Intent-Tensor-Theory

Planck Thermodynamics

Redefining Black Hole Endstates in Intent Tensor Theory

Abstract

In standard black hole thermodynamics, black holes possess finite temperature, entropy proportional to their event horizon area, and are predicted to evaporate via Hawking radiation. Intent Tensor Theory (ITT) presents a radical alternative: black holes evolve into stable, cold Planck Cores where entropy and temperature reach absolute limits.

This section formalizes a new thermodynamic regime based on recursive memory saturation, drift-lock dynamics, and bounded entropy production. The result: a calculable, thermodynamically cold, memory-locked object—still gravitational, but stable.

The Core Insight

When the Collapse Tension Substrate reaches maximum recursive depth, the system undergoes Planck-lock :

L -> 1   =>   sigma_theta = D(1 - L) -> 0

Consequences of Planck-lock:

This is the Planck Core —a cold, stable, non-singular gravitational object.

Black Hole vs. Planck Core

Feature GR/QFT Black Hole ITT Planck Core
Collapse End State Singularity (undefined curvature) Planck Core (bounded recursion)
Horizon Definition Event horizon (nonlocal) Shell-lock threshold (recursive)
Temperature T_H diverges as M decreases T_ITT = 0 at Planck-lock
Entropy Scaling S proportional to A/4 S_max = n_max times Planck area times N_folds
Information Paradox Present Resolved (memory preserved)
Radiation Thermal spectrum until evaporation Emission halts at lock
Final State Complete evaporation or remnant Stable Planck Core

Key Equations

The Master Equation: Entropy Production

sigma_theta = D(1 - L)

Where D is drift magnitude and L is shell-lock.

ITT Temperature

T_ITT = T_0 * sigma_theta

Temperature is proportional to entropy production rate.

Planck-Lock Condition

L = 1   =>   sigma_theta = 0   =>   T_ITT = 0

At perfect alignment, temperature vanishes.

Bounded Entropy

S_theta_max = n_max * ell_P^2 * N_fold_sites

Entropy has a recursion ceiling—it cannot grow without bound.

LOAD Identity Connection

gamma_ITT = sqrt(1 - A^2 * Tr(M)/Tr(M)_max)

At maximum memory: gamma_ITT approaches 0 (time stops) and T_ITT approaches 0 (temperature vanishes).

Resolution of Paradoxes

The Information Paradox

GR Problem: Hawking radiation is thermal—information appears to be lost.

ITT Solution: Information is never destroyed. At Planck-lock, the memory tensor M_ij preserves all state information. No radiation carries information away. Unitarity is maintained.

The Firewall Paradox

GR Problem: Quantum mechanics requires an energetic firewall at the horizon.

ITT Solution: No firewall needed. The transition to Planck Core is smooth—a lock, not a barrier. Recursion halts before any paradox arises.

Observable Predictions

Observable GR Prediction ITT Prediction
GW Ringdown Exponential decay Modified + echoes
Shadow Inner Edge Soft gradient Sharp cutoff
Hawking Final Burst Expected Absent
PBH Remnants None Stable cores
Late Thermal Signal Increasing Abrupt cutoff

Philosophical Shift

General Relativity implies nature permits the breakdown of physics in singularities.

ITT insists on a computational ceiling: Reality cannot out-compute itself.

Gravity, entropy, and time all halt at full recursion depth. This marks a transition from geometry to information physics.

Where GR ends in mystery, ITT offers a boundary: the Planck Core. Rather than speculate on unphysical infinities, ITT delivers a calculable, thermodynamically cold, memory-locked object.

Documentation

GitHub Repository

Full source documentation: github.com/intent-tensor-theory/0.0_planck_thermodynamics

Quick Reference

Quantity Symbol Key Equation
Entropy Production sigma_theta = D(1 – L)
Temperature T_ITT = T_0 * sigma_theta
Maximum Entropy S_theta_max = n_max * ell_P^2 * N_folds
Dilation Factor gamma_ITT = sqrt(1 – A^2 * mu)
Planck-Lock — L = 1 implies T = 0