module module high

`IndisputableMonolith.Quantum.BlackHoleInformation`

Black hole models in Recognition Science are built from a mass parameter, yielding the Schwarzschild radius, Bekenstein-Hawking entropy proportional to mass squared, Hawking temperature, and checks on holographic saturation. Quantum gravity researchers would cite these for information accounting in collapse. The module sequences definitions from the imported RS time quantum without proofs.

claimBlack hole characterized by mass $M$, with Schwarzschild radius $r_s(M)$, horizon area $A(M)$, Bekenstein-Hawking entropy $S_{BH}(M) = A/4$, Hawking temperature $T(M)$, information capacity, and holographic bound, all in RS units where $c=1$, $G = phi^5 / pi$, $hbar = phi^{-5}$.

background

The module sits in the quantum domain and imports the fundamental RS time quantum from Constants, described as: The fundamental RS time quantum (RS-native). τ₀ = 1 tick. It defines a black hole by its mass then derives radius, area, entropy, temperature, capacity, and bound, plus structures for falling entries and a ledger to track information.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

Supplies black hole entropy and information capacity constructions that integrate with the phi-ladder mass formula and J-uniqueness from the forcing chain. It supports holographic bound analysis in the D=3 spatial setting and connects to the eight-tick octave periodicity.

scope and limits

Does not prove information preservation during evaporation.
Does not model the black hole interior geometry.
Does not incorporate the Recognition Composition Law directly.
Does not address rotating or charged black holes.
Does not derive Hawking radiation from the J-cost functional equation.

depends on (1)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import

declarations in this module (25)

structure BlackHole L51
def schwarzschildRadius L58
def horizonArea L61
def bekensteinHawkingEntropy L65
theorem entropy_proportional_to_mass_squared L69
def hawkingTemperature L75
theorem hawking_temperature_pos L79
def informationCapacity L91
def holographicBound L95
theorem bh_saturates_holographic L98
structure FallingEntry L106
structure BlackHoleLedger L115
def addEntry L124
theorem information_preserved_on_infall L130
structure HawkingQuantum L136
structure EvaporationProcess L145
theorem information_conservation L156
theorem page_curve L163
theorem no_information_paradox L189
theorem no_firewall L205
theorem er_equals_epr L214
structure BlackHolePredictions L227
def rsPredictions L236
structure BlackHoleFalsifier L249
theorem current_understanding_consistent L258