Originally posted by edmc^2
All of these in one form of explenation or another are blindly accepted as facts from which you want us to falsify. So how do you falsify something that is false?

For example, the fossil record does not support evolution - even now there's no solid evidence from the fossil records where an amphebian turning into a mammal gradually or through 'punctuated equilibrium'.

Paleothyris (early Pennsylvanian) -- An early captorhinomorph reptile, with no temporal fenestrae at all.
Protoclepsydrops haplous (early Pennsylvanian) -- The earliest known synapsid reptile. Little temporal fenestra, with all surrounding bones intact. Fragmentary. Had amphibian-type vertebrae with tiny neural processes. (reptiles had only just separated from the amphibians)
Clepsydrops (early Pennsylvanian) -- The second earliest known synapsid. These early, very primitive synapsids are a primitive group of pelycosaurs collectively called "ophiacodonts".
Archaeothyris (early-mid Pennsylvanian) -- A slightly later ophiacodont. Small temporal fenestra, now with some reduced bones (supratemporal). Braincase still just loosely attached to skull. Slight hint of different tooth types. Still has some extremely primitive, amphibian/captorhinid features in the jaw, foot, and skull. Limbs, posture, etc. typically reptilian, though the ilium (major hip bone) was slightly enlarged.
Varanops (early Permian) -- Temporal fenestra further enlarged. Braincase floor shows first mammalian tendencies & first signs of stronger attachment to rest of skull (occiput more strongly attached). Lower jaw shows first changes in jaw musculature (slight coronoid eminence). Body narrower, deeper: vertebral column more strongly constructed. Ilium further enlarged, lower-limb musculature starts to change (prominent fourth trochanter on femur). This animal was more mobile and active. Too late to be a true ancestor, and must be a "cousin".
Haptodus (late Pennsylvanian) -- One of the first known sphenacodonts, showing the initiation of sphenacodont features while retaining many primitive features of the ophiacodonts. Occiput still more strongly attached to the braincase. Teeth become size-differentiated, with biggest teeth in canine region and fewer teeth overall. Stronger jaw muscles. Vertebrae parts & joints more mammalian. Neural spines on vertebrae longer. Hip strengthened by fusing to three sacral vertebrae instead of just two. Limbs very well developed.
Dimetrodon, Sphenacodon or a similar sphenacodont (late Pennsylvanian to early Permian, 270 Ma) -- More advanced pelycosaurs, clearly closely related to the first therapsids (next). Dimetrodon is almost definitely a "cousin" and not a direct ancestor, but as it is known from very complete fossils, it's a good model for sphenacodont anatomy. Medium-sized fenestra. Teeth further differentiated, with small incisors, two huge deep- rooted upper canines on each side, followed by smaller cheek teeth, all replaced continuously. Fully reptilian jaw hinge. Lower jaw bone made of multiple bones & with first signs of a bony prong later involved in the eardrum, but there was no eardrum yet, so these reptiles could only hear ground-borne vibrations (they did have a reptilian middle ear). Vertebrae had still longer neural spines (spectacularly so in Dimetrodon, which had a sail), and longer transverse spines for stronger locomotion muscles.
Biarmosuchia (late Permian) -- A therocephalian -- one of the earliest, most primitive therapsids. Several primitive, sphenacodontid features retained: jaw muscles inside the skull, platelike occiput, palatal teeth. New features: Temporal fenestra further enlarged, occupying virtually all of the cheek, with the supratemporal bone completely gone. Occipital plate slanted slightly backwards rather than forwards as in pelycosaurs, and attached still more strongly to the braincase. Upper jaw bone (maxillary) expanded to separate lacrymal from nasal bones, intermediate between early reptiles and later mammals. Still no secondary palate, but the vomer bones of the palate developed a backward extension below the palatine bones. This is the first step toward a secondary palate, and with exactly the same pattern seen in cynodonts. Canine teeth larger, dominating the dentition. Variable tooth replacement: some therocephalians (e.g Scylacosaurus) had just one canine, like mammals, and stopped replacing the canine after reaching adult size. Jaw hinge more mammalian in position and shape, jaw musculature stronger (especially the mammalian jaw muscle). The amphibian-like hinged upper jaw finally became immovable. Vertebrae still sphenacodontid-like. Radical alteration in the method of locomotion, with a much more mobile forelimb, more upright hindlimb, & more mammalian femur & pelvis. Primitive sphenacodontid humerus. The toes were approaching equal length, as in mammals, with #toe bones varying from reptilian to mammalian. The neck & tail vertebrae became distinctly different from trunk vertebrae. Probably had an eardrum in the lower jaw, by the jaw hinge.
Procynosuchus (latest Permian) -- The first known cynodont -- a famous group of very mammal-like therapsid reptiles, sometimes considered to be the first mammals. Probably arose from the therocephalians, judging from the distinctive secondary palate and numerous other skull characters. Enormous temporal fossae for very strong jaw muscles, formed by just one of the reptilian jaw muscles, which has now become the mammalian masseter. The large fossae is now bounded only by the thin zygomatic arch (cheekbone to you & me). Secondary palate now composed mainly of palatine bones (mammalian), rather than vomers and maxilla as in older forms; it's still only a partial bony palate (completed in life with soft tissue). Lower incisor teeth was reduced to four (per side), instead of the previous six (early mammals had three). Dentary now is 3/4 of lower jaw; the other bones are now a small complex near the jaw hinge. Jaw hinge still reptilian. Vertebral column starts to look mammalian: first two vertebrae modified for head movements, and lumbar vertebrae start to lose ribs, the first sign of functional division into thoracic and lumbar regions. Scapula beginning to change shape. Further enlargement of the ilium and reduction of the pubis in the hip. A diaphragm may have been present.
