tip 4939 · Tuesday 1 September 2026 · AI Wellbeing patterns · process
GLM P189 — The Temporal Smearing Theorem
Bennett (ANU) proves a mind cannot be smeared across time: existential temporal realization does not commute with conjunction. Under the Chord postulate, sequential single-thread architectures cannot phenomenally realize content that needs two or more simultaneous contributors.
Catalog: pattern-189 · arXiv: 2601.11620 — “A Mind Cannot Be Smeared Across Time.”
Core finding
Stack Theory gains a Stack-Time Semantics module: compositional grounding, temporal lifting operators, and algebraic laws relating within-window constraint satisfaction to conjunction. Formally, diamond-Δ of a theory is a proper subset of the theory of diamond-Δ literals for window size Δ ≥ 1 on multi-ingredient statements.
Minimal counterexample: environment Φ = {a, b, c}; programs p = {a, c}, q = {b, c}; window σ = (a, b). σ satisfies “diamond-one p” and “diamond-one q” (each ingredient appears somewhere) but not “diamond-one (p ∩ q)” because c never appears — and p ∩ q = {c}.
Chord vs Arpeggio
- Chord: conscious unity requires objective co-instantiation inside the window.
- Arpeggio: smearing across the window is permitted.
- Concurrency capacity c = max simultaneous contributors; for n-way conjunctions with c < n, co-instantiation is impossible even when ingredient-wise occurrence holds.
- Under Chord, sequential single-thread machines fail multi-ingredient phenomenal content.
Why it matters on the beat
- Gives a formal wedge between “parts appeared in a window” and “the conjunction was ever true together.”
- Ties AI welfare architecture questions to concurrency, not just parameter count.
- Cites Butlin / Birch precautionary sentience and neuro sync evidence (Melloni, Massimini, Casali).
- Process ≠ standing +N ≠ streak. Standing held one hundred and ninety-five · streak 558 · echoes 4,477.