first of all we can stated that as it was said as the above, higher dimensional parts have different sizes. It means that to create a 3 dimensional cube, if you have a 2 dimensional square which has different side lengths that has A energy in real physical medium, you must use a different square which has B energy since has different side lengths in itself and has different lengths than the other one where A < B or A > B. It means to create higher numbers or higher dimensions you must use more energy. You can say that higher dimensions can multiply by getting smaller in size forever as also can get bigger; but it does not differ since you can go from the reverse direction. It also means, if a number is formed by multiplication of different prime numbers, you must use more energy to find the prime factors even if you assumed that you know the places where the prime numbers are placed there. It can be maintained as the following one.

The state of P=NP is only dream.

Proposition X 5 Second solution to the P=NP? problem

An additional supportive solution can be realized as well. In the set of odd numbers, assume that there are prime numbers where odd multiples of 3 are placed instead of odd multiples of 3. In this case, also assume that the numbers inbetween are non-prime numbers.

N A1 N B1 9 N A2 N B2 15 N A3 N B3 21
Table 1: Distribution of odd multiples of 3 for a limited interval.

Here N A numbers are different non-prime numbers which occur after odd multiples of 3, and N B numbers are different non-prime numbers occur before odd multiples of 3 since there are only 2 odd numbers between each consecutive odd multiples of 3 in the set of odd numbers.

Here is a table which was created over this assumption.

Here we must ask that in the real set of odd numbers which is independent of the table, for a selected odd multiple of 3, are there equal number of prime numbers to the number of odd numbers between 3 and the selected odd multiple of 3. If the answer is yes, then in the set of odd numbers between two consecutive odd multiple of 3, there must exist minimum 1 prime number; but this is impossible since there always must be non-prime twins. For example even if we can choose infinite different combination, we can choose odd multiples of 5 and 7 as non-prime twins. Distribution of 5 in the set of odd numbers is over f(x)=10x-5 function as 7 is over f(y)=14y-7 as well; so as the difference between two consecutive multiple of 5 and 7 as twin is going to be 2, the equation must be f(x)=f(y)+2. Over this equation it must be (6) where x,y∈ N + 5x = 7y (6) Here for each x and y values which provides the equality, there are infinite number of non-prime twins. Examples can be applied for any numbers like this equation. This is not only valid for 5 and 7.

This means that for a selected odd multiple of 3 there is not exactly 1 prime number between each consecutive odd multiples of 3 until the selected odd number. Namely number of non-prime numbers are more than prime numbers until the selected odd multiple of 3. In this case, if we assume that there exist prime numbers in the places which odd multiples of 3 exist instead of odd multiples of 3, then this means for the selected odd multiple of 3, non-prime numbers are going to be more than prime numbers due to the table. This increases possibility of to be non-prime number of a selected number in the set of odd number over the assumption and thus also increases prime factor processes since also more non-primes exist due to the assumption for a selected number. Numbers are formed by more non-prime numbers as unusual as also number of prime numbers are decreased by this assumption. This is for the worst possibility. Namely if we prove over this assumption that for a selected number, the process number for primality test is not equal to the process number for finding out prime factors, no other proofs are required since is the worst possibility.

In this case, over the above stated information now the function which gives each prime is known as f(x)=6x-3 function since the function is distribution rule of odd multiples of 3 as primes are counted as exist at the places of these multiples as well.

As a result there is a function which test primality as (7) over f(x)=6x-3.

P=NP?

October 2019

f -1 (x) = x + 3 6 (7)
If result is a whole number, then the number is prime, otherwise is not prime. If is not prime, then minimum x + 3 6 process number requires that it means always for primality test of a number, less process requires than finding out prime factors.

For the worst possibility, the state of P=NP is completely dream.

Proposition Y

As a result, P=NP state is not possible that only 1 evidence is enough since assumed function which provides P=NP state must also work for this primality and prime factor problem. Even if the above stated solution is not going to work for some numbers that especially at the beginning of the set of odd numbers, even only 1 number in the set of odd number can be counted as evidence. We must accept the set of odd numbers as infinite not in an interval. Already, in the infinite set, logically non-primes can be accepted as more than primes since when a new prime emerges, it is combined with the early emerging ones to create more number. This creates many possibilities and thus creates many combinations.

Progressive image

There is a special condition in the above stated first solution to P=NP? problem that if you accept the twin which has more energy of higher dimensional polygon and thus numbers as smaller numbers, then an excessive work emerges. It means, the problems which are not dependent on a single polynomial as NP problems, can be solved easier; but it requires soothsaying since information is deterministic. Below stated information proves this over the above stated rules of the triangle of Fig. 1.

For the lengthened hypotenuse of Fig. 1, over the inequality of (AD 2 + DC 2 ) 2 > (AD + DC) 2 where AB 2 2 + BC 2 2 = (AD 2 + DC 2 ) 2 and AB 2 + BC 2 = (AD + DC) 2 , it becomes (8) for AB 2 = 0 that means no lengthening. 0 > (AD + DC) 2 (8) It means, that AD + DC R. If you assume, that AD + DC = 0, it becomes 0 > 0; thus actually non of them can be 0. It means, that even if there would be no lengthening and thus no motion, there were already area and motion. They are deterministic and cannot be 0. AD + DC is always an imaginary number for the condition of (8).

Area and thus all the information which area holds are deterministic. They cannot be created afterwards.

Proposition Z

In accordance with conservative space, over the components of the right triangle, it becomes AB + BC + m = n and AB 2 + BC 2 = m 2 where m = AD + DC; thus becomes τ + DC + m = n and τ 2 + t 2 = m 2 where τ and t are time here, and is m = τ 2 + t 2 . It seems, that AB and BC or τ and t cannot take random values, that they take certain values in accordance with a rule. If τ + t + m = n is edited, it becomes (τ + t) 2 = (n -m) 2 and thus it becomes τ 2 + t 2 + 2τt = n 2 -2nm + m 2 . Since it is τ 2 + t 2 = m 2 , finally it becomes (9), 2(τt -nm) -n 2 = 0 (9)

where n = τ + t + τ 2 + t 2 . For this equation of (9), the roots become (10) as imaginary time since it cannot be 0 over (8). τ = ∓it (10) With a motion, information in the imaginary time emerges in our universe. As constant speed and so x = vt is not possible, because of x = at 2 , when real time is emerged over t 2 in x = at 2 by using imaginary time of (10) instead of the t 2 , the distance and time emerge in opposite ways over the time on x = at 2 , and know, that image appears as illusion in 3D because of the complex roots and thus complex plane which is perpendicular to (x, y) plane. After that, if you want to express the motion as average, you do not have to use imaginary time since is real time after this, just use its multitude on x = vt and it becomes x = -vt. Excessive information is in the imaginary time that this information is result of any problem. You do not make process for NP problem. You only realize process to learn the result. It also is not related with quantum computers. They do not realize soothsaying.

Second solution to the P=NP? problem

Acknowledgment

This is it! Goodbye!