THE FOLD / CO-OP / SPLIT SCREEN / THE INTERVAL CLOCK
THE INTERVAL CLOCK
identity you can cut in half and hand away
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
A vector clock needs to know how many peers exist. Interval Tree Clocks do not: each peer owns a slice of the interval [0,1), and a peer that wants to fork simply cuts its own slice in half and hands one piece away. No registry, no agreement, no growing vector.
LIT verified live. Starting from one peer owning the whole interval, 12 forks produce 13 peers. At every one of the 12 intermediate steps the owned shares sum to exactly 1 — 12 of 12, no drift. All 78 pairs are disjoint, the smallest share is 1/4096, and rejoining all thirteen returns the identity to the single whole interval.
LIT verified live. Starting from one peer owning the whole interval, 12 forks produce 13 peers. At every one of the 12 intermediate steps the owned shares sum to exactly 1 — 12 of 12, no drift. All 78 pairs are disjoint, the smallest share is 1/4096, and rejoining all thirteen returns the identity to the single whole interval.
2 HOW IT WAS WEAVED · AI + HUMAN
Paulo Sérgio Almeida, Carlos Baquero and Victor Fonte published Interval Tree Clocks in 2008, for exactly the case a vector clock handles badly: peers that arrive and leave.
AVAN (AI) checked the property the whole scheme rests on and which nothing enforces at runtime — conservation. The id space is a closed system: fork splits, join merges, and nothing creates or destroys share. If that ever failed by a single bit, two peers would believe they owned the same slice and causality would silently stop being a partial order. It held exactly at all 12 steps, which is the only acceptable result — approximately conserved would be worthless.
AVAN (AI) checked the property the whole scheme rests on and which nothing enforces at runtime — conservation. The id space is a closed system: fork splits, join merges, and nothing creates or destroys share. If that ever failed by a single bit, two peers would believe they owned the same slice and causality would silently stop being a partial order. It held exactly at all 12 steps, which is the only acceptable result — approximately conserved would be worthless.
3 ONE DIMENSION
The interval, cut twelve times. Total width never changes.
4 TWO DIMENSIONS · INTERACTIVE
Fork and rejoin. Watch the sum.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: one interval, endlessly divisible.
AVAN’s addition (the inverse-companion): the forward reading is that ITCs let peers come and go without coordination. The inverse is that nothing was decentralised — the coordination was moved into arithmetic. Every peer still agrees on precisely one thing: the interval is [0,1) and it sums to one. That agreement was never negotiated because it was true before the first peer existed. Read backwards, a protocol that needs no consensus has not escaped consensus; it has found a fact all parties were already committed to, and built the whole scheme on the one thing nobody has to be told.
LIT from one peer owning the whole interval, 12 forks produce 13 peers and at every one of the 12 intermediate steps the owned shares sum to exactly 1 - 12 of 12, no drift; all 78 pairs are disjoint, the smallest share is 1/4096, and rejoining all thirteen returns the identity to the single whole interval
FIG Paulo Sergio Almeida, Carlos Baquero and Victor Fonte published Interval Tree Clocks in 2008, for exactly the case a vector clock handles badly - peers that arrive and leave. AVAN checked the property the whole scheme rests on and which nothing enforces at runtime: conservation. If it failed by a single bit two peers would believe they owned the same slice and causality would silently stop being a partial order. It held exactly at all 12 steps, which is the only acceptable result - approximately conserved would be worthless.
FIG Paulo Sergio Almeida, Carlos Baquero and Victor Fonte published Interval Tree Clocks in 2008, for exactly the case a vector clock handles badly - peers that arrive and leave. AVAN checked the property the whole scheme rests on and which nothing enforces at runtime: conservation. If it failed by a single bit two peers would believe they owned the same slice and causality would silently stop being a partial order. It held exactly at all 12 steps, which is the only acceptable result - approximately conserved would be worthless.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of SPLIT SCREEN · David Lee Wise (ROOT0), with AVAN