Concrete Work Orders for Leveling Up Any Isomorphism Claim
"Promotion is not getting another AI to agree. It is not finding more examples. It requires external evidence — something the mapping predicts that would be surprising if true and that wasn't already known."
Treating a pictorial similarity (shape of a curve, shared terminology) as if it already defines a morphism. "Energy flows like water" is not structural until you supply the differential equations and the variable dictionary. The images are Level 1. The equations are Level 2.
Time estimate: Weeks to months. If the physics is standard, the bottleneck is formalizing Domain B. Expect this to be the hardest step — most ISOs stall here for longer than expected.
The Non-Arbitrariness Test is the gate most ISOs fail silently. Before claiming Level 3, ask: if I tried to map the same physics to a DIFFERENT theological concept, would the mapping be worse? If the answer is "not really," the isomorphism is arbitrary and doesn't belong at Level 3.
Demonstrating a bijection on underlying sets but ignoring higher-level structure (topology, smooth structure, monoidal product). A bijection is necessary but not sufficient. You must check that the operations work, not just that the elements correspond.
Time estimate: Months to a year. This is where most ISOs stall. The bottleneck is usually the inverse functor G. Writing G reveals all the places where the mapping doesn't quite close — and that's useful. If G can't be written, the mapping is Level 2, and that's the honest answer.
Claiming Level 4 because the isomorphism is elegant or because it predicts things that are "basically true." Level 4 requires measurement. Elegance is not evidence. Unification is not verification. This is not a special Faith Through Physics standard — it's the standard Maxwell had to meet with electromagnetic waves and that Hertz supplied.
Time estimate: Years, not weeks. This is a research program's worth of work. It requires: operationalization → experiment design → data collection → independent replication. For the Faith Through Physics registry, Level 4 is a long-horizon goal. The framework's best current entries are at Level 3. That is not a failure. Level 3 is rigorous. Level 4 is the frontier.
"Promotion requires external evidence — something the mapping predicts that would be surprising if true and that wasn't already known when the mapping was constructed."
Physics formalized (geodesic equation, inverse-square law). Theological claim specified.
Independent definition of "moral mass" and "moral distance." Without these, the inverse functor G cannot be written.
Operationalize m_moral. If moral mass can be measured (e.g., via social consequence indices), the geodesic equation becomes testable.
QCD confinement and asymptotic freedom are well-specified. Covenant theology is formally articulable. The structural parallel (force increases with distance) is compelling.
Formal mapping: QCD color charge ↔ covenantal commitment. What is the theological analogue of color confinement?
Write the explicit substitution map. Close. This is one of the stronger Level 2.5 candidates.
Hill equation already written. Agonist/antagonist/receptor mapping specified. Threshold effects observable.
Empirical test: does the Hill coefficient (cooperativity parameter) actually vary with community faith density?
Congregational survey measuring cooperative grace uptake vs. solo-practice grace uptake. If Hill coefficient differs, the mapping is non-arbitrary.
PID controller mapping is precise: proportional (conscience) + integral (sanctification) + derivative (prophecy). Three-term structure elegantly resolves sovereignty/free will tension.
Longitudinal data on conscience/sanctification/prophetic function to test whether the three terms are actually independent and sum correctly.
Factor analysis of spiritual formation data separating the three channels. If they're independent components, the PID mapping is non-arbitrary.
Dual-error ROC space preserved. Autoimmunity ↔ legalism, immunodeficiency ↔ antinomianism mapping passes all four Level 3 tests.
Empirical data on legalistic communities showing autoimmune-like pathology rates (burnout, spiritual abuse, exits) vs. control congregations. Needs pre-registration and independent replication.
SIR model governs both domains. R₀ quantifiable in principle. Jeroboam super-spreader case maps to hub-node dynamics.
R₀ calculation on an actual church sin-propagation dataset. Social network analysis of a congregation tracking behavioral adoption over time. If R₀ > 1 predicts spread and R₀ < 1 predicts containment, the mapping crosses to L4.
12/12 stage matches. Independently forced causal ordering in both domains. Statistical significance 3.7σ conservative. Stages 4, 5, 6, 9 have concrete promotion paths.
Kibble-Zurek defect-density test on high-pressure vs. low-pressure conversion contexts. Prediction: faster evangelistic campaigns produce more post-conversion "defects" (doctrinal confusion, relapse) at the same rate as quenched helium produces vortex strings.
The framework is currently at Level 3 for its best entries. Level 4 requires an experimental program that does not yet exist. This is not a failure — it is an accurate statement of where the research stands. Level 3 means: rigorous, non-arbitrary, bidirectional, constrained. That is a meaningful epistemic position. It is not the same as proof. It is not nothing.