Conjecture of relation between residues of Feynman integrals and mixed Tate motives

Question

In many articles (for example in articles given by M.Marcoli) there is statement that there is the following conjecture

Residues of Feynman integrals in scalar field theories are always periods of mixed Tate motives

I have three questions related to this conjecture

1) What is the recent knowledge of this conjecture ? Is it proven or partially proven ? (Articles which I read have at least five/six years).

2) One of the supporting evidence were computations collected by Broadhurst and Kreimer. Where can I found more actual data (if such exist) ?

3) Is it a generalization of this conjecture on bosonic/fermionic field theories ?

Answer 1

1) Counterexamples were found in the paper Brown, Francis; Schnetz, Oliver: "A $K3$ in $\phi^4$". Duke Math. J. 161 (2012), no. 10, 1817–1862. It is now the general feeling that most $\phi^4$-Feynman integrals are not mixed Tate.

2) In 2008, Schnetz has compiled a list of Feynman integrals in Quantum periods: A census of $\phi^4$-transcendentals. These were obtained using numerical computations. Meanwhile, for all results rigorous proofs have been found.

3) No clue.