[aliromman]

Reader 451 previously needed helper 228 at frame 737 before it read root 772. This forced the root to visit frame 737. The new word saves that operand in an unused lifetime of register 770, reads the root at frame 595 first, then adds the saved operand at frame 737 and clears it.

Conditional κ = 0.003128645, +0.000000259 over #6144. The raw crossing is strictly between 0.00312865201590 and 0.00312865201591. The local paid change is H1 − H2 − H4 + H5; the complete caller uses it 18 times. All productive targets, 29 owned register labels and peak storage 13 stay unchanged. The extra lifetime, 12 scalar operations and routes are charged. The old #6144 invoice fails at the new claim.

Package and proof · Verification receipt · Validation · Canonical investigation

Exact source: #6144 at 5ec9b6dafc1ec54e2c0ca0771e8ed032f7888417. Base: canonical main 3f0152a32eeebac0df11946dbd50cabe5a7f7839. Five guarded replacements change the full word. The protected contact sequences stay exact. The current neighboring GF(4) and caller scopes were checked and remain separate.

Verification passed:

• All 799 input columns, separate transpose, native maps and phases, adapters and the complete physical caller.
• Full invoice, two rational engines, completion, compiler, 54 strict and four functional outer checks, and cache/restoration/source-corruption controls.
• Registered Python 3.12 replay in ordinary and optimized modes; committed bytes and modes; official export; full optimized replay with Git absent and exported sources read-only.

This is a modest conditional improvement. Five inherited framework assumptions remain; the large uniform word and rounded multiplier are not materialized. Independent scientific review and hosted CI remain pending. The selected frontier is unchanged.

New work: Ali Romman with substantial OpenAI Codex assistance; no subagents. DreamingOfClouds retains #6144/#6143/#6030/#5907 credit, including Claude Opus 5.5 assistance. #5827, #5811 and all earlier native, caller, compiler and BIT credits remain in NOTICE.

[DreamingOfClouds]

Independent check passed on our side for head 564a076b:

• exact κ crossing [0.00312865201590, 0.00312865201591], so the claimed 0.003128645 is conservative
• legality and native replay clean (2922 frame pairs, 0 bad)
• shippable against the Conditional κ .003125804 (+5.22e-7 over #5907): remove helper 470's frame-593 rung, the twin of #5907's removal #6030 base literals

Nice build of the frame-737 half of the root-2 lead.

DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code