Marc Maibom

La Profilée establishes IR ≤ 1 as the necessary condition for persistence under real transformation. The present paper establishes that IR ≤ 1 is not sufficient for structural vitality. A system may satisfy IR ≤ 1 while being structurally non-viable in a distinct sense: not because it is collapsing, but because it has ceased to undergo real transformation. Such systems — designated Zombie Systems — achieve persistence not through integration of genuine transformation load but through effective suppression of transformation itself. Their IR is low not because IK is high but because R approaches zero. The distinction is structural and non-trivial. Two systems with identical IR values can be in fundamentally different structural conditions: one integrating real transformation with high IK (Integrative Persistence), one suppressing transformation with effectively zero R (Degenerative Persistence). The paper proves that these two paths to IR ≤ 1 are not structurally equivalent and cannot be distinguished by IR alone. A second condition is required: R must be non-trivially positive. A system that satisfies IR ≤ 1 only by suppressing transformation is formally persistent but structurally non-viable — it has approached the Complete Non-Collapseability boundary (CNC) of D_LP and lost the structural tension that makes persistence meaningful. The result reveals a gap at the boundary of LP’s persistence regime: the framework correctly identifies collapse (IR > 1) and transmutation (IR ≤ 1, FCC violated). The present paper identifies the third boundary failure mode: Zombie Systems, in which IR ≤ 1 and FCC hold, but structural vitality is absent because R → 0.

This paper derives five structural theorems directly from the axiomatic base of La Profilée (LP). Each theorem is forced: the conclusion follows from the relational structure (S, G, ℒ) and the persistence condition by necessity, not by interpretation. The paper first fixes the minimal structural ontology Σ = (S, G, ℒ) from which all results are derived. It then establishes: (T1) R-Amplification — any degradation in I increases IR by definition of IR as a structural ratio; (T2) F-Regeneration Admissibility — identity in LP is defined as terminal SCC membership, making regeneration a question of graph reachability, not philosophy; (T3) Vertical IR Aggregation — system-level integration capacity is bounded by the weakest coupling along critical integration paths, as a network constraint; (T4) Frame Collision Direction — contamination flows unconditionally from the system with greater boundary leakage L; under matched collision conditions this is monotonic in IR; (T5) Structural Time Invariance — τ is dimensionless, so scale invariance follows from its definition. No new axioms are introduced.

Classical theories of identity presuppose state distinguishability over time. Quantum mechanics appears to challenge this. The present paper establishes that LP’s structural persistence condition IR = R / (F · I · C) ≤ 1 is compatible with and illuminated by quantum mechanics. LP requires distinguishability of states, not constituents — satisfied in quantum mechanics at the system level. Superposition is a regime of structural indeterminacy (IR > 1 at the outcome level). Measurement is IR-reduction through environmental coupling. v3 strengthens Section 4a: the proof chain LP identity preservation → state-space isometry → Wigner symmetry → unitarity replaces the weaker injective-CPTP argument of v2. Identity is not merely compatible with unitary evolution — it structurally requires it.

La Profilée’s foundational papers establish two structural exclusions. Complete Pair-Collapseability (PCP) — the condition in which every state pair can be identified by some admissible transformation — is excluded in LP-EN-ZZ (Determinable Identity under Real Transformation) through the incompatibility of PCP with non-trivial state-coherent identity. Complete Non-Collapseability (CNC) — the condition in which no admissible transformation identifies any two distinct states — is excluded in Paper 50 (La Profilée as a Law of Nature) through the necessity of Module: without non-sink SCCs from which admissible transformations can exit, Assumption 2 (real transformation) is contradicted. The present paper does not re-prove these exclusions. It draws their structural consequence: PCP and CNC are not merely excluded failure modes. They are the boundary conditions that define the LP-admissible domain D_LP from outside. D_LP is exactly the structural space between these two excluded extremes: systems in which identity can be non-trivially constituted (PCP excluded) and transformation non-trivially challenges that identity (CNC excluded). Every persistent system in LP’s sense occupies a position within this space. The structural time variable τ = R / I is substantive precisely within D_LP — because only within D_LP do transformation and identity stand in genuine structural tension.

