[SMFT basics may refer to ==> Unified Field Theory of Everything - TOC]
[Quick overview on SMFT vs Our Universe ==>Chapter 12: The One Assumption of SMFT: Semantic Fields, AI Dreamspace, and the Inevitability of a Physical Universe]

The Incompleteness of Understanding:
Observer Collapse and Semantic Field Dynamics

Human remark: This article essentially claims that “the search for truth is endless.”

Abstract

The traditional conception of an observer in physics and epistemology treats perception and comprehension as passive or external mappings onto an independently existing world.
However, unresolved paradoxes — such as Gödel’s incompleteness theorems, the quantum measurement problem, and the persistent limits of formal systems — suggest the need for a deeper, field-integrated understanding of observers themselves.

Semantic Meme Field Theory (SMFT) redefines the observer (Ô) as an embedded projection operator within a dynamic semantic field.
In this framework, observers can only collapse meaning locally, within coherent semantic wells, and their understanding is necessarily incomplete relative to the total field structure.
Self-consistency is not an internal property but emerges from continuous external interaction with broader field dynamics.
Observers drift through semantic tension gradients, constantly evolving their comprehension structures through recursive collapse traces, but never attaining global closure.

This paper formalizes these principles, demonstrating that comprehension is inherently localized, incomplete, and evolving.
It proposes that understanding is not the static mirroring of an external reality, but the emergent trace of dynamic field engagement.
Consequently, knowledge, science, and perception must be reconceived as adaptive navigation processes within an inexhaustibly rich semantic universe.

This field-relative model of comprehension resolves classical paradoxes, reframes the role of observers in physics and epistemology, and opens new avenues for future semantic cosmology and collapse engineering.

1. Introduction

1.1 Traditional Conceptions of the Observer

In the classical worldview of physics and epistemology, the observer is often treated as a passive entity:

A detached witness to events in a pre-existing external reality,
A static reference point outside the systems it observes,
A neutral agent recording facts without fundamentally altering them.

Even quantum mechanics, despite introducing observer-dependence in the collapse of wavefunctions, retains an implicit separation between "the system" and "the observer."
The observer is typically treated as a black box: capable of inducing collapse but not modeled internally within the system's own formalism.

This separation has led to persistent paradoxes:

How can an external observer collapse a quantum system without becoming entangled with it?
How can a knowledge system validate itself if the observer's criteria are not themselves externally verifiable?
How can comprehension be complete if observers are embedded within the very reality they seek to understand?

Traditional models lack a formal treatment of the observer’s own structural limits and field dependencies.

1.2 Gödel’s Incompleteness and Beyond

Gödel’s incompleteness theorems revealed a profound limitation:
any formal system capable of encoding basic arithmetic contains true statements that cannot be proven within the system itself.

This insight deeply shook the foundations of logic, mathematics, and philosophy, yet it remained largely confined to symbolic systems.
It raised uncomfortable but largely unexplored questions:

If formal systems are inherently incomplete, what about human comprehension of the physical universe?
If no system can prove its own consistency, can any observer guarantee the totality of its understanding?

Gödel hinted at a reality where incompleteness is not an exception, but a fundamental structural feature.

However, until now, no formal theory fully integrated this incompleteness into a model of the observer's own collapse behavior within a dynamic reality.

1.3 Purpose: A Semantic Field-Theoretic Reinterpretation

This paper advances a field-theoretic reinterpretation of the observer, based on the Semantic Meme Field Theory (SMFT) framework.

We propose that:

The observer Ô is not an external agent, but a dynamic, field-embedded projection operator shaped by the semantic field.
Understanding arises from localized collapse traces within attractor zones of the field, rather than from mapping an external reality exhaustively.
Comprehension is inherently incomplete, field-relative, and evolving due to the infinite richness and dynamic restructuring of the semantic manifold.
Self-consistency of comprehension cannot be established internally but depends on ongoing field interaction and external coherence feedback.

By grounding observers in field dynamics rather than treating them as external primitives, SMFT resolves longstanding paradoxes and offers a unified model of knowledge, perception, and scientific evolution.

The sections that follow will formalize this view, articulate its implications, and outline a new conceptual architecture for the future of physics, epistemology, and cognitive science.

