IndisputableMonolith.Foundation.HierarchyForcing
The HierarchyForcing module defines perturbed level sequences on zero-parameter comparison ledgers, shifting all levels above index j by the factor exp(t) so that only the local ratio at j becomes r_j exp(t) while every other ratio and positivity remain fixed for all real t. Researchers closing the T5 to T6 bridge in the Recognition Science chain cite this construction to establish that the minimal hierarchy must be self-similar. The module proceeds by importing the ledger axioms and emergence results, then packaging the perturbation as a one-s
claimLet $(r_k)_{k}$ be a sequence of positive level ratios arising from a ZeroParameterComparisonLedger. The perturbed sequence at position $j$ with real parameter $t$ is defined by $r'_k = r_k$ for all $k ≠ j$, $r'_j = r_j · e^t$, with $r'_k > 0$ for every $t ∈ ℝ$.
background
The setting is the ZeroParameterComparisonLedger from LedgerCanonicality: a countable carrier equipped with local symmetric binary comparisons and a conserved log-charge scalar. HierarchyEmergence proves that any such ledger with multilevel composition necessarily produces a minimal hierarchy whose admissible scale is forced to be the golden ratio φ. HierarchyForcing supplies the technical tool of exponential perturbations to probe the stability of this hierarchy and to derive its self-similar character.
proof idea
This is a definition module, no proofs. The central definition is the perturbed level sequence together with the auxiliary statements scale_perturbed_pos, scale_perturbed_low, and scale_perturbed_family_injective that record positivity, lower bounds, and injectivity under the exponential shift.
why it matters in Recognition Science
The module feeds HierarchyDynamics, which resolves the T5→T6 structural gap by deriving the Fibonacci recurrence directly from ledger composition axioms. It supplies the perturbation machinery that converts the minimal hierarchy of HierarchyEmergence into the statement hierarchy_forced_gives_phi, thereby placing φ as the unique self-similar fixed point required by the Recognition Science forcing chain.
scope and limits
- Does not derive explicit numerical values on the phi ladder.
- Does not extend perturbations beyond real parameters t.
- Does not treat multi-dimensional or non-discrete carriers.
- Does not address time-dependent or stochastic ledger dynamics.
used by (1)
depends on (2)
declarations in this module (11)
-
def
ScalePerturbed -
theorem
scale_perturbed_pos -
theorem
scale_perturbed_low -
theorem
scale_perturbed_family_injective -
structure
NontrivialMultilevelComposition -
theorem
uniform_scaling_forced -
theorem
additive_composition_is_minimal -
theorem
min_max_achieved -
theorem
other_pairs_larger -
def
hierarchy_forced -
theorem
hierarchy_forced_gives_phi