Joint Local Sieves and First-Arrival Dynamics of Goldbach Imbalances: Exact Modular Correlations, Void Probabilities, Factorial Cumulants and a Conditional Poisson Law
- 1Imperial College London
Abstract
We investigate the distance from the centre of an even integer to its nearest Goldbach representation, emphasizing the guaranteed-reset progression N≡10pmod60. Candidate representations occur at the lattice sites N/2±6j, and the first successful site defines a first-arrival process in the normalized imbalance interval. For arbitrary finite families of candidate sites we prove an exact Chinese-remainder-theorem density formula for surviving local congruence classes. The associated two-site multiplier is explicitly repulsive in the generic case and attractive when i≡± jpmodℓ. A four-site selection gives an exact joint non-occurrence theorem modulo $7$. Computations over 483,333 even targets in [106,3·107] compare sieve-predicted pair correlations with actual prime pairs and examine the void probability using the first three factorial cumulants. We formulate and prove a conditional moment-to-Poisson theorem that isolates the stronger, presently unavailable, high-order prime-tuple estimates required for an exponential first-arrival law. All finite residue-count identities are unconditional; numerical fits, heuristic Euler products, and asymptotic conjectures are labeled separately.
Related
- Quantum-Enhanced Inference of Conditional Future Probabilities with Reduced Memory Cost
- Conditional splitting probabilities for hidden-state inference in drift-diffusive processes
- Isogenic forebrain organoids uncover early neurodevelopmental alterations and imbalances in neuronal function leading to hyperexcitation in Gaucher disease
- Sustained Ion Imbalances Enhance Ferroptosis
- Climate change and citrus nutrition: mechanisms, nutrient imbalances, and inclusive management
BibTeX
@misc{bilokon2026joint,
title = {{Joint Local Sieves and First-Arrival Dynamics of Goldbach Imbalances: Exact Modular Correlations, Void Probabilities, Factorial Cumulants and a Conditional Poisson Law}},
author = {Paul Alexander Bilokon},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23463921},
url = {https://zenodo.org/records/23463921},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Joint Local Sieves and First-Arrival Dynamics of Goldbach Imbalances: Exact Modular Correlations, Void Probabilities, Factorial Cumulants and a Conditional Poisson Law
AU - Paul Alexander Bilokon
PY - 2026
DA - 2026/10/19
PB - Zenodo
DO - 10.5281/zenodo.23463921
UR - https://zenodo.org/records/23463921
AB - We investigate the distance from the centre of an even integer to its nearest Goldbach representation, emphasizing the guaranteed-reset progression N≡10pmod60. Candidate representations occur at the lattice sites N/2±6j, and the first successful site defines a first-arrival process in the normalized imbalance interval. For arbitrary finite families of candidate sites we prove an exact Chinese-remainder-theorem density formula for surviving local congruence classes. The associated two-site multiplier is explicitly repulsive in the generic case and attractive when i≡± jpmodℓ. A four-site selection gives an exact joint non-occurrence theorem modulo $7$. Computations over 483,333 even targets in [10^6,3·10^7] compare sieve-predicted pair correlations with actual prime pairs and examine the void probability using the first three factorial cumulants. We formulate and prove a conditional moment-to-Poisson theorem that isolates the stronger, presently unavailable, high-order prime-tuple estimates required for an exponential first-arrival law. All finite residue-count identities are unconditional; numerical fits, heuristic Euler products, and asymptotic conjectures are labeled separately.
ER -