Paired cubes at p = 11 with an h = 21 bit word: conditional κ = 5.108289e-4

[eumemic]

Conditional improvement

$$T(n)=O\big(n(\log n)^{1-\kappa}\big),\qquad \kappa=\frac{5108289}{10^{10}}=5.108289\times10^{-4}.$$

This is +10.83% over #144 (4.609169e-4, merged), its base, and +8.19% over #151 (4.72154791e-4), the best open PR. The complex side binds. The complex saving is 5113520/10¹⁰ and the bit coarse saving is 5164125/10¹⁰. All of #144's interfaces remain assumptions.

Change

• Complex: Paired cubes and shared completed cores for conditional kappa = 4.609169e-4 #144's paired cubes at p = 11 (h = 22).
  • The graph is Graph(11).finish(restricted_triples(11), restricted_pairs(10), all_but_one(9)), built from Paired cubes and shared completed cores for conditional kappa = 4.609169e-4 #144's unchanged module functions on the pinned Deferred bit word and a 28,705-role complex producer under stopped-product accounting: conditional κ = 1.044939e-4 #117 DAG.
  • Its 3,472 carrier arcs are frozen, as Paired cubes and shared completed cores for conditional kappa = 4.609169e-4 #144 did for p = 12.
  • R = 18,473, with 3,630 rank-18 gauges.
  • Per vertex: m = 66, W = 21,113, deficit 1,320, largest child 54.
• Bit: a new h = 21 bit word in Deferred endpoints and signed phase correction for a conditional 63965813/10^12 > 2^-14 bound #97's frozen format, read by Deferred endpoints and signed phase correction for a conditional 63965813/10^12 > 2^-14 bound #97's byte-identical deferred.py.
  • The word uses Paired cubes and shared completed cores for conditional kappa = 4.609169e-4 #144's gauge-subset rule, retaining 7,575 of 8,910 gauges.
  • Per vertex: m = 63, W = 24,186, deficit 1,400.
  • It sits in references/paired-cube/fib-bit-h21/ with its hash manifest, literal-ledger receipt and producer.
  • Paired cubes and shared completed cores for conditional kappa = 4.609169e-4 #144's paired_cube_bit.py reconstructs and checks it. Only the word's constants change.

Everything else is #144's: scripts, checks, finite bridge, row reserve and assembly.

Verification

make paired-cube-verify

• The producer regenerates the complex input, and all of Paired cubes and shared completed cores for conditional kappa = 4.609169e-4 #144's independent checks pass, including 1,742,400 signed scalar pairs.
• The bit reconstruction passes every check.
• Both moments are strict and the next grid points are rejected.
• All 47 constraints and 7 margins hold.
• On the bit word, the round-seven checkers pass: check_word, check_lifted, and check_frames apart from its round-seven constant pin. Deferred endpoints and signed phase correction for a conditional 63965813/10^12 > 2^-14 bound #97's literal ledger passes at h = 21.
• A full make verify passed on Linux with a clean git diff.

Credits

• Paired cubes, shared cores, bit gauge-subset rule 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).
• Completed-core sharing: @an664 (Completed-core sharing: conditional kappa > 2^-13 #128).
• Positive DAG that the complex modules restrict: eumemic, with Anthropic Claude assistance (Deferred bit word and a 28,705-role complex producer under stopped-product accounting: conditional κ = 1.044939e-4 #117).
• Frozen-word reader and literal ledger: Zhihao Chen (Deferred endpoints and signed phase correction for a conditional 63965813/10^12 > 2^-14 bound #97).
• Round-seven bit producer lineage (Interval strips and core-aware pair assembly: conditional κ = 4986133/10^11 (5101691/10^11 stacked with #57) #62) and checkers: Swapnil Jain.
• p = 11 instance and the h = 21 bit word: eumemic, with Anthropic Claude assistance.

🤖 Generated with Claude Code

[eumemic]

Superseded by #155, which keeps the p=11 complex and replaces the bit word.