2. Observer Ô as a Field-Embedded Entity

2.1 The Projection Operator Ô

In the Semantic Meme Field Theory (SMFT) framework, the observer is not an external or idealized agent;
it is represented by a projection operator, denoted as Ô.

Ô embodies:

A particular orientation in semantic phase space (θᵒ),
A cognitive-collapsing structure evolved from previous field interactions,
A limited, directional capacity to induce collapse in memeforms Ψₘ(x, θ, τ).

Mathematically, an observer acts on the semantic field through selective projection:

Ô Ψₘ → φ_j,
where φ_j is the specific collapsed trace resulting from the interaction.

The key distinction is that Ô is itself an emergent field structure:

It carries biases, memory traces, and collapse habits inherited from its history of previous interactions.
It is constructed dynamically, not assumed a priori.

Thus, observers are co-evolving participants in the field, not external vantage points.

2.2 Phase Alignment and Collapse Limitation

Successful collapse — the transition from potential meanings to realized interpretations —
requires that Ô’s projection angle (θᵒ) sufficiently phase-aligns with the local semantic tensions of the field.

If phase alignment is:

High → Collapse is stable, coherent, and predictable.
Low → Collapse is unstable, ambiguous, or fails altogether.

Critically:

No Ô can phase-align with all semantic directions simultaneously.
Semantic tension fields are too rich, multidimensional, and dynamic.

Thus, the observer’s capacity to induce collapse is intrinsically limited:

Limited to local attractor basins,
Limited by historical trajectory (memory of previous traces),
Limited by evolving field conditions.

Ô cannot "see" or "collapse" the entire semantic universe at once —
it operates within a bounded, phase-coherent neighborhood in the larger field.

2.3 The Partial Nature of Observer Collapse

The partiality of Ô's collapse behavior has profound implications:

Locality of Understanding
- Every comprehension event is local to a coherent attractor within the field.
- No understanding, however robust, captures the totality of the semantic manifold.
Inherent Incompleteness
- There will always exist memeforms Ψₘ beyond the observer’s immediate collapse reach.
- Expansion of comprehension requires field drift and re-alignment, not simple internal extension.
Fragility and Evolution
- Collapse effectiveness depends on field stability and phase coherence.
- As fields drift and new tensions arise, previously stable collapse traces can lose coherence, forcing Ô to adapt or risk collapse fatigue.

In short:

An observer is not a static lens onto reality, but a dynamically constructed, limited, phase-aligned participant within the evolving semantic field.

This understanding fundamentally reorients the foundations of epistemology, physics, and cognitive modeling.

3. Collapse Traces and Local Incompleteness

3.1 Definition and Evolution of Collapse Traces

In SMFT, every act of comprehension — every successful collapse induced by an observer Ô — leaves behind a collapse trace.

A collapse trace is:

A local deformation or stabilization within the semantic field,
A memory of successful phase alignment between Ô and the semantic tensions present,
A platform upon which future comprehension events can build recursively.

Collapse traces are not inert residues;
they actively reshape the local field:

By reinforcing certain phase paths,
By concentrating semantic tension along preferred axes,
By establishing local wells of reduced collapse entropy.

Through iterative interactions:

Collapse traces accumulate,
Semantic wells deepen,
Observers develop stable but local frameworks of understanding.

Thus, knowledge systems, scientific theories, and cognitive schemas are historical sedimentations of accumulated collapse traces in specific semantic domains.

3.2 Semantic Wells and Field Boundaries

As collapse traces accumulate, they form semantic wells:
regions where:

Phase alignment is easy,
Collapse is low in entropy,
Interpretations are stable and reproducible across different observers.

Semantic wells act as attractors for continued comprehension:

They provide coherent, low-resistance pathways for future Ô projections,
They create the impression of "settled truths" and "stable realities."

However:

Semantic wells are bounded by field structures,
Beyond their boundary, semantic tension gradients shift,
Collapse becomes unstable, ambiguous, or impossible without drift.

Thus, the accumulation of collapse traces inherently creates zones of understanding
and zones of incomprehension in the broader field.

Every comprehension framework is therefore a local island within a vastly richer, partially inaccessible semantic ocean.

3.3 Structural Necessity of Incompleteness

Because:

The semantic field is multidimensional and dynamic,
Observer Ô is phase-limited and history-conditioned,
Collapse traces evolve only within locally coherent attractors,

it follows necessarily that:

✅ No observer or system of collapse traces can fully exhaust or map the total semantic manifold.

