You are mistaken.
I have shown you two examples where the lines of descent are clear and unbroken because the fossil record is very complete. There are many more. The degree of certainty regarding lines of descent is proportional exactly to the amount of fossils one has. Furthermore evolutionary theory is entirely about closely related evolving populations of organisms that share a gene pool. Thus the establishment of
cladograms through genetic and fossil records is sufficient evidence for its validity. The idea of who begat who ala Bible or those obsessed with lineage is
completely useless for validating the theory of evolution. Apart from cladograms, the only other descent tree that are useful are gene trees which do provide scientifically relevant information. The reason is simple...because sexual reproduction causes random shuffling of genes from mother-father to sibling, in only a few generation, no characteristic feature of your descent line survives the shuffling process. Hence generational descent trees are utterly useless apart from old (and unscientific) conceptions of regal lineages etc. (Its different in bacteria, who reproduce asexually and whose descent trees really do matter). Please read the article below to gain a basic understanding of how to develop cladograms that have useful scientific information.
Understanding Evolutionary Trees
No evolutionary scientist cares about descent lines (as its unscientific and tells us nothing). But the cladograms for fish to amphibian evolution is indeed accepted in all science. Textbooks showing the universal scientific consensus are there:-
Gaining Ground
If new species are found (and will be found), they will be added as branches to the cladogram, but the structure of the cladogram is unlikely to change given the evidence we have for it. However there are currently no gaps in the fish to amphibian fossil record as the stages of evolution are well captured by the current fossils,and validated by genetics. New species will of course be discovered showing new variation in the theme, but while they increase understanding, they do not fill any gap.
Its like this, a new coffee shop down the street may add to our experience in coffee drinking, but does not fill any gap in our knowledge of coffee. Not the case in all cases, there are places where lack of fossils create genuine gaps, like how flowers evolved and diversified,
but fish to amphibian evolution is not such a case.
Punctuated evolution is also a form of gradualism that occurs through the usual mutation and natural selection processes over millions of years. Read a book on the topic.
Actually the fish to amphibian transition and all the evidence I linked to is a case of punctuated evolution. Its punctuated, because the transition happened quite rapidly..which for biologists mean
10-15 million years. Rapidity is in relation to the usual units of time in a field, and for earth's history hundreds or millions of years are usual units of time. Furthermore, every species along a transitional gradient is a fully complete form adapted to the environment it lives in.
Where do you get the erroneous idea that transitional species and their organs are not fully complete and adaptive and functional in their environment? Indeed species like Tiktaalik which is transitional between fish and amphibians, was well adapted to the shallow estuarine environments it lived in, and to which its transitional fin-limb appendages were well adapted.
Evolutionary theory will be falsified if partially formed creatures and hopeful monsters are ever uncovered. Do you even know what the theory is and what kind of fossils it predicts? Where do you get all this false information about evolution from.
Who has been lying to to you?
Here is the correct theory and its predictions:-
What is Evolution?
What is Evolution?