computation_limits_summary
computation_limits_summary assembles eight statements on fundamental computation bounds in Recognition Science, covering the positive fundamental tick as minimum time quantum, the resulting maximum rate, irrationality of phi blocking exact simulation, positive Landauer erasure energy scaling with temperature, and the Bremermann limit. Information theorists or physicists deriving resource bounds from discrete time and irrational constants would reference this list. The definition is a static enumeration pulling from tick and cost primitives with
claimThe summary list contains the statements: fundamental time quantum τ₀ > 0 (minimum time quantum), maximum computation rate = 1/τ₀ > 0, φ is irrational (exact simulation requires transcendental precision), no rational algorithm exactly computes φ, Landauer energy k_B T ln(2) > 0 (cost to erase 1 bit), Landauer bound scales linearly with temperature, Bremermann limit = 2/ℏ > 0 (operations/second/joule), and φ > 1 (RS hierarchies grow exponentially).
background
In the Information.ComputationLimitsStructure module the local setting is the derivation of computation limits from three RS sources: temporal discreteness via the fundamental tick, irrationality of constants such as φ, and thermodynamic costs. Upstream Constants.tick defines the fundamental RS time quantum (RS-native) as τ₀ = 1 tick, with the eight-tick octave as the fundamental evolution period. Cost definitions from MultiplicativeRecognizerL4 and ObserverForcing supply the J-cost of recognition events, while Breath1024.T supplies the period type.
proof idea
The definition directly constructs the List String by enumerating the eight IC-002 statements. It references upstream definitions such as tick for the time quantum and cost for energy bounds, with no tactics or lemmas applied beyond the enumeration.
why it matters in Recognition Science
This definition supplies a compact reference list for the IC-002 results on computation limits, highlighting the role of the fundamental tick and φ irrationality in bounding resources. It aligns with the framework landmarks of the eight-tick octave and the forcing chain steps that fix D = 3 and the alpha band. No parent theorems are listed in the used_by edges.
scope and limits
- Does not derive or prove any of the listed limits.
- Does not supply numerical values in RS-native units.
- Does not connect to specific downstream theorems.
- Does not address quantum computation beyond the listed Bremermann bound.
formal statement (Lean)
179def computation_limits_summary : List String := [
proof body
Definition body.
180 "IC-002.1: Fundamental tick τ₀ > 0 (minimum time quantum)",
181 "IC-002.2: Maximum computation rate = 1/τ₀ > 0",
182 "IC-002.4: φ is irrational (exact simulation requires transcendental precision)",
183 "IC-002.7: No rational algorithm exactly computes φ",
184 "IC-002.8: Landauer energy k_B T ln(2) > 0 (cost to erase 1 bit)",
185 "IC-002.9: Landauer bound scales linearly with temperature",
186 "IC-002.11: Bremermann limit = 2/ℏ > 0 (operations/second/joule)",
187 "IC-002.14: φ > 1 (RS hierarchies grow exponentially)"
188]
189
190/-- IC-002 Status Certificate -/