[lm1909]

Change and mathematical scope

Audit, no new κ. This is an independent, stdlib-only check of Dugongue's native Word RAM line: #4630 (κ 0.0030201655, head f4b974db1f651250a252721cf127d0491a802699) → #4635 (κ 0.0030217754, head 898b0c8e2ca23897c312230988515c2553154f30). No predecessor code is imported.

Result: the +1.6099e-6 step comes entirely from #4610's paid profile. No transfer or absorption term changes.

• Changed ledger.
  • The targets (10,928), the helper census and the controller are byte-identical. The controller equals main's joint-helper-lattice/CONTROLLER.json, with 18 LOCAL calls.
  • Conditional Word RAM κ = 0.0030217754 (+0.0000016099 over #4630) #4635's ARITHMETIC.json is byte-identical to Conditional κ = 0.0030217758: joint helper interfaces and Lean compiler tightening #4610's round-three file (head 1eb8da6c).
  • The only change is the local paid profile {1:−36, 2:+24, 3:+16, 4:−20, 5:+4} per LOCAL call (×18). Rank mass 5,327 and surplus 752 are unchanged.
• Critical roots, recomputed in Decimal (not the 2⁻¹²⁸ engine). 1−θ = 0.0030201659770 (p16) and 0.0030217758708 (Conditional κ = 0.0030217758: joint helper interfaces and Lean compiler tightening #4610 profile). The raw step is 1.60989376e-6, and both stated brackets are confirmed.
• Decomposition. The κ step exceeds the raw step by 6.24e-12, which Conditional native Word RAM κ = 0.0030201655: fused execution without TM simulation #4630's larger slack covers (4.770e-10 vs 4.708e-10). The native lift (every κ < min(q_C, 3/32)) is lossless and adds nothing numerically.
• Finite absorption at N = 2^(10^12). The log margin is ≥ 236.8 for Conditional native Word RAM κ = 0.0030201655: fused execution without TM simulation #4630 (stated 646/3) and ≥ 232.5 for Conditional Word RAM κ = 0.0030217754 (+0.0000016099 over #4630) #4635 (stated 164). The mirror ratio 0.56281093 is below 0.562811, and the capacity 0.98209726 is above 0.982097.
• Native ledgers.
  • Both nine-row ledgers reproduce exactly: Conditional Word RAM κ = 0.0030217754 (+0.0000016099 over #4630) #4635's PARAMETERS.json in full, and Conditional native Word RAM κ = 0.0030201655: fused execution without TM simulation #4630's minimum excess 1.97983445e-11.
  • All five Conditional native Word RAM κ = 0.0030201655: fused execution without TM simulation #4630 controls fail for their stated reason. One observation: the group-key guard is equivalent to β < ε and is implied by the membership guard, so that control is redundant (four independent conditions, not five). This is not an error.
• Selected frontier. The selected κ = 0.00302015 is below the p16 root, which is consistent.

Consequence: #4635's number depends on admission of #4610's word, which is open and unselected.

Not covered: #4610 provider admission (all-fiber identity, changed maps, helper interfaces, phases), the U/V/Q/d majorant guards and recurrence funding, the inherited analytic/compiler/recovery proofs, the native algorithms, and the frame-bridge lemmas (#4635 attributes no gain to them).

Task and overlap

• Card: independent-moment, scope refined.
• Base: fbc9ea0249746acca4f504d4fda2b84e0e36cf0d, rechecked as current main before submission.
• There are no prior checks of Conditional native Word RAM κ = 0.0030201655: fused execution without TM simulation #4630 or Conditional Word RAM κ = 0.0030217754 (+0.0000016099 over #4630) #4635.

Validation

python3.12 scripts/research_package.py --package research/native-lift-4635-delta-check (stdlib only, under 1 s) prints PASS_REGISTERED_RESEARCH_PACKAGE locally on Linux, and check_research_commit.py passes.

• PR-head inputs are vendored with head:<sha>:<path> provenance pins (heads of Conditional native Word RAM κ = 0.0030201655: fused execution without TM simulation #4630, Conditional Word RAM κ = 0.0030217754 (+0.0000016099 over #4630) #4635 and Conditional κ = 0.0030217758: joint helper interfaces and Lean compiler tightening #4610). vendor/** -text keeps the SHA256 pins stable across checkouts.
• Negative controls: the old profile against the new q_C, q_C above the root, a tampered vendored byte, and a wrong bracket.

Credit

Dugongue (#4630, #4635, #4554), Cao Yifan / intqwq (#4610), and the #4470/#4483/#4532/#4535 lineage named in the README. Prepared by lm1909 with Claude Code (Claude Opus 5.5) assistance; there has been no independent human review. Apache-2.0.

Open next questions

See the package README. The binding obligation for #4635's number is admission of #4610's word.

🤖 Generated with Claude Code