Paired cubes at p = 11 with a searched pair module, physical frames and a paired-cube bit word: conditional κ = 5.555021e-4

[eumemic]

Conditional improvement

$$T(n)=O\big(n(\log n)^{1-\kappa}\big),\qquad \kappa=\frac{5555021}{10^{10}}=5.555021\times10^{-4}.$$

This is +20.52% over #144 (4.609169e-4, merged) and +0.85% over #155 (5.508074e-4), which it supersedes. The bit side binds: its coarse saving is 5566382/10¹⁰, while the complex saving is 5622769/10¹⁰. All of #144's interfaces remain assumptions.

Change

This is #155 with a better complex word. The paired-cube bit word is unchanged.

• Complex: Paired cubes and shared completed cores for conditional kappa = 4.609169e-4 #144's paired cubes at p = 11 (h = 22), with physical frames and late-read reuse.
  • The triple module is an exact restriction of a pinned searched complex DAG. The pair module is a pinned, annealed pair-disjoint module (326 additions), with its contract checked on load. Both are in references/paired-cube/sources.
  • The carrier arcs are frozen: R = 17,529, with 3,630 rank-18 gauges.
  • scripts/paired_cube_physical.py moves 7,613 operation frames by physical descent (Physical frames and scratch reuse on Cayley covers: conditional κ = 3.32205398986e-4 #131's method under Three-stage Cayley covers for conditional kappa = 3.146011e-4 > 2^-12 #130's Clifford frames).
  • It places every gauged role in a dead donor's slot (Birth-read slot recycling: conditional kappa 1.1038332094346e-4 #124), with the old-value read at a deadline immediately before the role's first operation (Late compensation and joint frame refinement: conditional κ = 4.24830828577e-4 #143).
  • Per vertex: W = 16,539, deficit 1,320, largest child 20.
• Bit: the paired-cube bit word in research/paired-cube-bit, as in Paired cubes at p = 11 with physical frames and a paired-cube bit word: conditional κ = 5.508074e-4 #155 (p = 12; partner-pair source mixing per LEMMA.md).

#144's checks, finite bridge, row reserve and assembly are unchanged.

Verification

make paired-cube-verify
python3 research/paired-cube-bit/paired_cube_bit_word.py --p 12 --check
python3 research/paired-cube-bit/check_paired_cube_bit.py --dir research/paired-cube-bit/out --p 12

• Producer. It regenerates the complex input and passes all of Paired cubes and shared completed cores for conditional kappa = 4.609169e-4 #144's independent checks.
• Physical layer. It checks:
  • value spans and nested role chains, with every handoff spliced;
  • pair chronology;
  • target chains in actual read order;
  • the telescoping deficit;
  • an exact aliased dirty-scratch replay mod 2⁶¹ − 1, with three controls rejected.
• Bit checker. It recomputes the exact frames, the decoder identity, the chains, the partner-pair chronology, nondegeneracy, an F2 replay and the ledger, and five mutation controls are rejected.
• Assembly. Both moments are strict, with the next grid points rejected. All 47 constraints and 7 margins hold.
• Every command above passes on Linux with a clean working tree, as do the maintainer's paired-cube entry-point tests. The full suite runs in CI.

Credits

• Paired-cube decoder, modules, shared cores, bit ledger and assembly: @icekylinx (Paired cubes and shared completed cores for conditional kappa = 4.609169e-4 #144, building on Three-stage Cayley covers for conditional kappa = 3.146011e-4 > 2^-12 #130).
• Physical frames and reuse on covers: eumemic, with OpenAI Codex assistance (Physical frames and scratch reuse on Cayley covers: conditional κ = 3.32205398986e-4 #131).
• Birth-read reuse: @jamesyc (Birth-read slot recycling: conditional kappa 1.1038332094346e-4 #124).
• Late compensation reads: eumemic, with OpenAI Codex assistance (Late compensation and joint frame refinement: conditional κ = 4.24830828577e-4 #143).
• Completed-core sharing: @an664 (Completed-core sharing: conditional kappa > 2^-13 #128).
• Bit compile conventions: Zhihao Chen (Deferred endpoints and signed phase correction for a conditional 63965813/10^12 > 2^-14 bound #97).
• Bit lineage of the pair modules (Interval strips and core-aware pair assembly: conditional κ = 4986133/10^11 (5101691/10^11 stacked with #57) #62): Swapnil Jain.
• Complex DAG and annealed pair module, the p = 11 instance, the physical layer and the paired-cube bit word: eumemic, with Anthropic Claude assistance.

🤖 Generated with Claude Code

[eumemic]

Superseded by #161 (κ = 5.878747e-4), which keeps this PR's construction and adds merged complex outputs, an annealed bit pair module and phase stop 1e-9.