Scholar / Unpublished Manuscript
A manuscript in progress. Classical general relativity predicts infinities where collapsing matter and the early universe evolve toward infinite curvature. This framework assigns division by zero a finite, observer-dependent value, x/0 = Ω·e^(iτ), and derives testable predictions from it. Search the chapters below, or ask Astro.
12 of 12 chapters.
Chapter 1 · Part I · Core Theory
Builds a new number system where dividing by zero gives a finite value: a fixed universal size Ω tied to the Planck length, times a phase factor that depends on the observer. Extends the complex numbers into a graded algebra so every operation physicists need still works.
Chapter 2 · Part I · Core Theory
Explains where the observer-dependent phase comes from: the accumulated twist (holonomy) of an observer connection traced along the observer's path, combining gravitational geometric phase, dynamical phase, and measurement context. Derives transformation rules proving different observers still get the same physics.
Chapter 3 · Part I · Core Theory
Derives the framework's equations of motion from a generalization of the action principle behind Einstein's equations. In ordinary conditions everything matches standard general relativity; at would-be singularities it predicts finite, observer-independent curvature instead of infinities.
Chapter 4 · Part I · Core Theory
Verifies the new equations respect spacetime symmetries and standard conservation laws (energy-momentum via Noether's theorem), and that the algebra does not contradict itself.
Chapter 5 · Part I · Core Theory
The headline testable claim: the curvature at a black hole's center is a finite number set by the black hole's mass, identical for every observer, rather than an infinity.
Chapter 6 · Part II · Observational Predictions
Predicts how a finite Ω-scale core at a black hole's center would change gravitational waves from mergers: post-merger echoes, altered ringdown tones, inspiral phase shifts, and changed radiation reaction.
Chapter 7 · Part II · Observational Predictions
Catalogs other observable consequences of the observer-dependent machinery: gravitational geometric-phase effects, measurement-entanglement signatures, relativistic transformation effects, and cosmic variability.
Chapter 8 · Part II · Observational Predictions
Shows how the framework slots into quantum field theory practice: corrections to effective field theories, modified renormalization-group flow, vacuum-fluctuation effects, and changes to black-hole evaporation.
Chapter 9 · Part II · Observational Predictions
Concrete numbers for LIGO-Virgo-KAGRA, LISA, the Event Horizon Telescope, pulsar timing arrays, and cosmological redshift effects. Includes predicted ~10⁻⁴-level deviations from general relativity for LISA.
Chapter 10 · Part II · Observational Predictions
Quantifies the uncertainty budget behind every prediction, from numerical-relativity simulation errors to detector calibration and astrophysical noise.
Chapter 11 · Part II · Observational Predictions
The scorecard: every existing measurement (GW150914 ringdown, the M87* shadow, pulsar timing) matches classical general relativity within errors, and the framework's predicted deviations sit below today's detection thresholds.
Chapter 12 · Part II · Observational Predictions
A testing roadmap: LIGO A+ (2025 to 2030), LISA (2030 to 2040), next-generation detectors (2040+), with explicit pass/fail criteria the theory must meet.
Conversation
Astro is a model served from the DGX Spark that knows this manuscript end to end. Ask it to explain a chapter, defend a prediction, or steelman an objection.
Status
This is an unpublished manuscript, not a peer-reviewed paper. It has not been submitted to a journal or posted to a preprint server. The manuscript's own analysis reports null statistical significance against current data and flags open problems: dimensional inconsistencies in some predictions, tension with cosmic microwave background bounds, and an observer connection not yet derived from first principles.
It is published here so others can study it, check the math, and argue with it. That is the point.