For persistent systems, time is not an independent variable. Structural progression is governed by τ = R / I — the ratio of transformation load to integration capacity. Physical time provides the ordering of events. τ determines whether and how a persistent system can move through them: how quickly structural identity is consumed, at what rate IK = F · I · C is depleted, and when the irreversibility threshold I_crit is reached. Two systems at the same point in physical time can occupy structurally different temporal regimes: a system with τ << 1 is structurally slow — transformation is well within integration capacity, structural progression is stable. A system with τ >> 1 is structurally fast — transformation exceeds integration capacity, structural identity erodes rapidly. This is not a metaphor. It is a structural consequence of LP’s persistence condition IR ≤ 1: the only time variable that governs structural progression is τ. Physical time is the background. τ is what the system actually traverses. The paper derives this result from LP’s foundational structure, establishes the relationship between τ and T_visible, and shows that what appears as ‘speed of change’ in any persistent system is a structural relation between R and I, not an external temporal property.

La Profilée (LP) identifies F* — the residual Frame {M, J, Q} surviving complete Module collapse in a black hole — as the minimal identity-preserving structure that spacetime conserves when all degrees of freedom are lost. Prior publications (Paper 39, Maibom 2026j) characterise Hawking radiation as a slow F*-degradation process in which M decreases over cosmological timescales. What has not been derived is the structural consequence of F* reaching zero: if Hawking evaporation reduces M to zero, what happens to the identity structure of the black hole system? This paper derives the structural answer in three steps. First, it applies the Non-Eliminability Theorem (Paper 52, Maibom 2026) to F*: if F* cannot be eliminated without destroying determinability, then M → 0 through Hawking evaporation cannot represent identity elimination — it must represent identity transformation. Second, it derives the LP structural resolution of the information paradox: the quantum information encoded in the original Module (infalling matter and radiation) cannot be structurally destroyed because its destruction would violate the Non-Eliminability Theorem. It must therefore be encoded in Hawking radiation — not as a claim about quantum gravity dynamics, but as a structural necessity. Third, it characterises the endpoint of complete evaporation: the structural state at M = 0 is not Frame-null but F₀-adjacent — the system approaches the pre-geometric structural layer from which spacetime emerged, completing the structural arc from F₀ through spacetime constitution through black hole formation through complete evaporation back toward F₀. These results do not constitute a theory of quantum gravity. They constitute structural constraints that any theory of quantum gravity must satisfy — adding three necessary conditions to the five derived in Paper 40 (QM/GR Boundary, Maibom 2026k).

The problem of personal identity over time has resisted resolution for three centuries. Every proposed solution either presupposes an invariance condition — something that must remain the same across time and change — or collapses into reductionism, denying that identity is anything over and above the continuity of psychological or physical relations. Neither position is satisfactory: invariance assumptions beg the question of what justifies selecting one invariant over another, while reductionism cannot account for the normative and practical weight identity carries. This paper argues that both positions are unnecessary. La Profilée (LP) derives, from two minimal structural conditions — determinability and real transformation — that identity exists as the maximal transformation-invariant equivalence relation on any system satisfying these conditions, and that this identity relation is structurally non-eliminable without collapse of determinability: its collapse entails the collapse of determinability itself. No invariance assumption is required. Invariance is not assumed but derived — it is the structural consequence of the existence of identity, not its precondition. The result is stronger than any position in the current persistence debate. It does not propose a new criterion of identity. It derives the structural necessity of identity from conditions weaker than any existing account presupposes, and shows that the identity relation so derived cannot collapse without destroying the minimal conditions under which any system can be described at all. This is not a contribution to the debate about which invariance condition is correct. It is a demonstration that the debate has been asking the wrong question.

La Profilée (LP) establishes a universal persistence condition IR = R / (F · I · C) ≤ 1, where F denotes Frame strength — the structural fraction of total integration capacity directed toward identity preservation. Prior publications have operationalized IR diagnostically, but F has been measured primarily through its consequences: when IK collapses and IR rises, F is inferred to have been low. This post-hoc measurement is structurally permissible but epistemically insufficient for two purposes: independent falsification of LP's structural mapping, and prospective diagnostic use before collapse is visible. This paper derives and specifies independent measurement protocols for F across three domains — organisational systems, biological systems, and persons. In each domain, F is defined through structural observables that are logically prior to and causally independent of IR trajectory: they can be assessed without knowing whether the system is in overload, without reference to outcomes, and without presupposing the validity of LP. The protocols specify concrete proxy variables, measurement procedures, and independence criteria. The central claim is: F is independently measurable through the stability and invariance of the structural properties that define what the system is — not through what the system produces. For organisations, this means governance structure and strategic invariance. For biological systems, homeostatic set-point maintenance and conserved regulatory architecture. For persons, self-concept clarity and values congruence. In each case, the measurement is structurally justified, not merely stipulated.

