ITT vs. GR Comparison

Complete Side-by-Side Analysis: Black Holes in General Relativity vs. Planck Cores in Intent Tensor Theory

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1. Fundamental Concepts

Concept	General Relativity / QFT	Intent Tensor Theory
Nature of Spacetime	Continuous manifold	Recursive substrate (CTS)
Gravity Source	Mass-energy curves geometry	Memory alignment creates curvature
Information Carrier	Not specified / problematic	Memory tensor M_ij
Time	Coordinate / proper time	Emergent from drift sigma_theta
Fundamental Scale	Planck length ell_P	Maximum recursion n_max

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2. Black Hole Formation

Aspect	GR/QFT	ITT
Collapse Mechanism	Gravitational contraction	Recursive memory accumulation
Critical Threshold	Schwarzschild radius r_s = 2GM/c^2	Shell-lock threshold L approaches 1
Horizon Type	Event horizon (global)	Recursive boundary (local)
Interior	Spacetime continues inward	Recursion depth increases
Endpoint	Singularity	Planck Core

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3. Temperature

Property	GR/QFT	ITT
Formula	T_H = hbar c^3 / (8 pi G M k_B)	T_ITT proportional to sigma_theta
Mass Dependence	T proportional to 1/M	T approaches 0 as L approaches 1
Large Mass	Cold	Cold (agrees)
Small Mass	Hot (diverges)	Cold (approaches zero)
Zero Mass Limit	T approaches infinity	T = 0
Minimum Temperature	None	0 K (at Planck-lock)
Maximum Temperature	Unbounded	Finite (bounded by D_max)

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4. Entropy

Property	GR/QFT	ITT
Formula	S = k_B c^3 A / (4 G hbar)	S_max = n_max * ell_P^2 * N_folds
Basis	Geometric (area)	Computational (recursion)
Scaling	S proportional to M^2	S proportional to n_max
Upper Bound	Bekenstein bound	Recursion ceiling
Information Encoding	Surface holography	Volume + shell memory
At Evaporation	Decreases	Saturates

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5. Radiation

Property	GR/QFT	ITT
Mechanism	Hawking radiation (pair creation)	Drift-induced emission
Spectrum	Thermal (blackbody)	Modified thermal
Duration	Until complete evaporation	Until Planck-lock
Final State	Complete evaporation	Radiation ceases
Energy Output	~ M c^2 total	Limited by sigma_theta
Final Burst	Yes (gamma-ray)	No

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6. Endstate

Property	GR/QFT	ITT
Name	Singularity / Remnant	Planck Core
Curvature	Infinite	Bounded
Size	Zero (point)	r_PC ~ sqrt(n_max) * ell_P
Mass	Zero or undefined	Finite Planck Core mass
Temperature	Undefined or infinity	0 K
Entropy	Unclear	S_theta_max
Stability	Unstable (evaporates)	Absolutely stable

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7. Information

Property	GR/QFT	ITT
Information Paradox	Present	Resolved
Information Location	Lost to singularity?	Preserved in M_ij
Unitarity	Violated or unknown	Preserved
Retrieval	Impossible after evaporation	Never lost
Encoding	Holographic (surface)	Memory tensor (volume + shell)

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8. Time Behavior

Property	GR/QFT	ITT
At Horizon	Infinite redshift	gamma_ITT decreases
At Singularity	Undefined	Time stops (gamma = 0)
Time Dilation Source	Spacetime curvature	Substrate load (LOAD identity)
Infalling Observer	Reaches singularity in finite proper time	Experiences lock
External Observer	Never sees crossing	Sees gradual lock

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9. Quantum Effects

Property	GR/QFT	ITT
Hawking Radiation	Thermal pair creation	Drift-limited emission
Entanglement	Firewall paradox	Lock preserves entanglement
Quantum State	Mixed after evaporation	Pure (unitary evolution)
Planck-Scale Physics	Unknown/singular	Bounded recursion

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10. Observational Predictions

Observable	GR/QFT	ITT
GW Ringdown	Exponential decay	Modified + echoes
Shadow Inner Edge	Soft	Sharp
Hawking Burst	Expected	Absent
PBH Remnants	None	Stable cores
Late Thermal Signal	Increasing	Cutoff

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11. Summary Table

Feature	GR/QFT Black Hole	ITT Planck Core
End State	Singularity	Bounded Core
Temperature	Diverges	Zero
Entropy	Area-scaled	Recursion-bounded
Radiation	Until evaporation	Halts at lock
Information	Lost?	Preserved
Time	Undefined at singularity	Stops at lock
Stability	Evaporates	Absolutely stable
Paradoxes	Information, Firewall	Resolved

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