Instancology: A Formal Framework for Quantum-Cosmo

Instancology: A Formal Framework for Quantum-Cosmological Resolution

1. Foundational Axioms: The Instance-Field

Let the instance-field ? be a dynamical, layered network structured by the issuance of discrete units called instances. Each instance i? ∈ ? is defined as a tuple:

i? = (e?, τ?, ??)

Where:

- e?: An eventual emergence (e.g., a quantum transition, a spacetime articulation).

- τ?: A temporal span (the persistence duration of the instance).

- ??: A relation set (directed and weighted links to other instances, possibly defined via sheaf cohomology).

Reality stabilizes when d??/dτ? ≤ Θ_decay.

2. Quantum Mechanics: Collapse via Instance Saturation

Modified Born Rule:

P(j) = |?ψ? | ψ?|? / Σ? S(i?, i?), where S(i?, i?) is instance-overlap.

Prediction: Decoherence deviates from unitary predictions when relational entanglement is low.

Test: Weak measurement setups detect non-Markovian decoherence spikes near Θ_decay.

3. Spacetime as a Relational Instance-Network

The spacetime metric g_μν(x) emerges from instance-density ρ(?):

g_μν(x) ∝ log(∫_{x-Δx}^{x+Δx} ρ(?) dτ)

When ρ(?) → ∞, instance-field fractures (no point-singularity).

Test: Gravitational wave detectors should observe non-Poissonian holographic noise.

4. Consciousness as Instance-Binding Dynamics

C = {i? | ?? ∩ ?_self ≠ ?}, i.e., instances resonating with self-binding structure.

Implication for AI: Consciousness requires relational instancing, not mere computation.

5. Experimental Forecasts and Deviations

Prediction                         | Experiment                          | Expected Signature

Instance-collapse decoherence      | Weak measurement + tomography       | Non-Markovian spikes at Θ_decay

Spacetime granularity              | Holometer/Fermi-GBM reanalysis      | Log-fractal holographic noise

Entanglement as relational loss    | Bell tests w/ instance suppression  | Visibility decay ∝ S(i?, i?)

6. Philosophical Leap, Scientific Anchor

- Not metaphysics alone: Falsifiable by relational-temporal perturbation.

- Unified substrate: QM, GR, and consciousness within the instance-field.

- Mathematical novelty: Sheaves, stochastic decay, topological fragmentation.

7. Concluding Frame: Instancology as Post-Theory Epistemics

Instancology identifies the conditions under which a universe appears as an instance.

In the deepest layer, not things, but issuance—not causes, but coherence—not emergence, but instance.

Future science must trace relational issuance across scales, minds, and machines.