# Study 2: Blogger readiness

**Ready as part of a grouped working-model report**, with the title and text explicitly saying conditional mathematics. This is not evidence of a new physical device, physical discovery, worldwide novelty, or clinical proof.

I read both complete supplied derivations, the supplied result summary, and all of `verify_two_models.py`. The code uses only the Python standard library and writes CSV/JSON outputs. I copied it to `review/isolated-reproduction/code/` and ran that isolated copy once. It exited successfully. The exact network CSV and summary JSON match the supplied files byte for byte. The two floating-point CSVs agree within 1e-12 relative/absolute tolerance, with small last-bit differences recorded in the JSON report; all text and structure agree. Original source files remain unchanged. This is an internal consistency/reproduction review, not formal verification or external peer review.

## N0755 — closed, anchored thermal reconstruction

The grounded-Laplacian argument is consistent: positive known conductances, known net powers and at least one temperature anchor in each unknown-node component make the linear system uniquely solvable. The maximum principle bounds reconstructed temperature error by the largest anchor error when powers and conductances are exact. The supplied inverse-norm bound handles power and anchor perturbations under the same model.

The code reproduced four exact rational examples and their zero balance residuals, rejected the unanchored singular case, checked four extreme anchor-error sign combinations, and retained an explicit weak-link power-error counterexample. A unit-conductance chain with one zero-temperature anchor and known end power 4 yields temperatures 4, 8 and 12 in arbitrary model units.

Keep the failure cases adjacent: unknown losses or powers, floating components, and uncertain conductances prevent the general missing-measurement claim. A small residual can hide compensating errors. No physical reconstruction experiment was performed.

## N0751 — differential swelling response

The matched-gain linear first-order equations consistently give constant-input rejection, a step transient, a band-pass transfer function, and a smooth-input derivative approximation with a stated error bound. For g=A=1, fast time constant 1 and slow time constant 4, the supplied model predicts peak time 1.8483924814931874 and peak amplitude 0.4724703937105774; the maximum frequency gain is 0.6 at angular frequency 0.5. These are arbitrary-unit model values.

The code reproduced 1,000-step and 2,000-step RK4 comparisons, with maximum errors about 4.98e-10 and 3.08e-11, and 241 transfer-function frequency comparisons. It also checked static mismatch, equal-path cancellation, and attenuation at extreme frequencies.

Keep the limits adjacent: gain mismatch produces a static false signal; equal time constants eliminate the ideal change signal; high frequencies are attenuated. Chemical specificity, noise floor, hysteresis and real material response are untested. The derivative approximation assumes a stable causal response and bounded input curvature; it does not apply to arbitrary sharp changes.

## Publishing wording

Use “Two conditional models: when reconstruction and change sensing work—and when they fail.” Say “the written model derivations and a repeated finite code check agree under their assumptions.” Do not say “we proved the physical hypotheses,” “new theorem,” “breakthrough,” or “experimentally verified.” The supplied prior-literature links remain background provenance; they were not independently fetched or assessed in this bounded review.

No blocking mathematical or packaging inconsistency was found in this review. The scoped claim is conditional model behavior, with physical validation and novelty left unresolved.