honestly, looking at these two side-by-side, it’s basically a wrap for the antihydra “conjecture.” if the 5-state copycat (#5,542,797) is already a proven non-halter, there’s like a 99.9% chance antihydra is just a slightly “extra” version of the same thing.
they both start with that same 4-one bootloader, and at 10m steps, the “training” looks identical—they’re just dense shredders carrying numbers across the tape to do math. the only real difference is that 45-degree slant, but that’s just a visual drift; it doesn’t change the core instructions.
why it’s mathematically impossible for it to halt:
the self-healing logic:in the 5-state machine, it only hits state E (the halt check) when it’s mid-math and already has a 1 to latch onto. it never even sees a 0 in that state.
the antihydra shield: antihydra is even “creepier” because it has state F. even if it hits a 0, it writes an “insurance 1” and moves left. if it finds a 1 there (which it always does because it’s a dense shredder), the F1 → 0RA rule kicks it right back to state A.
the bottom-left trap:** both machines have their --- halt in the same spot (E0 or F0). but since they follow preset instructions and always write 1s when they see 0s in the main states, they literally can’t fall off the cliff. they build the floor as they walk on it.
cracking this is huge because it puts us one step closer to BB(6). once we prove antihydra is just a “slanted” version of the 5-state bouncer we already solved, the trophy is basically waiting for whoever writes the formal certificate. it’s not a mystery anymore; it’s just a deterministic engine that’s too productive to ever die. Or i could just be dumb.