THE FOLD / RESPAWN / THE CONTINUE / THE SELF-BRANCH

THE SELF-BRANCH

a call that never leaves

1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION

On ARM64 a call is BL: six opcode bits and a 26-bit signed displacement, scaled by four, measured from the instruction itself. A compiler that has not linked yet writes the displacement as zero and leaves a note for the linker. Zero means this instruction. Every unlinked call is therefore a call to itself — a tight infinite loop that assembles cleanly, disassembles cleanly, and never returns.

LIT verified live by decoding a real linked image of 127 words against the ARMv8-A field layout. 0x94000000 decodes as BL with displacement 0. Encode and decode round-trip at 11 of 11 displacements including both extremes of the signed field. In the linked image there are 4 call sites, 0 of them left at zero, 4 of 4 landing exactly on a declared function entry — and 2 carry negative displacements, which is what recursion looks like from underneath.

2 HOW IT WAS WEAVED · AI + HUMAN

David (human) found this in his own compiler and wrote it up rather than quietly fixing it. His bridge.js emitted bl as 0x94000000 with the comment resolved by the linker — and nothing was the linker. He built link.js, which lays the regions out, records each symbol’s offset, and patches every intra-module call; calls to symbols outside the module are left at zero and reported, never silently kept. Dropped 5 August 2026.

AVAN (AI) decoded the linked image independently rather than trusting the linker’s own report — pulling the 26-bit field out by hand, sign-extending it, and asking where each call actually lands. The four sites resolve to i13_fib at word 21 and i13_poly at word 81, with fib’s two self-calls at words 54 and 63 both reaching back to word 21 at −33 and −42. The linker’s own report agrees, which is the point of checking it twice.

3 ONE DIMENSION

One word, thirty-two bits, and where the call is hiding.

4 TWO DIMENSIONS · INTERACTIVE

The image, its call sites, and what each one points at.

5 THREE DIMENSIONS + AVAN’S INVERSE

The green forward object: the image as a column, with the calls drawn as arcs.

AVAN’s addition (the inverse-companion): the forward reading is “an unpatched call is a bug.” The inverse is that zero was chosen precisely because it is safe to leave. A displacement field has to hold something before the target is known, and every value in it names some instruction — there is no null in a 26-bit signed integer. Zero was picked because a self-branch is the most obviously wrong thing the field can say, so a program that reaches one hangs immediately rather than running off into whatever happened to be nearby. Read backwards, the infinite loop is not the failure; it is the designed failure, chosen over the silent one, and it only became dangerous when nobody was checking whether the note to the linker had been read.

LIT decoding a real linked image of 127 words against the ARMv8-A field layout, 0x94000000 decodes as BL with displacement 0; encode and decode round-trip at 11 of 11 displacements including both extremes of the signed field; and in the linked image there are 4 call sites, 0 left at zero, 4 of 4 landing exactly on a declared function entry, with 2 carrying negative displacements - which is what recursion looks like from underneath

FIG From David's i13c-bridge-tools, dropped 2026-08-05. He found this in his own compiler and wrote it up rather than quietly fixing it: bridge.js emitted bl as 0x94000000 with the comment 'resolved by the linker', and nothing was the linker. He built link.js, which lays the regions out, records each symbol's offset, and patches every intra-module call; calls to symbols outside the module are left at zero and REPORTED, never silently kept. AVAN decoded the linked image independently rather than trusting the linker's own report - pulling the 26-bit field out by hand, sign-extending it, asking where each call actually lands. The four resolve to i13_fib at word 21 and i13_poly at word 81, with fib's two self-calls at words 54 and 63 reaching back to word 21 at -33 and -42. The linker's report agrees, which is the point of checking twice.

◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE CONTINUE · David Lee Wise (ROOT0), with AVAN