La Profilée (LP) establishes a universal persistence condition IR = R / (F · I · C) ≤ 1, where F denotes Frame strength — the structural fraction of total integration capacity directed toward identity preservation. Prior publications have operationalized IR diagnostically, but F has been measured primarily through its consequences: when IK collapses and IR rises, F is inferred to have been low. This post-hoc measurement is structurally permissible but epistemically insufficient for two purposes: independent falsification of LP's structural mapping, and prospective diagnostic use before collapse is visible. This paper derives and specifies independent measurement protocols for F across three domains — organisational systems, biological systems, and persons. In each domain, F is defined through structural observables that are logically prior to and causally independent of IR trajectory: they can be assessed without knowing whether the system is in overload, without reference to outcomes, and without presupposing the validity of LP. The protocols specify concrete proxy variables, measurement procedures, and independence criteria. The central claim is: F is independently measurable through the stability and invariance of the structural properties that define what the system is — not through what the system produces. For organisations, this means governance structure and strategic invariance. For biological systems, homeostatic set-point maintenance and conserved regulatory architecture. For persons, self-concept clarity and values congruence. In each case, the measurement is structurally justified, not merely stipulated.

The Admissible Reduction Theorem, established in “The Admissible Reduction Theorem” (Paper 65), proves that any persistence condition defined on an LP-admissible system satisfying the structural role constraints reduces to IR = R / (F · I · C) ≤ 1 under reparameterization. The present paper draws the structural consequences of this result. Three corollaries follow directly. First, within D_LP no alternative existence-persistence boundary is structurally possible: any candidate either reduces to IR ≤ 1 or is not a persistence condition in the structural sense. Second, the existence dimension of D_LP is formally closed: the question of which condition governs persistence on the existence dimension has exactly one answer within D_LP. Third, domain-specific persistence theories — across thermodynamics, quantum systems, fluid dynamics, biology, and organisations — are not alternatives to LP but instantiations of IR ≤ 1 in domain-specific variable spaces. These corollaries do not require new proofs beyond Paper 65. They are consequences of a proven theorem. The paper concludes with the closure statement for LP: within the admissible domain, the persistence question on the existence dimension has exactly one structural answer — not because LP defines it that way, but because the structural role constraints of persistence, combined with the uniqueness of the integration capacity form, leave no other option.

La Profilée formalizes persistence under real transformation through the constraint IR = R / (F · I · C) ≤ 1. This condition governs existential continuity: a system persists if and only if its integration capacity absorbs incoming transformation load. The present paper identifies a structural gap in this account. IR is an existence condition — it does not determine whether a persisting system remains the same system. A system may satisfy IR ≤ 1 while its Frame has drifted beyond the boundary of its original persistence class. In this case the system exists but is no longer identical to itself. We formalize this distinction through the Frame Continuity Condition (FCC) and define Transmutation as the regime in which IR ≤ 1 holds while FCC is violated. Transmutation is shown to be structurally irreducible to both Persistence and Collapse. The result closes a gap at the core of LP: the framework was constructed to answer the Heraclitean–Parmenidean problem, and FCC is the condition that completes that answer.

Paper 57 established the Frame Continuity Condition (FCC) as the identity complement to LP’s existence condition IR ≤ 1. FCC requires that Frame drift from origin does not exceed identity tolerance δ_F. The present paper addresses the determination of δ_F. We argue that δ_F is neither empirically stipulated nor universally fixed, but structurally derived from a distinction internal to Frame itself: F_constitutive, the identity-bearing core of the Frame, and F_operational, its variable expression. δ_F is the maximal displacement of F_operational compatible with F_constitutive remaining intact. This derivation makes δ_F system-relative without making it arbitrary, and operational without requiring external calibration. The result extends LP’s measurement program to the identity dimension and closes the determination problem opened by FCC.