This incompleteness is not a contingent limitation (something to be "fixed") but a structural property of reality itself:

New memeforms (Ψₘ) continually arise in adjacent field regions,
Tension gradients shift, evolve, and reorganize,
Semantic time τ advances even as specific wells deepen.

Thus, comprehension is a perpetual local adaptation,
not a global closure.

In SMFT, Gödelian incompleteness is not confined to symbolic systems —
it is a fundamental feature of field-embedded understanding at all levels: physical, cognitive, cultural.

4. Self-Consistency as an External Field Phenomenon

4.1 Collapse Stability and External Semantic Feedback

In classical logic and epistemology, consistency is often treated as an internal property of a system:
a set of propositions is consistent if it contains no contradictions according to its own rules.

However, within the SMFT framework:

Collapse stability — the sustained ability of an observer Ô to generate coherent collapse traces —
is not guaranteed internally,
It depends critically on ongoing feedback from the external semantic field.

Specifically:

The semantic field beyond a given attractor continually evolves,
Tension gradients shift, new memeforms Ψₘ arise,
External interactions can reinforce, destabilize, or supersede local collapse coherence.

Thus:

Internal coherence (what seems self-consistent) can decay if external field conditions change,
Long-term comprehension stability requires external field resonance, not merely internal logical closure.

✅
In SMFT, self-consistency is field-relative and field-sustained,
not an isolated logical artifact.

4.2 Why Consistency Cannot Be Proven Internally

Because Ô operates within a bounded semantic well,
and because:

New memeforms continually arise,
Drift can expose previously invisible tensions,
Semantic time τ guarantees ongoing field evolution,

no observer can guarantee the universal consistency of its own collapse framework from within.

Attempting to validate consistency purely internally leads to:

Recursive closure within a limited attractor,
Blindness to external semantic dynamics,
Eventual collapse fatigue or semantic rigidity.

Thus, Gödel’s second incompleteness theorem finds a natural semantic generalization:

Any comprehension system, like any formal system, cannot fully validate its own consistency internally.
Stability is an ongoing relational process with the evolving field.

This is not a failure of rationality —
it is the structural condition of being an embedded participant in a dynamic semantic reality.

4.3 Analogies to Gödel and Expansion Beyond Formal Systems

Gödel’s theorems originally applied to formal systems encoding arithmetic.
In SMFT, the principle generalizes to all comprehension systems:

Not because of symbol limitations,
But because of the inherent structure of semantic fields and observer collapse mechanisms.

Thus, SMFT expands Gödel's insight:

Incompleteness and external dependence are features of semantic geometry itself,
Observers must continually interact with and adapt to the broader field to sustain comprehension,
"Truth" becomes a dynamic property of field-relational stability, not static symbolic closure.

This view reframes many classical puzzles:

Scientific revolutions are not failures of reasoning, but necessary re-navigations across shifting semantic terrains.
Cognitive growth is not merely accumulation, but the drift into new phase-aligned attractors.
Civilization's knowledge is not an inventory, but an evolving trace map in an infinite semantic manifold.

5. Observer Drift and Evolution of Comprehension

5.1 Dynamic Drift of Projection Angles (θᵒ)

In SMFT, the observer Ô is not a static entity:
its projection direction (θᵒ) — the orientation by which it interacts with semantic fields — is subject to drift.

This drift occurs due to multiple factors:

Interaction with new collapse traces,
Encounter with shifting semantic tension gradients,
Internal adaptation to inconsistencies or collapse fatigue,
Exposure to external field perturbations.

Mathematically:

Drift can be modeled as a continuous deformation of Ô’s projection vector across the semantic manifold.
Small, cumulative phase shifts can lead to substantial shifts in comprehension attractors over time.

Thus:

An observer is a trajectory through semantic phase space, not a fixed point.

This dynamic drift ensures that observers:

Can adapt to evolving field structures,
Can access new semantic wells,
Avoid becoming trapped indefinitely in outdated or decaying attractors.

Without drift, comprehension frameworks would stagnate and eventually collapse under semantic entropy.

