IndisputableMonolith.Verification.T5.ConstraintForcing
Packages the abstract recognition cost between two positive values as the symmetric log-ratio cost, and forces the T5 constraint suite: exchange invariance, identity zero, reciprocal symmetry, and unit normalization. Workers on the T5 J-uniqueness chain cite it for the cost interface and the forced symmetries. Argument shape is definitional setup plus ledger-derived forcing lemmas, with curvature treated as a removable gauge.
claimRecognition cost between positive values is the symmetric log-ratio cost $C$. It is required to obey exchange invariance $C(x,y)=C(y,x)$, identity vanishing $C(x,x)=0$, reciprocal symmetry $F(x)=F(1/x)$ for the one-argument form, and unit normalization. Curvature terms are gauge and cancel in dimensionless comparisons. This is the T5 constraint package on admissible costs.
background
T5 in the Recognition Science forcing chain is J-uniqueness: the admissible cost is forced to $J(x)=(x+x^{-1})/2-1$, equivalently $\cosh(\log x)-1$. Before uniqueness, one must state which functional constraints any candidate cost must satisfy. This module is that constraint layer inside Verification.T5.
Upstream, LedgerCost derives two of those constraints from the T3 ledger (double-entry bookkeeping): symmetry $F(x)=F(1/x)$ is forced by the ledger, and a unit constraint is likewise ledger-derived, with a no-go that the remaining constraint cannot be obtained the same way. Constants supplies the RS-native tick $\tau_0=1$.
Locally the module introduces the abstract recognition cost as the symmetric log-ratio between two values, together with predicates for exchange invariance, reciprocal symmetry, identity recognition zero, and unit normalization, and a cost-function interface tying them together.
proof idea
Definition-and-forcing module, not a single theorem. It fixes the recognition cost as the symmetric log-ratio (exchange-invariant, identity zero by construction), states the cost-function interface, and records the forced properties: reciprocal symmetry and unit normalization as forced lemmas, plus curvature-as-gauge and cancellation in dimensionless ratios. Exchange-invariance and identity axioms sit at the interface; ledger-derived facts from LedgerCost supply the symmetry/unit half of the T5 package. No single end-to-end uniqueness proof lives here; that is downstream J-uniqueness.
why it matters in Recognition Science
Sits on the T5 rung of the UnifiedForcingChain: without a clean constraint interface, J-uniqueness cannot be stated. It turns ledger structure (T3) into cost axioms that any admissible $J$ must meet, matching the Recognition Composition Law setting where $J$ is the unique solution once constraints and regularity are fixed. Downstream consumers are the T5 uniqueness developments that quote exchange invariance, $F(x)=F(1/x)$, identity zero, and unit normalization as the hypothesis package. The curvature-gauge lemmas keep dimensionless physics free of additive junk, which matters when matching the RS cost to $\cosh(\log x)-1$. No used_by edges are recorded on this page yet; the module is infrastructure for the verification side of T5 rather than a leaf theorem.
scope and limits
- Does not prove full T5 J-uniqueness or identify J with (x+x^{-1})/2-1.
- Does not derive every constraint from the ledger; inherits LedgerCost's no-go on the underivable remainder.
- Does not fix dimension D=3, the eight-tick period, or phi; those are other chain steps.
- Does not supply numerical constants (alpha band, masses) or empirical tests.
- Does not assert a unique cost without extra regularity hypotheses stated elsewhere.
depends on (2)
declarations in this module (16)
-
def
RecognitionLogCost -
theorem
recognition_exchange_invariance_axiom -
theorem
recognition_identity_axiom -
def
IsCostFunction -
theorem
reciprocal_symmetry_forced -
theorem
unit_normalization_forced -
theorem
curvature_is_gauge_normalization -
theorem
curvature_cancels_in_dimensionless -
def
ExchangeInvariant -
def
ReciprocalSymmetric -
def
IdentityRecognitionZero -
def
UnitNormalized -
theorem
t5_constraints_are_forced -
theorem
t5_constraints_forced_from_ledger -
theorem
t5_constraints_imply_reciprocal_from_ledger -
theorem
t5_constraints_implies_reciprocal_from_ledger