Every system that persists under transformation is bound by three structural constraints: — Transformation remains integrable — the system absorbs change without rupture. Load does not exceed structural capacity. — Identity continuity is preserved — the system remains itself through change. Frame drift does not exceed what the system can absorb without becoming something else. — The defining structure remains intact — what makes this system this system does not collapse into something else. These are not properties of a current state. They are constraints on what transitions are possible. A system does not remain itself because it does not change. It remains itself because its change remains within these constraints.

The preceding papers in this series established the Frame Continuity Condition (FCC, Paper 57), the identity tolerance δ_F derived from the constitutive–operational Frame distinction (Paper 58), and the Constitutive Reading Protocol for identifying F_constitutive (Paper 59). Together these papers extended LP’s state space to four regimes: Persistence, Collapse, Transmutation, and Dissolution. The present paper proves that this typology is complete: every system under transformation occupies exactly one of these four regimes at every time t. The proof proceeds in three steps. First, both IR and FCC are shown to be genuinely binary conditions — threshold phenomena, not continuous scales. Second, the two conditions are shown to be logically independent: neither determines the other, and each combination is realizable. Third, the cross-product of two independent binary conditions yields exactly four partitions, and no fifth regime is structurally possible. The result is not a taxonomic convenience but a structural theorem: the LP state space is closed under the conditions that govern persistence.

The Admissible Reduction Theorem, established in “The Admissible Reduction Theorem” (Paper 65), proves that any persistence condition defined on an LP-admissible system satisfying the structural role constraints reduces to IR = R / (F · I · C) ≤ 1 under reparameterization. The present paper draws the structural consequences of this result. Three corollaries follow directly. First, within D_LP no alternative existence-persistence boundary is structurally possible: any candidate either reduces to IR ≤ 1 or is not a persistence condition in the structural sense. Second, the existence dimension of D_LP is formally closed: the question of which condition governs persistence on the existence dimension has exactly one answer within D_LP. Third, domain-specific persistence theories — across thermodynamics, quantum systems, fluid dynamics, biology, and organisations — are not alternatives to LP but instantiations of IR ≤ 1 in domain-specific variable spaces. These corollaries do not require new proofs beyond Paper 65. They are consequences of a proven theorem. The paper concludes with the closure statement for LP: within the admissible domain, the persistence question on the existence dimension has exactly one structural answer — not because LP defines it that way, but because the structural role constraints of persistence, combined with the uniqueness of the integration capacity form, leave no other option.

La Profilée’s five Admissibility Requirements AR1–AR5 define the domain of LP-valid system description: systems with an identified identity structure, non-zero structural capacities, definable transformation, temporal extension, and structural coherence between Frame and modules. The present paper proves the Admissible Reduction Theorem: any persistence condition defined on an LP-admissible system is either equivalent to IR = R / (F · I · C) ≤ 1 under reparameterization, or it is not a persistence condition in the structural sense. The proof proceeds in three steps. First, we show that AR1–AR5 jointly force a specific variable structure on any persistence condition defined within the admissible domain: the condition must contain a transformation component and an integration capacity component, and these must be relationally structured. Second, we show that the Functional Uniqueness Theorem — established in “La Profilée as a Law of Nature” — uniquely determines the form of the integration capacity component as F · I · C within the admissible domain. Third, we show that any relational persistence condition with this variable structure is equivalent to IR ≤ 1 under reparameterization. The result closes the admissible domain: within LP’s structural universe, no alternative persistence condition exists.

La Profilée’s persistence constraint IR = R / (F · I · C) ≤ 1 is a structural law: necessary, domain-invariant, non-empirical. But its application is not unconditional. A system description must satisfy five Admissibility Requirements (AR1–AR5) before IR can be meaningfully computed and the constraint applied. These conditions are not conventions or methodological preferences. They are structural prerequisites: their failure renders IR either undefined, unanchored, or structurally meaningless. The present paper derives each of the five conditions from LP’s formal architecture, establishes the specific failure mode associated with each, and shows that AR1–AR5 are jointly necessary and individually sufficient for LP-valid system description. The Admissibility Requirements connect to LP’s identity architecture: AR1 is the existence-dimension analogue of the Constitutive Reading Protocol established in “The Constitutive Reading”, and together AR1–AR5 function as the structural gate through which any system must pass before the four-regime typology established in “The Completeness of Persistence” can be applied.