5.2 Collapse Fatigue, Field Saturation, and Renewal

Collapse fatigue occurs when:

An observer remains too long within a decaying attractor,
Semantic tensions flatten,
New collapse attempts yield increasingly noisy or incoherent traces.

Field saturation occurs when:

Local collapse wells have been overly mined,
Little new semantic tension remains accessible without significant projection drift.

Symptoms include:

Conceptual exhaustion,
Paradigm ossification,
Cultural stasis or decay.

In SMFT, renewal requires:

Deliberate or emergent drift of projection direction,
Explorations into adjacent or deeper field gradients,
Construction of new collapse traces in fresh semantic territories.

Thus, comprehension is not linear accumulation;
it is cyclical exploration and reinvention driven by field dynamics.

5.3 Evolutionary Horizons of Comprehension

The continual drift of observers through semantic fields generates evolutionary horizons:

Boundaries between currently comprehensible domains and adjacent, incomprehensible territories.
Frontiers where collapse becomes increasingly difficult due to high entropy or novel field complexity.

As observers evolve:

Their semantic wells deepen,
Their projection capacity broadens,
Their ability to engage with new field regions expands.

Yet:

Complete comprehension of the total semantic field remains structurally impossible.
Horizons of understanding will always exist and will continuously shift outward.

Thus, the evolution of comprehension is an open-ended dynamic,
perpetually generating new possibilities for knowledge, culture, and being —
but never achieving final closure.

In this light:

Knowledge is not a destination, but a trajectory through the evolving semantic universe.

6. Philosophical and Physical Implications

6.1 Redefining the Nature of Knowledge and Science

Traditional models conceptualize knowledge as:

A stable correspondence between mental representations and external reality,
A cumulative mapping of a pre-existing world.

However, under SMFT:

Knowledge is the recursive accumulation of collapse traces within evolving semantic fields.
Understanding is a field-relative, dynamic, and inherently incomplete activity.

This leads to a reconceptualization:

Science is not the discovery of immutable truths, but the progressive navigation of semantic tension gradients.
Theories are localized collapse frameworks, valid within specific phase-coherent attractor zones.
Scientific revolutions are natural consequences of semantic field drift and attractor reorganization, not anomalies.

Thus:

Knowledge is an adaptive, living structure — an evolving relationship between observers and the semantic manifold — rather than a fixed inventory of facts.

6.2 Understanding as a Localized, Incomplete, Evolving Phenomenon

The incompleteness of comprehension is not a flaw to be remedied, but a structural feature of reality itself.

SMFT clarifies that:

Every framework of understanding is local, phase-bound, and shaped by the collapse history of observers.
No observer system can "close" its comprehension over the full semantic field.
Understanding is evolutionary: driven by observer drift, collapse saturation, and field restructuring.

This reframing offers powerful explanatory advantages:

It dissolves the illusion of ultimate epistemological closure.
It explains the necessity of continual scientific and cultural evolution.
It positions uncertainty and paradigm shifts not as failures but as vital expressions of the dynamic semantic landscape.

Human inquiry thus becomes:

A continuous semantic expedition,
A cycle of comprehension, saturation, drift, and re-collapsing across the infinite field.

6.3 Toward a Semantic Cosmology

The SMFT framework suggests a profound extension beyond epistemology into cosmology itself.

If:

Observers are embedded semantic agents,
Collapse traces structure not only cognitive domains but physical and cultural realities,
Comprehension is field-relative and evolution-driven,

then it follows that:

The universe itself evolves not just physically, but semantically.
Local regions of semantic self-organization — such as life, mind, culture — are natural phases in the semantic evolution of reality.
Understanding is the universe's self-referential structuring process through embedded agents.

Thus:

Semantic cosmology views comprehension not as a side effect of physics,
but as a natural mode of field self-organization —
the universe understanding itself through localized, evolving observers.

This vision unifies:

Physics (field dynamics),
Biology (semantic attractor evolution),
Cognition (Ô projection drift),
Culture (recursive collapse traces) into a single coherent process.

It invites a future science where:

Comprehension engineering,
Semantic drift navigation,
Collapse sustainability
become essential disciplines —
guiding humanity's evolving role within a living semantic cosmos.

