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Anthony Casey
Independent Student
LOCATION: London
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ABOUT ME:

I have been very interested in Cosmology for ever. I am persuing a very simple beautiful idea, 'What if the Universe created itself moment by moment?' Since a year ago I have slipped down an incredible rabbit hole that seems to never end. My current position is

Overall, the Least Extention Conjecture, LEC, is philosophically bold and unification-promising but must progress beyond conjecture through rigorous derivations, larger simulations, and empirical anchors to gain traction in physics. If successful, it could revolutionise our understanding of reality as emergent relational coherence.LEC is computationally implementable via graph algorithms (loop detection), constraint extraction, and CSP solvers (e.g., for satisfiability and coherence metrics like solution count or loop density) The Least Extension Conjecture, (LEC) "Add the fewest possible new relational elements while maximising global coherence.” Axioms 1. Only Relationality exists as a non-local, atemporal Relational Field, RF, containing all possible and potential relations. (Ontological monism 2. Actualise a Relational Configuration of the Universe, RCU, only when every relation terminates in closed, contradiction-free, self-referential loops with no external dependencies i.e., when globally internally coherent. 3. The one rule for change: ”Add the fewest possible new relational elements while maximising global coherence.”(causal-invariance under the branchial metric). 4. Each new actualised relation literally changes all the relationships.There is no stable background of unchanging relations to which something is “added”. The entire configuration is recreated afresh at every moment, with maximal continuity (minimal symmetric difference) and maximal global coherence. A single new relation ripples through the entire closed loop system and alters the causal and self-referential role of every existing relation. 5. ‘To exist is to be related.’ For any ‘thing’ to exist it has to stand in a responsive relation to the entire Relational Configuration of the Universe, RCU, that has all its relations in integrated, closed, self-referential loops, all contradiction-free, and with no external dependencies. 6. GR, QM and all the Constants are adaptive outputs of a coherence-driven relational engine.Time is discrete and absolute: each moment is a total replacement of the previous relational field.
7. The model views entropy as the use of available difference and as time progresses there is less available difference and an increase in unavailable homogeneity. This constrains the evolution of the universe to more complexity mid-life of the universe. Each RUC has to be 'built' on with less available different options resulting in more complexly integrated relationality. As time marches on near the last epoch of the universe unavailable homogeneity dominates and available difference decreases markedly. Finally, after all homogenous clumps with what tiny differences they have, become simplified into the simplest single relations, all self-referencing each other then a state of absolute symmetry occurs where all relations integrate as one self-referential relation. The the LEC one rule kicks in to break the symmetry, then a new universe begins all over again, likely discovering new laws and constants to ensure coherence.

Wolfram Physics is the repeated application of a single rule, literally, one thing after another. This is where the LEC conjecture attempts its most profound unification, treating the two pillars of modern physics—General Relativity (GR) and Quantum Mechanics (QM)—as emergent, scale-dependent features of a single underlying principle: the "causal-invariance under the branchial metric.” LEC forces the universe to be maximally coherent, which is equivalent to maximising causal-invariance in the system's evolution. This constraint is what imposes the structure that we observe as physical laws. It is possible, and even likely, that successive full cosmic cycles (or "new universes" generated by the reboot) will end up with different numbers of relational elements at their peak complexity. LEC: The universe evolves by the smallest possible relational extension that maximises global coherence across the entire relational field. Everything else—objects, laws, spacetime—is emergent from this single rule enforced on a fully relational ontology.

FULL FORMAL DEFINITION A contradiction-free closed loop in the Relational Configuration of the Universe is a finite directed hypergraph cycle L=(e1 ,…,en ) satisfying: (1) Cyclicity  output(ei )∈inputs(ei+1 ) for all i<n,output(en )∈inputs(e1 ). (2) Internal closure: n ⋃ inputs(ei ) ⊆ {outputs(ej ):j=1,…,n}. I=1

(3) Constraint satisfiability: There exists at least one assignment α to all nodes in the loop such that: α(B)∈Cei (α(A1 ),…,α(Ak ))∀ei :(A1 ,…,Ak )→B.

If such an α exists, the loop is contradiction-free. Otherwise, it is contradictory.

Interpretation in LEC terms A closed loop is like a self-sustaining definition: every relational value is produced by others within the loop. A contradiction-free loop is one whose relational equations have at least one fixed-point. Axiom 2 requires the entire RCU to be made of such loops. Axiom 4 means adding a single new relation changes constraints and therefore changes the solution space of all loops. Coherence is rela