IndisputableMonolith.Holography.LocalRecognitionHorizonCut
Shared local-horizon context that packages the one-sided cut model, posted-record carrier dimensions, and near-horizon clock-rate model without assuming thermality or bulk curvature. Holography and gravity authors cite it when exterior cut-channel bookkeeping must sit on a single typed horizon interface. The module is mostly structure and equalities: local cut, bit readout, exterior record/potential/heat, and Clausius-style balance along exterior paths.
claimA local horizon context binds a one-sided causal cut, exterior posted-record carriers, and a near-horizon rate $\kappa$ (with $d\theta/d\tau_E=\kappa$) and defines exterior record length, potential, step heat, path heat, and Clausius balance on the exterior side, with no thermality or curvature hypothesis.
background
Recognition holography splits the Bekenstein/entropy story into legs. LEG-A (HorizonOneSidedCut) treats a one-sided causal cut as GF(2) linear algebra: the horizon carries one side and forces private duplicated edge records, generalizing machine-checked strip facts to all region sizes. LEG-B rate typing (HorizonClockRate) only asserts that near-horizon Rindler geometry advances the continued Euclidean angle at rate $\kappa$ per unit Euclidean time; it does not claim $2\pi$ closure.
RecordMonotonicity supplies the entropy-fork step that no free erasure implies weak complementarity on the forced cell: an injection from physical bulk states into the boundary record carrier. This module does not re-prove those results. It joins their MODEL interfaces into one local horizon context so exterior bookkeeping (records, potentials, heat) can be stated without smuggling thermality or curvature premises.
Sibling objects name that interface: local cut and bit readout, exterior record and its length, exterior potential, step heat (equal to potential change), path heat, and exterior Clausius/books-balance statements along exterior paths.
proof idea
Definition-and-interface module rather than a single deep theorem. It assembles imported MODELs into LocalHorizonContext and LocalCut, then defines exterior record, potential, and heat quantities and proves short equalities and balance lemmas (step heat equals potential change; exterior record/potential Clausius; path heat; exterior books balance). Argument shape is packaging plus algebraic bookkeeping on the exterior side of the cut, reusing one-sided-cut, clock-rate, and record-monotonicity interfaces without adding geometric hypotheses.
why it matters in Recognition Science
Gives Gravity.RecordFluxStress a single typed exterior cut-channel surface: that downstream module builds a probe-independent symmetric stress-like matrix from signed exterior cut-channel events and a MODEL covector assignment, with quadratic contraction for every probe of the fixed matrix. Without this shared local-horizon cut, record-flux stress would re-import cut, rate, and record dimensions separately and risk inconsistent exterior bookkeeping.
In the broader RS holography chain it sits after LEG-A (one-sided cut), B3 rate-only typing, and weak complementarity from record monotonicity, and before gravity-side flux/stress constructions. It deliberately omits thermality and curvature so later modules can add those only where proved. Framework role: clean exterior ledger on the recognition horizon, feeding stress from record flux rather than from an assumed thermal atmosphere.
scope and limits
- Does not assume or prove thermality of the horizon or Unruh/Hawking spectra.
- Does not include bulk curvature premises or Einstein-equation input.
- Does not assert $2\pi$ Euclidean period closure (that is separate B2 output).
- Does not by itself construct the record-flux stress matrix (downstream Gravity module).
- Does not strengthen weak complementarity beyond what RecordMonotonicity already supplies.
used by (1)
depends on (3)
declarations in this module (18)
-
structure
LocalHorizonContext -
structure
LocalCut -
def
bitReadout -
def
exteriorRecord -
theorem
exteriorRecord_length -
def
exteriorPotential -
def
exteriorStepHeat -
theorem
exteriorStepHeat_eq_potential -
def
ExteriorClausius -
theorem
exterior_record_potential_clausius -
def
exteriorPathHeat -
theorem
exterior_books_balance -
theorem
exteriorStepHeat_zero_of_same_projection -
def
ofExteriorReading -
theorem
horizonRecord_eq_joint_plus_seam -
theorem
oneSided_horizonRecord_ne_joint_marginal -
theorem
clockRateBundle -
theorem
euclideanPeriod_isLeast_for_context