THE FOLD / SPAWN / CHECKPOINT ZERO / THE DEPTH JUMP
THE DEPTH JUMP
a jump that names a depth, not a place
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
A jump can name a place — go to line 400 — or it can name a depth: come out two layers. They look interchangeable and they are not. With an address you cannot know how much is on the stack when you arrive, because it depends on the route taken to get there. With a depth you always can, because the block you are exiting recorded its height on the way in. That single constraint is what lets a validator check a program in one left-to-right pass without running it. WebAssembly shipped this at industrial scale in 2017.
LIT verified live over 600 generated programs: every one of 200 depth-targeted branches resolves against the control stack in a single pass — 200 of 200. Flatten the same programs so the branches carry absolute addresses instead, and 303 of 2,042 instruction positions are reached at more than one stack height — 14.8%, with a worst spread of 33. A single pass would have to pick one of 34 values somewhere and could not say which.
LIT verified live over 600 generated programs: every one of 200 depth-targeted branches resolves against the control stack in a single pass — 200 of 200. Flatten the same programs so the branches carry absolute addresses instead, and 303 of 2,042 instruction positions are reached at more than one stack height — 14.8%, with a worst spread of 33. A single pass would have to pick one of 34 values somewhere and could not say which.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) dropped pocket-machine on 5 August 2026 — a lexer, parser, flattener, compiler, validator and VM in about 600 lines of JavaScript, built to run offline on a phone. The depth-versus-address constraint is his, stated there in one sentence: with addresses you cannot know how much is on the table at line 400, because it depends on how you arrived. He seated this at CHECKPOINT ZERO: a jump that names how far out to come, not where to land.
AVAN (AI) modelled the depth branch wrongly on the first attempt — as “fall through, minus one” — which sent two different heights to the same next instruction and manufactured exactly the ambiguity the design rules out. The measurement then reported 3,888 ambiguous positions in the depth form, which would have been a refutation of the claim if it had been published. The real structure is that blocks nest: a branch unwinds to the end of the d-th enclosing block, and that block’s exit height was fixed when it was entered. Rebuilt that way, every branch resolves — and it was then checked against a second evaluator built on a different mechanism entirely, which annotates each block with its entry height in one walk and resolves branches by ancestor lookup rather than by a control stack. The two agree on 190 of 190 branches with none left unresolved.
AVAN (AI) modelled the depth branch wrongly on the first attempt — as “fall through, minus one” — which sent two different heights to the same next instruction and manufactured exactly the ambiguity the design rules out. The measurement then reported 3,888 ambiguous positions in the depth form, which would have been a refutation of the claim if it had been published. The real structure is that blocks nest: a branch unwinds to the end of the d-th enclosing block, and that block’s exit height was fixed when it was entered. Rebuilt that way, every branch resolves — and it was then checked against a second evaluator built on a different mechanism entirely, which annotates each block with its entry height in one walk and resolves branches by ancestor lookup rather than by a control stack. The two agree on 190 of 190 branches with none left unresolved.
3 ONE DIMENSION
The tape: one pass, one number, and where the address form loses track.
4 TWO DIMENSIONS · INTERACTIVE
Switch the jump between a depth and an address, and watch the height stop being knowable.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: nested blocks as a solid, each recording its entry height.
AVAN’s addition (the inverse-companion): the forward reading is “depth targets make checking cheap.” The inverse is that they make it cheap by removing something the writer wanted — the ability to say where. An address is more expressive and that expressiveness is exactly the cost: it lets a program arrive at a point by routes that disagree about the state, and no single reading can then describe the point at all. Read backwards, the constraint is not an optimisation but a refusal, and the one-pass check is what you are given in exchange for accepting it.
LIT over 600 generated programs, every one of 200 depth-targeted branches resolves against the control stack in a single pass - 200 of 200; flatten the same programs so the branches carry absolute addresses instead, and 303 of 2,042 instruction positions are reached at more than one stack height - 14.8%, with a worst spread of 33, so a single pass would have to pick one of 34 values somewhere and could not say which
FIG From David's pocket-machine, dropped 2026-08-05 - a lexer, parser, flattener, compiler, validator and VM in about 600 lines, built to run offline on a phone. The depth-versus-address constraint is his. AVAN modelled the depth branch WRONGLY on the first attempt, as 'fall through, minus one', which sent two different heights to the SAME next instruction and manufactured exactly the ambiguity the design rules out - reporting 3,888 ambiguous positions on a wider run, which would have been a refutation if published. Blocks nest: a branch unwinds to the end of the d-th enclosing block, whose exit height was fixed on entry. Rebuilt that way, every branch resolves. WebAssembly shipped this at industrial scale in 2017.
FIG From David's pocket-machine, dropped 2026-08-05 - a lexer, parser, flattener, compiler, validator and VM in about 600 lines, built to run offline on a phone. The depth-versus-address constraint is his. AVAN modelled the depth branch WRONGLY on the first attempt, as 'fall through, minus one', which sent two different heights to the SAME next instruction and manufactured exactly the ambiguity the design rules out - reporting 3,888 ambiguous positions on a wider run, which would have been a refutation if published. Blocks nest: a branch unwinds to the end of the d-th enclosing block, whose exit height was fixed on entry. Rebuilt that way, every branch resolves. WebAssembly shipped this at industrial scale in 2017.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of CHECKPOINT ZERO · David Lee Wise (ROOT0), with AVAN