Who agrees, and how

A hash chain detects an alteration by recomputing. That works whether the register is held by one party or a hundred. What one party cannot provide is a second opinion: if the only copy is rewritten consistently, recomputation finds nothing, because the copy agrees with itself perfectly.

Several independent copies turn a private edit into a visible disagreement. The chain provides the comparison and the copies provide something to compare against. Everything difficult about this session follows from that arrangement, because independent copies do not stay identical by themselves.

• Fork. Two valid continuations of the same register existing at once. Normal, frequent, and not a fault.
• Consensus rule. The mechanical test every holder applies to decide which branch is the accepted one.
• Longest chain wins. The usual rule, stated over the work accumulated in a branch rather than a raw count of entries.
• Reorganisation. What happens to the losing branch: its entries leave the accepted history, having never been invalid.
• Finality. How settled an entry is. A quantity that grows with depth, not a state that is reached.
• Depth. How many blocks sit after an entry. The only thing that changes as an entry ages.
• Permissionless. Anyone may write without being admitted first.
• Permissioned. Only admitted parties may write, and somebody admits them.
• Governance. Who can change the rules themselves, which is a separate question from who may use them.

Every holder of the register has to reach the same answer, alone, from the data in front of them, without asking anyone. Any rule that needs judgement needs a judge, and a judge is the administrator the arrangement exists to do without. So the rule must be computable, deterministic, and take no input beyond the branches themselves.

That requirement rules out everything a reasonable person would prefer. Not the branch with the more plausible entry, not the branch from the more reputable party, not the branch a majority of people think is fairer. Those are all better answers and none of them can be evaluated identically by strangers.

What it buys is convergence with no coordination at all. Holders who cannot talk to each other, who came online at different times, and who saw the branches in a different order still end on the same history, because they are all applying the same arithmetic to the same data.

What it costs is that no entry is ever certainly permanent. An entry you saw a minute ago can leave the accepted history when a longer branch appears, and the rule will discard it without hesitation. A count of entries would be trivial to inflate, so the rule is normally stated over the work accumulated in a branch rather than the number of blocks in it, which is where session 3 rejoins this one: a branch is expensive to extend precisely so that the longest one is hard to manufacture.

Everything above is an accidental fork, resolved automatically because both sides apply the same rule. There is a second kind, where the holders stop agreeing about what the rule is. One group changes the required format, or the difficulty, or who is admitted, and the other group declines.

No consensus rule can settle that, because the parties are no longer running the same test. The register simply becomes two registers with a shared past and separate futures, and which one anybody uses is a social question rather than a computable one. It is the clearest demonstration that the mechanism decides between histories, never between people.

Displacing an entry means producing a branch that wins the rule, which means redoing that entry's block and every block after it, each at the price session 3 measured. The further back the entry sits, the more blocks that is, and the more expensive the whole exercise becomes. That is a curve, not a threshold.

So there is no depth at which the system declares an entry safe, and any number you adopt is a decision about risk appetite rather than a fact you have been told. Different businesses reading the same register choose different depths for a release of goods and for a routine note, and both are being reasonable.

A process that acts the instant an entry appears has inherited the reorganisation risk without noticing. The entry may be removed afterwards, the process will not be consulted, and whatever it did in response has already happened in the physical world.

The fix is unglamorous: decide the depth required before acting, write it into the procedure, and make it different for actions that cannot be undone. Releasing a consignment from a cold store is not the same class of decision as recording that somebody looked at it.

One position holds that probabilistic finality is a fair trade and possibly the only honest one. Every settlement system in the world is probabilistic underneath, payments are reversed and registrations are corrected, and a mechanism that states its residual risk openly is more truthful than one that hides the same risk behind a legal declaration.

The opposing position is that businesses cannot operate on a history that might be revised, that the word final in commerce means something specific and enforceable, and that a system which never quite provides it has moved the problem to whoever writes the contract. On that view the probability is not a feature but an unpriced liability.

Both are defensible and the choice between them depends on what happens in the physical world when an entry is wrong. Nothing in the mechanism decides it for you.

Who may write. The question that decides whether the register records what happened or what one party wanted recorded. If a single organisation may write, the chain is an audit trail of that organisation's own claims, which can still be worth having.

Who may read. Independent verification requires the full register, not a report about it. A party who can only read a summary cannot check anything, and the tamper evidence is doing nothing for them.

Who runs the machines. Copies only count as independent if they are held by parties with different interests. Four machines in one data centre are one copy with extra electricity bills.

Who can change the rules. The quietest and often the most important. Whoever can change the difficulty, the format or the membership list can change what verification even means, and no amount of hashing constrains them.

One side says no, and means it as a technical objection rather than a slight. The hard problem being solved is agreement among parties who have not been vetted and cannot be excluded, and every expensive part of the design exists for that. Admit only approved writers and the problem disappears, along with the need for the mechanism. What is left is a replicated database with hash linked records, which is a fine thing to build and an older one, and calling it a blockchain imports credibility it did not earn.

The other side says yes, and that the objection confuses one implementation with the category. The properties that buyers actually want are a shared history no single member can silently revise, verification each member performs themselves, and a record whose alteration is visible to all of them. A permissioned system delivers those without paying for open membership it does not need, and refusing the name is a purity argument that leaves the useful design without a word for itself.

Both sides are arguing from the same facts about the same systems. The disagreement is about what the word is for, and it is worth knowing which side the person across the table is on before you get to the third slide.

The four answers describe what a system permits. What actually happens can be very different, because permission is not the same as participation. A register anyone may write to can end up with most of its blocks produced by a handful of parties, simply because producing blocks has a cost and costs favour scale.

So there is a fifth question, harder to answer and more revealing: not who is allowed to participate, but who actually does, and how concentrated that has become. A system open on all four axes and concentrated in practice has the governance profile of the small group doing the work, whatever its rules say.