In blocks miners have an additional commitment, the commitment has a two
fields, a desired weakblock target, and a weakblock commitment hash.

The median weak-target of the last 11 blocks is used as the current weakblock
target.

A weakblock has a weakblock header.

The weakblock header lists the last block and last 11 weakblock hashes and
the times that the author saw them at. This is used by a non-normative
algorithm (not described) to set the weakblock targets in blocks.

The weak block also lists a single parent weakblock id or Block ID which
the weakblock will be based on. A weakblock cannot be accepted without 
also processing its parent.

The header then contains a hash-root for a set of transactions which
are strictly appended to the parent's transaction set.

When a new weakblock is received, after checking the difficulty its
parent connectivity is checked. If needed the parent is fetched first.
Transactions validation runs on the weakblock. (improved script
result caching will be needed).

The node keeps a memory of up to two dozen (say) weak block chain tips,
meaning up to storage for up to two dozen maximum size blocks. 
When a new tip comes in, it either supplants an existing one (by extending
it) or it doesn't if it doesn't an eviction might be required, dropping
the shortest, oldest tip.

All weakblocks that make it into the set get relayed.

When a miner produces a block, it sets its block content to exactly that
of two weak blocks back from the best weakblock tip. 
(maybe go further back if there are ties at the best?)

It is permitted to add additional transactions beyond the weakblock, but
doing so will increase orphaning risk.

It sets its weakblock header to extend that best weakblock, and it adds its
preference of transactions to the new weakblock. 

When a block is found it can be related with respect to any of the
weakblocks a peer knows its other peer have, which might not necessarily
be the one the miner used to templatize it.  (or.. don't allow that?).

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Difficulty control:
miners should observe weak block header times, and take median times of
arrival, to figure out a strong consensus estimate of weak block rate
and adapt the target towards 60 seconds/weakblock, including orphaned
weak-blocks. [non-linear penality for excessive orphans?]



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Soft confirmation:
Miners could give a tiebreaking preference to blocks which were consistent
(no subtractions) with their weak-block parent, and preference to the
longest weak block chain.

If this was done it would allow the weakblock chain to provide two forms
of soft confirmation: hashpower estimation, and a small loss to miners
if they act inconsistently.  I think a lot of analysis would be required
to figure out what security this actually provides; but it falls
out of this scheme "for free".