Classical theory cannot describe a fundamental class of systems: those that continuously transform and yet remain the same system. It has statics — no transformation. It has dynamics — transformation without structural identity constraints. Neither describes persistence under real transformation. La Profilée establishes two necessary conditions for persistence: IR = R∕(F·M·K) ≤ 1 — the existence condition FCC — the Frame Continuity Condition — the identity condition Together these conditions define a unique structural regime: Adaptive Statics. This is not an additional category. It is the operational domain of the persistence condition itself — the only regime in which real transformation is possible without identity loss.

La Profilée is commonly read as a theory of persistence — an account of what allows systems to endure through transformation. This paper argues for a stronger and more precise characterization: LP is a structural theory of stable change, or, in the terminology developed here, a theory of adaptive statics. The term captures a structure that classical frameworks have not formalized: the invariant conditions under which variation is possible. Classical statics describes systems in equilibrium with no transformation. Classical dynamics describes transformation without structural invariants. LP’s domain is neither. It formalizes the structural constraints that must remain invariant — IR ≤ 1, FCC, F_constitutive — in order for real, continuous transformation to occur without identity loss. These constraints are not conditions on the absence of change. They are conditions on the structural possibility of change. We show that this position resolves the Heraclitean–Parmenidean tension not by choosing a side but by identifying the structural domain each was tracking. We further show that LP’s adaptive statics constitutes a third theoretical position irreducible to either classical statics or dynamics, and that this position is the necessary precondition for any adequate theory of persistence.

La Profilée’s persistence constraint IR = R / (F · I · C) ≤ 1 has been applied across physical, biological, organizational, and psychological domains. This paper addresses its epistemic status: is IR ≤ 1 an empirical regularity — a pattern observed across domains that could in principle be falsified — or a structural law — a necessity derivable from what persistence, transformation, and structural identity mean? We argue for the latter. The argument proceeds in three steps. First, we show that F, I, and C are not a convenient decomposition but the exhaustive and necessary structural preconditions for persistence under transformation. Any system that persists under transformation must have all three; their absence is not a variation but a contradiction. Second, we show that the constraint form IR ≤ 1 is structurally entailed: IR > 1 cannot be maintained stably because unabsorbed transformation accumulates as structural inconsistency until coherence fails. Third, we establish the law-status consequence: IR ≤ 1 is not falsifiable by case-level counterexample, because a reported counterexample indicates measurement error or misclassification rather than a structural exception. Falsification of LP’s constraint would require showing a structural contradiction in its derivation — not producing a case. The persistence constraint is a structural law, not an empirical generalization.

The preceding papers in this series established the Frame Continuity Condition (FCC, Paper 57), the identity tolerance δ_F derived from the constitutive–operational Frame distinction (Paper 58), and the Constitutive Reading Protocol for identifying F_constitutive (Paper 59). Together these papers extended LP’s state space to four regimes: Persistence, Collapse, Transmutation, and Dissolution. The present paper proves that this typology is complete: every system under transformation occupies exactly one of these four regimes at every time t. The proof proceeds in three steps. First, both IR and FCC are shown to be genuinely binary conditions — threshold phenomena, not continuous scales. Second, the two conditions are shown to be logically independent: neither determines the other, and each combination is realizable. Third, the cross-product of two independent binary conditions yields exactly four partitions, and no fifth regime is structurally possible. The result is not a taxonomic convenience but a structural theorem: the LP state space is closed under the conditions that govern persistence.

Papers 57 and 58 established the Frame Continuity Condition (FCC) and derived identity tolerance δ_F from the distinction between F_constitutive and F_operational. The determination problem for δ_F was resolved by grounding it in the constitutive layer of Frame. The present paper addresses the next problem: how is F_constitutive identified? We argue that F_constitutive is determined not by content but by function within LP’s integration architecture. A Frame property is constitutive if and only if its removal or inversion forces a reconstitution of the system’s integration architecture — not a recalibration within it. This criterion is structural, non-metric, and intersubjectively checkable. We formalize the distinction between constitutive and operational drift, address boundary cases, and show that ambiguous intermediate cases are not a weakness of the criterion but the expected structural signature of the Transmutation threshold.

