module module high

`IndisputableMonolith.CrossDomain.AttentionSpace`

The CrossDomain.AttentionSpace module defines attention networks and states realizing the complexity ceiling gap45 that leaves exactly 5 overflow slots. Researchers working on cross-domain mappings in Recognition Science would cite these structures. The module organizes definitions around tick phases and network counts to establish the gap and overflow relations.

claimThe module introduces attention networks and states such that the complexity ceiling gap$_{45}$ leaves exactly five overflow slots, satisfying attention fits under the gap and attention plus overflow equals the gap.

background

In the Recognition Science framework the attention space models cross-domain interactions via an eight-tick octave with D=3 spatial dimensions, so tick count equals 2 to the power D. The module defines AttentionNetwork as a structure carrying network count and TickPhase, together with AttentionState that tracks attention state count. These lead to the relations overflow equals D and the gap45 complexity ceiling that accommodates attention with five overflow slots.

proof idea

This is a definition module, no proofs. It supplies the types AttentionNetwork, TickPhase, AttentionState and the supporting lemmas networkCount, tickCount, tick_eq_twoPowD, attentionStateCount, gap45, overflow_eq_D, attention_fits_under_gap, attention_plus_overflow_eq_gap and network_surj.

why it matters in Recognition Science

The module supplies the attention-space component that realizes the gap45 ceiling within the CrossDomain layer. It feeds structures that connect to the unified forcing chain, enforcing the eight-tick octave and D=3 dimension while supporting the complexity-ceiling analysis.

scope and limits

Does not establish the full cross-domain mapping.
Does not compute explicit numerical values for network or state counts.
Does not address phi-ladder mass formulas or J-cost.
Does not contain proofs of the gap relations.

declarations in this module (15)

inductive AttentionNetwork L22
inductive TickPhase L26
theorem networkCount L30
theorem tickCount L31
theorem tick_eq_twoPowD L32
abbrev AttentionState L34
theorem attentionStateCount L36
def gap45 L40
theorem overflow_eq_D L41
theorem attention_fits_under_gap L44
theorem attention_plus_overflow_eq_gap L47
theorem network_surj L51
theorem tick_surj L55
structure AttentionSpaceCert L59
def attentionSpaceCert L67