One will, three pulls

The model

Mathematically, SYNCHRONY is a Lohe synchronization system on the unit sphere: every agent is a heading vector, and three channels compete for it. A rotating reference pole — the framework's "divine" channel — pulls steadily from one direction. The population's own centroid pulls each agent toward wherever the crowd already points. And a stochastic cultural field with an obliquely biased mean — the Zeitgeist, the framework's adversary — drags at everyone from an angle that is never quite opposite and never quite aligned. One agent carries a costed will: the player can steer, but steering spends a budget, and the budget is part of the physics.

The metaphysical vocabulary is a reading placed on the mathematics, not something the mathematics establishes. Inside the simulation, every metaphysical label has a neutral mathematical twin one hover away — "divine channel" is a rotating reference pole, "alignment" is a cosine — and the two registers never blur.

What this is, and is not

The simulation is an intuition pump, never evidence. Nothing it produces supports or refutes any metaphysical, psychological, social, or AI-related claim — a rule written into the project before its first result existed, and enforced by its own review machinery since. Where a registered prediction failed, the failure stands in the record, dated, never edited away; a record that only reports survivals would be an advertisement.

The honest-machine apparatus

The project's identity, as its own review panels converged on it, is not the model — it is the apparatus that keeps the model honest. The dynamics, numerics, and vocabulary are fixed in a frozen, versioned technical contract; nothing deviates silently. The kernel passed a seven-oracle verification ladder — from a closed-form reduction to determinism and convergence checks — before any graphics work was permitted. Predictions are pre-registered before their data exists, compiled into machine-scored clauses whose verdicts are three-valued: survived, killed, or unevaluable, with unevaluable terminal. Every agent's noise is keyed and consumed unconditionally, so each run is accompanied by bitwise-paired counterfactual twins — a twin with the will nulled, a twin with no budget — and agency is measured as the difference between a run and its twins, never as a fit.

Everything is deterministic and reproducible: the same configuration and seed produce the bit-identical run, and every exported clip burns its seed, parameters, and epistemic line into the frame — anyone who sees one can reproduce it exactly.

Goals

Three, in the project's own order: build a dynamical system worth staring at — every pixel live kernel output or labelled data, legible without lying; make the honesty machinery itself a research object, because pre-registration, refusal-first provenance, and adversarial review look portable to domains where the model is not; and map the model's phase structure by falsification — escape laws, metastability, heterogeneity — each claim registered before its data and corrected in the open when wrong. Across roughly a dozen campaigns so far, the apparatus has repeatedly caught its own author and its own orchestrating agents. That, the project's records conclude, is the finding.

Runs best on a desktop browser with WebGL. The simulation opens with a guided on-ramp; the sandbox and its full controls follow.

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