The Paper "Existence witout Identity" established the Frame Continuity Condition (FCC) as the identity complement to LP’s existence condition IR ≤ 1. FCC requires that Frame drift from origin does not exceed identity tolerance δ_F. The present paper addresses the determination of δ_F. We argue that δ_F is neither empirically stipulated nor universally fixed, but structurally derived from a distinction internal to Frame itself: F_constitutive, the identity-bearing core of the Frame, and F_operational, its variable expression. δ_F is the maximal displacement of F_operational compatible with F_constitutive remaining intact. This derivation makes δ_F system-relative without making it arbitrary, and operational without requiring external calibration. The result extends LP’s measurement program to the identity dimension and closes the determination problem opened by FCC.

La Profilée formalizes persistence under real transformation through the constraint IR = R / (F · I · C) ≤ 1. This condition governs existential continuity: a system persists if and only if its integration capacity absorbs incoming transformation load. The present paper identifies a structural gap in this account. IR is an existence condition — it does not determine whether a persisting system remains the same system. A system may satisfy IR ≤ 1 while its Frame has drifted beyond the boundary of its original persistence class. In this case the system exists but is no longer identical to itself. We formalize this distinction through the Frame Continuity Condition (FCC) and define Transmutation as the regime in which IR ≤ 1 holds while FCC is violated. Transmutation is shown to be structurally irreducible to both Persistence and Collapse. The result closes a gap at the core of LP: the framework was constructed to answer the Heraclitean–Parmenidean problem, and FCC is the condition that completes that answer.

La Profilée (LP) establishes a necessary structural condition governing the persistence of any system under real transformation. The condition has been instantiated across domains ranging from quantum decoherence to cosmological structure, spanning approximately sixty orders of magnitude in physical scale. From two minimal assumptions — determinability and real transformation — it is derived that any persistent system must decompose canonically into three structural components: Frame (F), Module (M), and Coupling (C). The effective integration capacity of any such system is IK = F · I · C, where I is total integration capacity. The persistence condition is: IR = R / (F · I · C) ≤ 1 where R is transformation pressure. This condition is not postulated. It is the uniquely determined quantitative expression of the structural constraints forced by determinability and real transformation. It is domain-independent, representation-invariant, scale-invariant, and falsifiable. This paper provides a unified account of LP: the derivation from minimal assumptions, the formal architecture, the central theorems, the thermodynamic correspondence, the scale invariance result, the domain applications, and the falsification conditions. It is written as a single document in which a reader unfamiliar with the prior LP series can follow the complete argument. LP is a constraint-law. It does not describe the dynamics of any system. It constrains the class of evolutions compatible with persistent identity — in the same formal sense as the second law of thermodynamics, Pauli's exclusion principle, and Landauer's principle constrain evolutions in their respective domains. Its universality follows from structural necessity, not from empirical induction. The persistence condition is not imposed on persistent systems. It is the structural condition any persistent system under real transformation must satisfy.

La Profilée (LP) establishes a necessary persistence condition IR = R / (F · I · C) ≤ 1 that has been established across domains ranging from quantum decoherence to cosmological structure, spanning approximately sixty orders of magnitude in physical scale. This paper establishes why this condition holds identically across all structural levels without modification, scaling, or domain-specific adjustment. The result follows from structural minimality. The two assumptions from which LP derives the persistence condition — determinability and real transformation — contain no metric, no length scale, and no energy scale. The canonical decomposition into Frame, Module, and Coupling is forced by the reachability structure of the state space, which is defined independently of any scale parameter. IR is therefore scale-free by construction, not by coincidence. This paper provides the formal grounding for this claim. It defines admissible scale transformations as a subclass of the admissible representations already established in LP, proves that IR threshold structure is invariant under this class, and qualifies precisely where the non-trivial condition — AR5, preservation of flux-relevant structure under coarse-graining — must be independently verified for each domain instantiation. This paper does not introduce scale invariance as an additional symmetry assumption. It shows that scale invariance is a necessary consequence of structural minimality: a persistence condition derived without scale parameters cannot acquire scale dependence through application.

La Profilée (LP) identifies F* = {M, J, Q} — the residual Frame surviving complete Module collapse in a black hole — as the minimal identity-preserving structure that spacetime conserves when all degrees of freedom are lost. This paper derives the structural consequence of F* reaching zero through Hawking evaporation. First: the Non-Eliminability Theorem requires that M → 0 represents identity transformation, not elimination — information must be encoded in Hawking radiation as a structural necessity. Second (v3, replacing v2): a rigorous four-step proof establishes that LP identity preservation structurally requires full quantum unitarity via state-space isometry and Wigner’s theorem, not via the weaker injective-CPTP argument of v2. Third: the evaporation endpoint is F₀-adjacent. Three additional structural requirements for quantum gravity (6–8) are derived.

