Lü suggests the idea of one treading on the tail of a tiger, that does not bite him. There will be progress and success.
10. Lü - Treading carefully.

For a better understanding it is advised to read the China Labyrinth</a> and the Structure of a Connexion first.

Treading carefully
The I Ching Connexion is based on a discovery rather than an invention. The same may be true, eventually, for its interpretation. There are new aspects to consider, like the relative positions of the actual and future hexagram, waning and waxing influences and the mediator. This is a record of a framework for interpretation as it suggested itself to me. How? I'm not sure. Where do thoughts and ideas originate? Strange things happen.

My advise is to rely on your own intuition as much as on my suggestions. May Whoever's up there be with you.

Yin and Yang
This is what the I says:

The closing of a door may be pronounced analogous to K'un, and the opening of it to Ch'ien. The transition in between may be called a change; and the continuous passing of one state to the other may be called the constant course of things. Ta Chuan - Section 1, Chapter XI-4.

Thus the closing of a door is a yin line changing into yang and the opening of a door is a yang line changing into yin.
This is the reason all yin-lines in a connexion are open and all yang lines closed. Yin-lines are receptive and change according to influences of adjacent hexagrams. You will find that for a yin line there are always precisely 8 hexagrams that meet the conditions for connecting up, and thus for influencing the hexagram via that particular line.
Yang lines don't have adjacent hexagrams and change according to their inner workings.
This is what the I says:

Ch'ien, thus originating, is able to benefit all under the sky. We are not told how its benefits are conferred, but how great is its operation! How great is Ch'ien! Strong, vigorous, undeflected, correct, and in all these: pure, unmixed, exquisite.
1. Ch'ien - The Creative Principle, Wen Yen, on the entire hexagram, d.3, d.4.

The Mediator
Yang is characterized by invariability, yin by variablity. These qualities are expressed in the mediator's nature: the hexagram it resides in has, by definition, yin lines in the positions where the actual hexagram changes its lines and yang lines where it doesn't.
If you care to investigate, you'll find that an actual hexagram, a future hexagram and the mediator can switch their roles at random! Pick any two hexagrams as actual and future hexagram and determine the mediator by its definition. Now pick any two of the three as the new actual and future hexagram, and the third will be the mediator!

In terms of interpretation, the mediator governs the transition from the actual hexagram to future hexagram, representing heaven's influence on earth. It represents the heavenly messengers, the 'Kwei Shen', or 'Spiritual Intelligences', as Legge translates the written characters when used binomially together.
'Kwei' is used for an earthbound spirit, in particular a human spirit disembodied, 'Shen' for one whose seat is in heaven. These two sides should both be taken into account: spiritual intelligences have the power of working someone's mind without one being aware of it, as happened to me when I was working at the solution of the octopuszle.
They also, by their very sense of humour, may have demon- as well as angel-like qualities inviting response.
In the words of the I:

Notes of the same key respond to one another; creatures of the same nature seek one another. Things that draw their origin from heaven move towards what is above; things that draw their origin from the earth cleave to what is below: so does everything follow its kind'.
1. Ch'ien - The Creative Principle, Wen Yen, nine in the fifth place, a.8.

Or to put it bluntly:

Spiritual Beings inflict calamity on the full and bless the humble.
15. Ch'ien - Modesty, commentary on the Judgement.

The mediator never represents the subject, therefore the lines do not apply. His nature may be known from the miscellaneous signs, that often pinpoint a main characteristic, and from those parts of the judgement and commentary that address the hexagram itself, or the nature of the interaction of the composite trigrams, rather than the subject.
Whether his influence is good or bad depends on the subject's relation to Whoever's up there. If help is extended to him or her from heaven, the mediator will always have a good influence!
As it is said in the I:

The great man is he who is in harmony, in his attributes, with heaven and earth; in his brightness, with the sun and moon; in his orderly procedure, with the four seasons; and in his relation to what is fortunate and what is calamitous, in harmony with the spirit-like operations of providence.
He may precede heaven, and heaven will not act in opposition to him; he may follow heaven, but only to act as heaven at the time would do. If heaven will not act in opposition to him, how much less will men! how much less will the spirit-like operations of providence!