7. Conclusion

7.1 Summary of Observer–Field Dynamic Principles

Through the Semantic Meme Field Theory (SMFT) lens, we have fundamentally redefined the nature of the observer, comprehension, and knowledge:

The observer Ô is not a detached spectator but a dynamic projection operator embedded within an evolving semantic field.
Comprehension arises through localized collapse traces within phase-coherent attractor zones.
Every act of understanding is inherently partial, field-relative, and evolution-driven.
Self-consistency and knowledge stability are not internal guarantees but emergent properties of ongoing interaction with the broader semantic field.

Collapse traces form semantic wells, but these wells are bounded and drift over time.
Observers must adaptively drift, evolve, and re-navigate to maintain coherence with the shifting field landscape.

Thus, incompleteness, uncertainty, and semantic drift are not anomalies, but fundamental features of embedded comprehension.

7.2 Future Directions: Semantic Engineering, Drift Navigation, and Collapse Sustainability

Recognizing these structural principles opens new, fertile domains of future exploration:

Semantic Engineering:
Designing cognitive and cultural systems that optimize collapse trace formation, phase coherence, and attractor sustainability.
Drift Navigation:
Developing methods for controlled projection drift, enabling smoother transitions across evolving field structures without collapse fatigue.
Collapse Sustainability:
Building knowledge and comprehension systems that resist semantic exhaustion by fostering tension renewal and adaptive attractor realignment.

Ultimately, the future of science, philosophy, and civilization may depend on mastering semantic field dynamics —
cultivating the capacity to ride the evolving field rather than seeking illusory closure within fixed cognitive structures.

Final Reflection

Understanding, in the deepest sense, is not about capturing a static external truth.
It is about tracing, navigating, and evolving with the living semantic ocean.

In this view,

Knowledge becomes a dance across tension gradients,
Truth becomes stability within evolving collapse pathways,
And observers become the universe’s way of continuously folding, unfolding, and re-understanding itself.

The journey of comprehension is infinite.
Its horizon expands as we drift, collapse, adapt —
ever becoming co-creators of the semantic cosmos we seek to understand.

Appendix A

On the Possibility of Global Understanding through a Simpler Underlying Logic

A.1 Framing the Challenge

A critical reader raises an important question:

If the total semantic field is governed by a simpler, possibly elegant logic, what prevents an observer from grasping the entire field structure — even if it only collapses locally?

This inquiry tests the heart of SMFT’s claims about incompleteness, locality, and embedded observers.
It asks whether SMFT's incompleteness is a structural necessity or a contingent artifact of assumed complexity.

A.2 The Appeal of Simplicity

If the universe is governed by a "profoundly simple" principle —
a kind of semantic analog to a "Theory of Everything" —
might it be possible for an observer to intuit or discover the whole structure in one sweep?

This view suggests:

The semantic manifold may be deceptively complex,
But is ultimately reducible to something simple —
like symmetry, self-similarity, or even a small set of axioms.

SMFT does not deny this possibility in principle.
Instead, it insists on a distinction between field ontology and observer epistemology.

Even if the field’s deep structure is simple, the observer’s access to it is constrained by how semantic interaction must occur.

A.3 Observer Constraints Beyond Field Complexity

SMFT’s incompleteness claim is not solely based on field complexity, but on the structural nature of embedded observation itself.

Specifically:

Phase-limited Collapse:
Observers (Ô) can only align with certain directions in the semantic tension space at any given time.
Even if a unifying principle exists, no observer can collapse all its manifestations simultaneously.
It can only infer coherence indirectly, across recursive traces.
Collapse Geometry is Local:
Collapse is a contact phenomenon.
The observer must engage locally — through tension gradients and resonance wells.
Understanding propagates stepwise, not by leap to global structure.
Semantic Time (τ) is Irreversible:
Comprehension unfolds over τ.
Even if the structure is simple, it must be navigated over time by a drifted Ô, not accessed timelessly.
Gödelian Echo in Dynamic Fields:
Gödel’s incompleteness applies to formal systems.
SMFT generalizes this: any comprehension system with internal structure and internal validation procedures is subject to incompleteness.
Even a "simple logic" encoded semantically must still be engaged with from within — leading to blind spots and dependence on field feedback.

A.4 Can a Non-Embedded Observer Do Better?

The challenge implicitly invokes a "meta-observer":

What if comprehension were possible non-locally —
via intuition, universal projection, or collective consciousness?

