Consensus

• Branch. One of two or more continuations of the same shared history. Each is a complete chain in its own right.
• Local validity. What verify() tests. Internal consistency of one chain, with no view of any other.
• Selection rule. The test each holder applies to decide which branch is the accepted one. Takes the branches and nothing else.
• Accepted history. The branch the rule currently selects. A status a chain has, not a property inside it.
• Reorganisation. The accepted history changing from one branch to another. Entries leave; none of them becomes invalid.
• Depth. How many blocks sit after an entry. The only quantity that changes as an entry ages.
• Blocks to redo. Depth plus the block itself. Deterministic, countable, and measured live in part 4.
• Finality. How settled an entry is. A quantity that strengthens with depth, and never a message that arrives.

A block records its position, its timestamp, its entry, the hash of the block below it and its nonce. Five fields, all of them looking down or inward. There is no field that names a competitor, no field that records how many other holders agreed, and no field that says this is the real one.

So the information needed to choose between branches does not exist inside either branch. It has to be manufactured by a rule applied from outside, over both of them at once, and that is a strictly separate piece of machinery from everything built in sessions 1 to 7.

Extend branch A three times and branch B once. Both still verify. Extend B four times so it overtakes A. Both still verify. There is no combination of presses that produces a problem from verify, because nothing either branch does is capable of making the other one inconsistent.

That is worth noticing as a practitioner rather than nodding at as a concept. Any monitoring built on verification alone will be silent through every reorganisation your system ever has.

Both branches are built from the same first four entries with the same fixed timestamps, so blocks 0 to 3 hash to the same four values in both, down to the last character. That is what makes the picture a fork rather than two unrelated registers: the branches share a prefix exactly, and diverge at a known index.

It also means the cost of abandoning a branch is bounded by where the split is, not by the length of the register. A holder switching branches keeps everything below the split and discards only what is above it.

Strip the phrase back to the arithmetic. For each branch, total the work accumulated in its blocks. Take the larger total. If the totals tie, keep whichever you already had and wait. That is a function of two arrays, it returns the same answer on every machine, and it needs no clock, no network poll and no opinion.

Stated over a raw count of blocks instead, the same function is inflatable wherever blocks are cheap to produce, which is why the work version is the one that survives. Session 4 is why a block is expensive and this session is what that expense is spent on.

A process that reads the register and does something physical has a decision to make that most such processes have never made explicitly: how deep an entry must be before it acts. The default, which is act on sight, is a choice too, and it is the one with the reorganisation risk fully accepted and nobody informed.

Make the depth different for different actions. Recording that somebody looked at a consignment and releasing that consignment from a cold store are not the same class of decision, and one of them cannot be undone by a later entry.

Suppose a branch wins the rule cleanly and everybody can see it was produced to displace a particular entry. One camp says the rule stands, and that this is not a hard case but the defining one. A rule that is followed except when the outcome is disliked was never a rule; it was a preference with extra steps, and the first time it is overridden every holder learns that somebody can override it, which is the property the whole arrangement exists to avoid. The cost of honouring the rule in a bad case is the price of it meaning anything in the ordinary ones.

The other camp says that treating the rule as the product rather than as a means is a category error. The rule exists to produce a usable shared history, and when it plainly fails to, the holders are entitled to coordinate and say so. Every real system has an intervention path, formal or otherwise, and pretending otherwise does not remove it, it just leaves it undocumented and available to whoever is best organised on the day.

Both positions are held by people who have operated these systems. They agree entirely on the mechanics and disagree about what a rule is for, and the answer decides whether your operating procedure has an escalation path in it or deliberately does not.

reforge is deterministic. Give it the same chain, the same index and the same difficulty and it searches the same nonces in the same order and returns the same number, every time. Running it twelve times on one register measures nothing and would look exactly like a careful bench.

So each of the twelve runs in a row uses a different register: the entries carry a distinct run marker, which changes every block hash and therefore every search. Twelve independent draws, one mean, and the trial count printed beside it, because session 4 showed what a single draw is worth.

The minimum and maximum printed on each row will be far apart, and at twelve trials the mean itself moves noticeably between presses. That is the honest picture. Press the button three times and watch the same row report three different means.

Anybody quoting you a single figure for the cost of displacing an entry is quoting one draw from a distribution with a long tail. The count of blocks is the part you can rely on.

Six blocks makes the table readable and understates the effect. In a register that gains entries continuously, the blocks-to-redo figure for any given entry increases on its own, without anybody doing anything, simply because entries keep arriving on top of it.

That is the mechanism behind every confirmation count anybody has ever quoted at you. The number itself is a risk appetite dressed as a technical fact, and two organisations reading the same register can reasonably pick different ones for different actions.

The depth argument works because an attacker redoing old blocks is racing everybody else, who are adding new ones. Falling behind is the normal outcome and the gap widens, which is what makes depth mean anything at all.

Give one party more capacity than the rest combined and the race reverses. They are not trying to catch a gap that grows; they are closing one that shrinks. The quantity that made depth protective is gone, and what remains is a question about capacity rather than about arithmetic. That is a qualitative change, not a larger number in the same table.

Say that nothing measured here bounds it, and that you are not going to supply a figure you have not measured. It is an unsatisfying answer and it is the only defensible one from this material.

Then move the conversation to what can be answered: who holds the copies, whether their interests differ, and what your process does if an entry it acted on leaves the accepted history. Those are answerable at Harbourgate, tonight, with names in them.