According to the conventional evolutionary-uniformitarian time scale of Earth history, multicellular organisms first appeared in abundance about 550 million years ago, in the "Big Bang of Evolution," the Cambrian explosion. But (again, according to the conventional time scale) a handful of odd multicellular organisms existed before the astonishing explosion of new forms in the Cambrian. These o...

Late Precambrian to early Cambrian sediments of the Amadeus Basin, Central Australia, contain two stable directions of magnetization. Lithologies are diverse and include red beds, green beds, and carbonates, all of which respond to thermal cleaning. Positive fold and unconformity tests, and a well-defined polarity zonation reveal the primary component and direction of magnetization. This direct...

We generalize the brick polytope of V. Pilaud and F. Santos to spherical subword complexes for finite Coxeter groups. This construction provides polytopal realizations for a certain class of subword complexes containing all cluster complexes of finite types. For the latter, the brick polytopes turn out to coincide with the known realizations of generalized associahedra, thus opening new perspec...

For an arbitrary Coxeter group W , Reading and Speyer defined Cambrian semilattices Cγ as sub-semilattices of the weak order onW induced by so-called γ-sortable elements. In this article, we define an edge-labeling of Cγ , and show that this is an EL-labeling for every closed interval of Cγ . In addition, we use our labeling to show that every finite open interval in a Cambrian semilattice is e...

Despite the protracted history of life on earth spanning well over 3.8 Ga, fossil record of the Precambrian (>543 Ma) largely documents only microscopic life. The mostly simple Precambrian life forms were followed by a sudden explosive radiation of multicellular animals at the turn of the Cambrian period (543-490 Ma) between 530 and 520 Ma ago, when almost two-thirds of the animal phyla make th...

We describe many different realizations with integer coordinates for the associahedron (i.e. the Stasheff polytope) and for the cyclohedron (i.e. the Bott-Taubes polytope) and compare them to the permutahedron of type A and B respectively. The coordinates are obtained by an algorithm which uses an oriented Coxeter graph of type An or Bn respectively as only input and which specialises to a proc...

The Middle Cambrian Oesia disjuncta, a monospecific genus, is known only from the celebrated Burgess Shale of British Columbia. It has been re−interpreted by Szaniawski (Acta Palaeontologica Polonica 50:1–8; 2005) as a chaetognath, a distinctive phylum whose exact position in the protostomes is still controversial. Unequivocal chaetognaths, that have no similarity to Oesia, are already known to...

Sparse material of an agnostid trilobite, previously referred to as Tomagnostus cf. corrugatus (Illing 1916), is recognized as a new species, T. brantevikensis n. sp. It occurs in the middle Cambrian (≈ Cambrian provisional Series 3) Triplagnostus gibbus and Acidusus atavus zones (Almbackenian regional Stage) in Scania, southernmost Sweden, but is very rare. The new species resembles T. corruga...

animal life on land. The current benchmark for evidence of plants on land is about 450,000,000 years ago (Late Ordovician). Tantalizing microscopic fossils of chemically resistant spore walls occur in land-derived rocks around the world, and predate this Late Ordovician age by over 50,000,000 years (Upper Cambrian) and possibly beyond. Figuring out what kinds of organisms (algae, primitive plan...

Ten phosphatized specimens of a small (<180 micrometers) animal displaying clear bilaterian features have been recovered from the Doushantuo Formation, China, dating from 40 to 55 million years before the Cambrian. Seen in sections, this animal (Vernanimalcula guizhouena gen. et sp. nov.) had paired coeloms extending the length of the gut; paired external pits that could be sense organs; bilate...