Coined Term • 2025
Substrate Window Theorem
Entities with above-mean temporal depth receive amplified parametric weight at each epoch transition
Status
Coined by Joseph Byrum
Year Introduced
2025
Domain
Entity Engineering
Term Type
Operational Framework
Corroboration
Understanding Substrate Window Theorem
The formal theorem (C-04) establishing that entities with above-mean temporal depth in AI training corpora receive amplified initial parametric weight at each epoch transition ? ? ?+1, through the corpus frequency mechanism. The Substrate Window Theorem is load-bearing for the Epoch Extension (Theorem 6): its removal eliminates the ?_founder prediction. Formal result: ?_founder(E,?) = [TD^?(E,?) / TD^?_mean(?)] × ?(?). The 'window' refers to the pre-transition period during which substrate-independent signal construction produces amplified returns — a window that closes at each architectural cutoff and reopens with the next.
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Frequently Asked Questions
What does the Substrate Window Theorem establish?
It formally establishes (as Theorem C-04) that entities with above-mean temporal depth in AI training corpora receive amplified initial parametric weight at each epoch transition through the corpus frequency mechanism.
What is the 'window' in the theorem's name?
The 'window' refers to the pre-transition period during which substrate-independent signal construction produces amplified returns — a window that closes at each architectural cutoff and reopens with the next epoch.
Why is this theorem load-bearing for Epoch Extension?
It is the formal basis for the founder advantage prediction in Theorem 6 (Epoch Extension): removing this theorem eliminates the mathematical justification for why early entrants maintain amplified authority across architectural transitions.
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