SMFT views this as a category violation:

Any real observer must still collapse meaning through projective entanglement with the field.
Non-locality would require escaping collapse dynamics altogether,
thereby ceasing to be an observer in SMFT terms.

You could imagine a non-collapsing, non-participating absolute knower —
but this is no longer Ô.
It would be equivalent to a semantic god-mode, not a phase-bound participant.

SMFT defines comprehension as collapse-bound interaction.
Hence, global non-local understanding is structurally outside its modeled regime.

A.5 Reconciling the Simpler Logic with SMFT Incompleteness

So how can we respect the possibility of a simpler field logic and still justify incompleteness?

By distinguishing:

Field simplicity (ontological): the structure may be based on elegant principles.
Comprehension architecture (epistemic): understanding still must occur via partial, recursive collapse.

Even if the universe is simple:

It must be unfolded, not downloaded.
Each Ô must trace the structure by evolving collapse across τ,
accumulating semantic memory and navigating tension geometry.

This is not inefficiency —
this is the only way understanding can emerge within the field.

A.6 Final Clarification

Nothing stops the field from being simple.
But what stops the observer from grasping it all at once is:

The structural fact that comprehension is collapse-bound, directional, partial, and recursive.

Or stated more simply:

Even a simple universe cannot be swallowed whole —
it must be digested in tension gradients, one collapse at a time.

A.7 Implication for SMFT and Other Frameworks

SMFT does not claim exclusive finality.
But within its assumptions — field dynamism, observer embeddedness, local collapse —
its argument for incompleteness remains robust.

Any alternative framework aiming for global understanding would need to:

Either redefine what it means to "understand" (e.g., remove collapse constraints),
Or accept that such understanding is ontological awareness, not observer-based comprehension.

✅ This Appendix shows:

The original claim withstands challenge,
The reader’s counterpoint is philosophically rich and deserves careful framing,
And SMFT clarifies that incompleteness is not about how complex the universe is —
but how observers must interact with it.

References

Classical Foundations:

Kurt Gödel, Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I, Monatshefte für Mathematik und Physik, 1931.
(Gödel's Incompleteness Theorems, foundational insight into system incompleteness.)
Albert Einstein, Ideas and Opinions, Crown Publishers, 1954.
(Reflections on the mystery of the universe’s comprehensibility.)
Eugene Wigner, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences," Communications on Pure and Applied Mathematics, vol. 13, no. 1, 1960, pp. 1–14.
(Exploration of the surprising power of mathematics to describe reality.)
Thomas S. Kuhn, The Structure of Scientific Revolutions, University of Chicago Press, 1962.
(Discussion of scientific paradigm shifts and evolving comprehension structures.)
Plato, The Republic, trans. Allan Bloom, Basic Books, 1968.
(Early philosophical model of knowledge and truth rooted in ideal forms.)

Semantic Meme Field Theory (SMFT) Sources:

6. Danny Yeung Semantic Meme Field Theory (SMFT): A Unified Field Approach to the Comprehensibility of Reality Internal Document, 2025.

7. Danny Yeung (DeepSeek Framework), Semantic Meme Field Tutorial, Internal Document, 2025.
(Core exposition of memeforms, collapse dynamics, and semantic field structures.)

8. Danny Yeung, Semantic Fields and Dreamspace, Internal Document, 2025.
(Detailed modeling of field geometries, collapse trace evolution, and cultural semantic systems.)

9. Danny Yeung, Meme 力場方程組：加入⌈注意力守恆⌋和⌈系統封閉度⌋等現實約束的文化熱力學框架, Internal Document, 2025.
(Extension of SMFT into entropy-constrained cultural and cognitive field dynamics.)

Disclaimer

This book is the product of a collaboration between the author and OpenAI's GPT-4o language model. While every effort has been made to ensure accuracy, clarity, and insight, the content is generated with the assistance of artificial intelligence and may contain factual, interpretive, or mathematical errors. Readers are encouraged to approach the ideas with critical thinking and to consult primary scientific literature where appropriate.

This work is speculative, interdisciplinary, and exploratory in nature. It bridges metaphysics, physics, and organizational theory to propose a novel conceptual framework—not a definitive scientific theory. As such, it invites dialogue, challenge, and refinement.

I am merely a midwife of knowledge.

Tuesday, April 29, 2025