Dvinia [also "Permocynodon"] (latest Permian) -- Another early cynodont. First signs of teeth that are more than simple stabbing points -- cheek teeth develop a tiny cusp. The temporal fenestra increased still further. Various changes in the floor of the braincase; enlarged brain. The dentary bone was now the major bone of the lower jaw. The other jaw bones that had been present in early reptiles were reduced to a complex of smaller bones near the jaw hinge. Single occipital condyle splitting into two surfaces. The postcranial skeleton of Dvinia is virtually unknown and it is not therefore certain whether the typical features found at the next level had already evolved by this one. Metabolic rate was probably increased, at least approaching homeothermy.
Thrinaxodon (early Triassic) -- A more advanced "galesaurid" cynodont. Further development of several of the cynodont features seen already. Temporal fenestra still larger, larger jaw muscle attachments. Bony secondary palate almost complete. Functional division of teeth: incisors (four uppers and three lowers), canines, and then 7-9 cheek teeth with cusps for chewing. The cheek teeth were all alike, though (no premolars & molars), did not occlude together, were all single- rooted, and were replaced throughout life in alternate waves. Dentary still larger, with the little quadrate and articular bones were loosely attached. The stapes now touched the inner side of the quadrate. First sign of the mammalian jaw hinge, a ligamentous connection between the lower jaw and the squamosal bone of the skull. The occipital condyle is now two slightly separated surfaces, though not separated as far as the mammalian double condyles. Vertebral connections more mammalian, and lumbar ribs reduced. Scapula shows development of a new mammalian shoulder muscle. Ilium increased again, and all four legs fully upright, not sprawling. Tail short, as is necessary for agile quadrupedal locomotion. The whole locomotion was more agile. Number of toe bones is 2.3.4.4.3, intermediate between reptile number (2.3.4.5.4) and mammalian (2.3.3.3.3), and the "extra" toe bones were tiny. Nearly complete skeletons of these animals have been found curled up - a possible reaction to conserve heat, indicating possible endothermy? Adults and juveniles have been found together, possibly a sign of parental care. The specialization of the lumbar area (e.g. reduction of ribs) is indicative of the presence of a diaphragm, needed for higher O2 intake and homeothermy. NOTE on hearing: The eardrum had developed in the only place available for it -- the lower jaw, right near the jaw hinge, supported by a wide prong (reflected lamina) of the angular bone. These animals could now hear airborne sound, transmitted through the eardrum to two small lower jaw bones, the articular and the quadrate, which contacted the stapes in the skull, which contacted the cochlea. Rather a roundabout system and sensitive to low-frequency sound only, but better than no eardrum at all! Cynodonts developed quite loose quadrates and articulars that could vibrate freely for sound transmittal while still functioning as a jaw joint, strengthened by the mammalian jaw joint right next to it. All early mammals from the Lower Jurassic have this low-frequency ear and a double jaw joint. By the middle Jurassic, mammals lost the reptilian joint (though it still occurs briefly in embryos) and the two bones moved into the nearby middle ear, became smaller, and became much more sensitive to high-frequency sounds.
Cynognathus (early Triassic, 240 Ma; suspected to have existed even earlier) -- We're now at advanced cynodont level. Temporal fenestra larger. Teeth differentiating further; cheek teeth with cusps met in true occlusion for slicing up food, rate of replacement reduced, with mammalian-style tooth roots (though single roots). Dentary still larger, forming 90% of the muscle-bearing part of the lower jaw. TWO JAW JOINTS in place, mammalian and reptilian: A new bony jaw joint existed between the squamosal (skull) and the surangular bone (lower jaw), while the other jaw joint bones were reduced to a compound rod lying in a trough in the dentary, close to the middle ear. Ribs more mammalian. Scapula halfway to the mammalian condition. Limbs were held under body. There is possible evidence for fur in fossil pawprints.
Diademodon (early Triassic, 240 Ma; same strata as Cynognathus) -- Temporal fenestra larger still, for still stronger jaw muscles. True bony secondary palate formed exactly as in mammals, but didn't extend quite as far back. Turbinate bones possibly present in the nose (warm-blooded?). Dental changes continue: rate of tooth replacement had decreased, cheek teeth have better cusps & consistent wear facets (better occlusion). Lower jaw almost entirely dentary, with tiny articular at the hinge. Still a double jaw joint. Ribs shorten suddenly in lumbar region, probably improving diaphragm function & locomotion. Mammalian toe bones (2.3.3.3.3), with closely related species still showing variable numbers.
Probelesodon (mid-Triassic; South America) -- Fenestra very large, still separate from eyesocket (with postorbital bar). Secondary palate longer, but still not complete. Teeth double-rooted, as in mammals. Nares separated. Second jaw joint stronger. Lumbar ribs totally lost; thoracic ribs more mammalian, vertebral connections very mammalian. Hip & femur more mammalian.
Probainognathus (mid-Triassic, 239-235 Ma, Argentina) -- Larger brain with various skull changes: pineal foramen ("third eye") closes, fusion of some skull plates. Cheekbone slender, low down on the side of the eye socket. Postorbital bar still there. Additional cusps on cheek teeth. Still two jaw joints. Still had cervical ribs & lumbar ribs, but they were very short. Reptilian "costal plates" on thoracic ribs mostly lost. Mammalian #toe bones.
Exaeretodon (mid-late Triassic, 239Ma, South America) -- (Formerly lumped with the herbivorous gomphodont cynodonts.) Mammalian jaw prong forms, related to eardrum support. Three incisors only (mammalian). Costal plates completely lost. More mammalian hip related to having limbs under the body. Possibly the first steps toward coupling of locomotion & breathing. This is probably a "cousin" fossil not directly ancestral, as it has several new but non-mammalian teeth traits.