1. Ch'ien - The Creative Principle, Wen Yen, nine in the fifth place, d.11.

Mediator math
If you use the connexion regularly, you may notice that the mediator will touch base in Ch'ien every now and then, but will very rarely appear in K'un. In other words, 'no lines changing' is a regular occurrence, but 'all lines changing' is not. This is because in a random context there's only a one in four chance of a line changing: after the first coin, the outcome of which is irrelevant, the second gives a fifty-fifty chance of the line being unchanging and so, again, does the third. Thus unchanging lines, in the long run, outnumber changing ones by a factor three.
The chance of 'all lines changing' is 1/4 to the sixth power, or 1: 4096, whereas the chance of 'no lines changing' is 3/4 to the sixth power, or 729: 4096. This explains the difference in frequency. It also explains why in the long run the average number of changing lines in a divination will be 6 x (1/4), or one and a half.
The mediator therefore will frequently appear in hexagrams with four or five yang lines and occasionally six. This shows its inclination towards heaven.

If no lines change, the mediator is in Ch'ien, displaying transcendent strength but withdrawn from earthly matters. The subject's actuality with regard to his question, whether it be good or bad, is not about to change, and he will have to rely on the interpretation of his one hexagram without heavenly intervention.

If all lines change, a rare occurence, the mediator is in K'un, displaying weakness and docility, but with capacity and sustaining power The future hexagram will be the actual's inverse, and change on a wide scale is sure to come, and all the more dramatic if the inverse displays very opposite characteristics or tendencies.

Groups and Positions
Different groups of a connexion represent different spheres of action. The appearance of the actual and future hexagram in different groups, signifies the subject's moving from one sphere to another. It may also denote the existence of physical or spiritual separation, related to the subject's situation or question. In either case the transition may occur unexpectedly.
The size of a group is related to the degree of isolation involved. Ch'ien is the extreme example of containment. It is a group in itself, therefore it stands 'undeflected, pure, unmixed and exquisite'.
One should keep in mind however that 'isolation' is not necessarily a negative aspect: many things require it to a certain degree, for instance study or vacation. But in a negative context the appearance of the future hexagram in a small group should be taken as a warning that a tendency towards isolation may be getting the better of the subject.

If the actual and future hexagram are in the same group, the distance between them may signifiy the timescale involved. Nearness means that things may develop faster than expected! If adjacent, the actual and future hexagram may, in an obviously fast transition, even figure as 'waning or waxing influences' on each other's lines. This can, in terms of interpretation, give rise to more interesting situations than I can possibly cover.

If the mediator is in a seperate group, its influence requires no consideration. If it is in the same sphere as the actual or future hexagram, greater nearness means greater involvement, even more so if it resides in either of them, but also if it is adjacent and thus, possibly, a waning or waxing influence.

Waning and waxing influences
Waning and waxing influences concern the changing lines in the actual hexagram in their transition to the future hexagram. Being intermediate, they are open to interpretation in both directions. The mediator indicates the changing lines, but does not distinguish between them.

If a yin line changes, the hexagram adjacent to it is called a waning influence. It is the last influence the hexagram receives through that particular line before its closing and can be found in that very position, in a lighter shade.

If a yang-line changes, the hexagram adjacent to the corresponding line in the future hexagram is called a waxing influence. It is the first influence the hexagram receives through that particular line after its opening and should be interpreted in that context. It can be found in the indicated position, in a darker shade.

An influence may be waning in one line and waxing in another! This indicates a shift of the influence, either in time or in approach, from one aspect of the question to another. The program then alternates the lighter and darker shades.

Without the connexion the lines of the future hexagram are often ignored or considered open only to global interpretation. Within the context of a connexion a more specific interpretation becomes possible.

The nature of an influence can, like the mediator's, be read from the miscellaneous signs and from those parts of the judgement and commentary that address the hexagram itself rather than the subject. It should be applied to the subject's situation in that particular line, either as an influence of the immediate past or an influence in the immediate future.

Very complex situations may arise, that require more than superficial analysis. As already mentioned, an influence may be waning in one line and waxing in another. Since lines also represent different levels of the subject's mind, this is not at all a contradiction. If they are adjacent, the actual hexagram itself may be a waxing influence in one of its own lines, or the future hexagram may be a waning influence. This may even happen simultaneously!
To further complicate matters, the mediator may at the same time be a waning or waxing influence, working specific lines on top of his general involvement. Only experience will show you the way in these rare but complex situations.
Trust yourself.
As it is said in the I:
When we minutely investigate the nature and reasons of things, till we have entered into the inscrutable and spirit-like in them, we attain to the largest practical application of them. Going beyond this comes a point, the nature of which is hardly knowable.
1. Ta Chuan - Section 2, Chapter V-3,4.

christian freeling