### Updates II

Let's spell this out clearly: Matti Pitkanen has calculated the observed radius of the Dark Matter ring using a TGD Bohr orbit analysis. An absurdly obvious resulting prediction is that the next observed dark matter ring will also sit at a Bohr radius.

Gukov et al have a new paper entitled Link Homologies and the Refined Topological Vertex, in which they look specifically at invariants of the Hopf link. "Our result is a first direct verification of a series of conjectures which identifies link homologies with the Hilbert space of BPS states in the presence of branes." Even cooler, check out the paper The Zeta-Function of a p-Adic Manifold, Dwork Theory for Physicists.

Gukov et al have a new paper entitled Link Homologies and the Refined Topological Vertex, in which they look specifically at invariants of the Hopf link. "Our result is a first direct verification of a series of conjectures which identifies link homologies with the Hilbert space of BPS states in the presence of branes." Even cooler, check out the paper The Zeta-Function of a p-Adic Manifold, Dwork Theory for Physicists.

## 5 Comments:

Dear Kea,

I found in the calculation besides a couple of typos and unpolished statements an error making result by a factor 10 too small. The conspiracy of errors produced the desired result as so many times earlier! This is really magic!

The replacement of v_0=2^(-11) with 3v_0 gives correct result and is allowed by the ruler-and-compass hypothesis.

Excellent, Matti. Actually, the factor of 3 is intriguing....

The appearance of n=3 is intriguing. Quite generally, a ratio of ruler-and compass integeres is allowed as multiplier of v_0. Power of two times product of distinct Fermat primes and there are four of them, and only 2 (3 and 5) differ signifantly from power of 2 for these purposes. In 15 per cent accuracy you can multiply or divide v_0 by 3 or 5 or multiply by 3/5 or 5/3 plus the power of 2 of course.

Why I believe that these integers are in a preferred role is that corresponding quantum phases are algebraically maximally simple: what you need is just square root function and a lot of rationals and these you got already in elementary school!;-)

Sad that the Dwork paper uses so totally different language that I am used to. Brany intuition might be useful in attempts to understand the generalization of imbedding space gluing together copies of H with discrete bundles structures H= M^4xCP_2 -->H/G along common points of base spaces.

Unfortunately I do not have any grasp to brane mathematics! Frustrating.

Matti

Your TGD imbedding space construction seems like a generalization of the recent Twistor Black Hole work of Neitzke et al, where they use a covariant c-map to relate (real) coordinates on M x CP^1 to complex coordinates on the twistor space Z.

I'm not sure what the brane interpretation is, but usually the M5 brane is related to CP^2. See Janssen et al's arxiv paper Giant Gravitons and Fuzzy CP^2.

Fascinating result; it shows a relation between the big and the small.

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