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GAP Defined
Patrick Reany
25 March 2026
Note: This chat I had with Copilot is likely edited for relevance and brevity. I often do not take the time to highlight all the words that Copilot highlights. Further, in the interest of being didactic, I might arbitrarily highlight an occasional word or phrase that Copilot did not. (Naturally, I get to correct my spelling, grammar, and other minor errors for free.)
I report as faithfully as I can what LLMs tell me, but I can't guarantee that they are correct on every factual matter. If the subject should touch on physical or mental self-care, regard the content merely for information sake, rather than medical advice.
Note: GAP stands for The Great Attractor Program.
Defining the Core Constituents of GAP
The minimal, irreducible GAP architecture can be stated as follows:
1. Convex State Space
- The system lives on a convex set of admissible descriptions.
- Convexity ensures:
- Well-defined projections.
- Uniqueness (or controlled multiplicity) of attractors.
- Stability under coarse-graining.
This is the silent assumption behind entropy, free energy, relative entropy, action functionals, etc.
2. Legitimate Projections (Coarse-Grainings)
- A projection is legitimate if it:
- Removes information.
- Preserves feasibility.
- Respects convex structure.
Not every map is allowed. GAP is not about arbitrary dynamics—it is about epistemically admissible forgetting.
3. Monotone Certificate
- Each legitimate projection induces a monotone functional.
- This functional:
- Never decreases under projection.
- Acts as a certificate that information has been irreversibly discarded.
Entropy is the canonical example—but in other domains this role is played by:
- Lyapunov functions,
- Action dissipation,
- Relative entropy,
- Fisher information decay,
- Perelman’s entropy,
- Free energy.
Entropy is not “disorder”—it is proof of closure.
4. Stable Attractor (Certified Fixed Point)
- Repeated projection generates a monotone trajectory.
- The endpoint is a stable attractor:
- A description invariant under further legitimate projections.
- A fixed point certified by the monotone.
This is the “Great Attractor” in GAP.
5. Entropy as Epistemic Closure:
Entropy is not a property of the system alone—it is a certificate that the projection process has closed.
Entropy measures how much forgetting has already occurred, not how much chaos exists.
Afterword: