IndisputableMonolith.Physics.NullRecognitionMode
Defines null recognition modes: zero total J-cost sequences of positive carrier ratios on the discrete tick lattice. Introduces carrier events, propagating modes, per-tick and total mode cost, gauge equivalence, and the canonical and zero NRM representatives. Physicists working the massless or pure-gauge sector of Recognition Science would cite it. The module is mostly definitions plus short cost-vanishing lemmas.
claimA carrier event is a positive recognition ratio $r > 0$ at one tick. A propagating mode is a sequence of such events. Per-tick cost is the J-cost of the ratio; total mode cost is the sum over ticks. A null recognition mode (NRM) is a mode with total cost zero. Gauge equivalence identifies modes that differ by a global rescaling. The canonical NRM and the zero mode are distinguished representatives with ratio $1$ and vanishing cost.
background
Recognition Science measures mismatch by the J-cost $J(x) = (x + x^{-1})/2 - 1$ (equivalently $\cosh(\log x) - 1$), imported from the Cost module. On the discrete tick lattice fixed by the eight-tick octave, a single recognition act is a positive ratio; a propagating mode is a time series of such ratios.
Null modes are those whose summed J-cost vanishes. Because $J \ge 0$ and $J(x) = 0$ iff $x = 1$, zero total cost forces every ratio to be unity up to gauge. Gauge equivalence quotients by global rescalings that leave the physical content unchanged, so the theory can pick a canonical representative.
The module therefore sits at the interface between the abstract cost functional and the massless or pure-gauge sector of the RS particle spectrum.
proof idea
This is primarily a definition module. CarrierEvent, PropagatingMode, perTickCost, totalModeCost, GaugeEquivalent, canonicalNRM and zeroMode are introduced as data. Short lemmas then record that the canonical and zero modes have ratio $1$, per-tick cost $0$, and total cost $0$, by direct unfolding of $J(1) = 0$ and summation. No deep forcing or uniqueness argument lives here; the work is bookkeeping that later physics modules can invoke.
why it matters in Recognition Science
Null recognition modes supply the RS analogue of massless or pure-gauge degrees of freedom: carriers that propagate without accruing J-cost. Downstream mass and coupling constructions need a clean zero-cost baseline against which massive rungs on the phi-ladder are measured. The canonical NRM and zero-mode lemmas close the bookkeeping so that total-cost identities elsewhere can subtract a genuine zero rather than an ad-hoc constant.
Within the forcing chain the module does not itself prove T5–T8, but it consumes the J-cost uniqueness already fixed upstream and prepares the kinematic setting in which eight-tick periodicity and three-dimensional propagation act on cost-free carriers. No used-by edges are recorded yet; the natural parents are later Physics modules that assemble free-field or gauge sectors.
scope and limits
- Does not prove uniqueness of J or force phi; those live in the UnifiedForcingChain.
- Does not derive mass formulae or the alpha band; only zero-cost kinematics.
- Does not assert dynamical equations of motion for the modes.
- Does not treat charged or massive carriers; only null (zero total cost) modes.
- Does not record downstream consumers; used_by is presently empty.
depends on (1)
declarations in this module (21)
-
structure
CarrierEvent -
structure
PropagatingMode -
def
perTickCost -
def
totalModeCost -
def
GaugeEquivalent -
def
canonicalNRM -
abbrev
zeroMode -
theorem
canonicalNRM_ratio -
theorem
zeroMode_ratio -
theorem
canonicalNRM_perTickCost -
theorem
nrm_totalCost_zero -
theorem
zeroMode_totalCost -
theorem
nullRecognitionMode_nonempty -
theorem
zeroCostMode_nonempty -
theorem
perTickCost_nonneg -
theorem
perTickCost_zero_of_total_zero -
theorem
ratio_eq_one_of_total_zero -
theorem
zeroCostMode_unique_up_to_gauge -
structure
NullRecognitionModeCert -
def
nullRecognitionModeCert -
theorem
nullRecognitionModeCert_inhabited