Run the whole candidate.
A complete prepared state now drives prospective viability, idle response, bit events and finite renewal. Compare close and hold laws on the same inputs, including the hidden changes that a net budget can miss.
The complete source programme
| Stage | Declared update | Status |
|---|---|---|
| Prepared state | T, cached L, response q, active stock r, finite bank, cursor, frozen C/H branch | Candidate carrier |
| Prospective viability | L+=T · 1[r>0] · (1−q_old) | Chosen stock/demand source |
| Response | C: h+=0; H: h+=I+q_old | Source-law alternatives; neither natively selected |
| Feedback and consumption | r+=r−omega+; q+ and cached L+ committed together | Candidate update |
| Renewal-only tick | At r=q=L=0, load the next prepared packet; advance cursor even for zero packets | Finite prepared supply |
| Stop | Full state unchanged; report exhausted/quiescent or latched/stranded | Model control outcome |
Integrity stays fixed in one labeled identity frame. An ordinal tick counts the programme update; it does not measure seconds. Cached prior L is not reconstructed from current stock.
What the finite proof gives
The integer potential V=4S+2|q|+|L_cache|+(B−k) strictly decreases on every committed tick. Both branches reach a full model fixed point.
For C, every prepared token produces one opening and one later closure; initially open responses add closures. The exact pulse duration includes zero refills and broken-seat cache cleanup. H can instead latch and strand remaining stock.
A response-null tick can still update the source cache or refill cursor. A zero net Hamming budget can still contain two opposite directed toggles. Stopping on either quantity loses those changes.
Keep the Hodge bridge explicit
The original latent witness uses chain amplitudes: R_e=c1,e²(c0,i²+c0,j²). RSP uses newly declared integer stocks. No carrier map identifies these objects, and a frozen integrity bit does not derive physical break/repair dynamics.
The next source programme must realize or reject this prepared carrier on an independently specified Hodge/transport source. Parallel AI construction and scope checks do not replace independent human review.
Inspect the realization gate →New: audit the programme’s Hodge realization contract →
New: construct the finite-window joint carrier and count its resources →