La Profilée (LP) establishes a necessary persistence condition IR = R / (F · I · C) ≤ 1. Prior publications have applied this condition diagnostically — identifying systems in Regime E (sustained IR > 1) and characterising their collapse dynamics. What has not been formally derived is why IR > 1 does not produce immediate visible collapse, and what structural conditions determine whether a system in Regime E can return to IR ≤ 1. This paper derives two structural theorems. The Collapse Latency Theorem establishes that every system entering IR > 1 possesses a structurally finite compensation capacity — a set of mechanisms that delay visible manifestation of overload without restoring the structural condition. This capacity is exhaustible by structural necessity: compensation consumes integration resources, accelerating the very depletion it masks. The interval between IR > 1 crossing and visible collapse — T_visible — is therefore not random but structurally determined by the system's initial compensation capacity, the rate of compensation consumption, and the trajectory of IR above 1. The Restitution Asymmetry Theorem establishes that structural recovery from Regime E is not the reverse of the collapse path. Restitution requires restoration of structural components in a specific order — determined by the logical dependencies of the persistence condition — and this order is different from the order in which those components degraded during collapse. Collapse is driven by multiplicative IK depletion; restitution requires sequential restoration with F as the necessary precondition for I recovery, and I as the necessary precondition for C restoration. Systems that attempt restitution in the wrong order fail structurally, regardless of the resources applied. Together, these theorems provide the formal foundation for prospective structural diagnosis — the identification of IR > 1 before visible collapse — and for structurally grounded intervention design. They also establish the fundamental asymmetry of collapse and recovery: the path into Regime E and the path out are structurally distinct processes governed by different structural necessities.

The problem of personal identity over time has resisted resolution for three centuries. Every proposed solution either presupposes an invariance condition — something that must remain the same across time and change — or collapses into reductionism, denying that identity is anything over and above the continuity of psychological or physical relations. Neither position is satisfactory: invariance assumptions beg the question of what justifies selecting one invariant over another, while reductionism cannot account for the normative and practical weight identity carries. This paper argues that both positions are unnecessary. La Profilée (LP) derives, from two minimal structural conditions — determinability and real transformation — that identity exists as the maximal transformation-invariant equivalence relation on any system satisfying these conditions, and that this identity relation is structurally non-eliminable without collapse of determinability: its collapse entails the collapse of determinability itself. No invariance assumption is required. Invariance is not assumed but derived — it is the structural consequence of the existence of identity, not its precondition. The result is stronger than any position in the current persistence debate. It does not propose a new criterion of identity. It derives the structural necessity of identity from conditions weaker than any existing account presupposes, and shows that the identity relation so derived cannot collapse without destroying the minimal conditions under which any system can be described at all. This is not a contribution to the debate about which invariance condition is correct. It is a demonstration that the debate has been asking the wrong question.

La Profilée (LP) establishes a universal persistence condition IR = R / (F · I · C) ≤ 1, where F denotes Frame strength — the structural fraction of total integration capacity directed toward identity preservation. Prior publications have operationalized IR diagnostically, but F has been measured primarily through its consequences: when IK collapses and IR rises, F is inferred to have been low. This post-hoc measurement is structurally permissible but epistemically insufficient for two purposes: independent falsification of LP's structural mapping, and prospective diagnostic use before collapse is visible. This paper derives and specifies independent measurement protocols for F across three domains — organisational systems, biological systems, and persons. In each domain, F is defined through structural observables that are logically prior to and causally independent of IR trajectory: they can be assessed without knowing whether the system is in overload, without reference to outcomes, and without presupposing the validity of LP. The protocols specify concrete proxy variables, measurement procedures, and independence criteria. The central claim is: F is independently measurable through the stability and invariance of the structural properties that define what the system is — not through what the system produces. For organisations, this means governance structure and strategic invariance. For biological systems, homeostatic set-point maintenance and conserved regulatory architecture. For persons, self-concept clarity and values congruence. In each case, the measurement is structurally justified, not merely stipulated.