# Study 1: Blogger readiness

**Ready for one grouped companion, labeled conditional mathematical/model results.** No new physical experiments, clinical findings, novelty certification, external peer review, or formal proof-assistant verification is claimed.

## Review performed

Read all three complete derivations, source verification code and output summary. The benign standard-library script was copied to `proof-review/code/` and run once; it wrote only isolated results. Every regenerated output CSV and the summary JSON is byte-identical to the frozen supplied version. This reproduces 333 output rows: two layout certificates, six ODE comparisons, five closure quadratures and 320 exact rational skin parameter cases. Frozen source remained unchanged. No new data, literature search or experiment was performed.

## H0199 — Reference layout and worst-case reconstruction

For calibrated point samples of an L-Lipschitz field with adversarial absolute error bounded by epsilon, minimax uniform reconstruction error is L*h(S)+epsilon. A specified 3x3 interior square grid has coverage radius sqrt(2)/6 versus a boundary-only lower bound of 1/2.

Assumptions: Compact Euclidean domain and fixed nonempty reference set. Known nonnegative Lipschitz bound L and bounded adversarial measurement error. References do not perturb the field; readings are calibrated point observations. Objective is worst-case uniform error over the defined field class.

Limits and counterexamples: Strict grid advantage requires L>0. No superiority on every individual field or random-noise/integrated-error metric. No measured deposition result, finite reference-area effect, or physical uptake inference is established. The earlier polynomial simulation uses different estimators and field classes.

Reproduced checks: Two exact rational one-dimensional minimax certificates; square-grid squared radius 1/18 versus boundary-only lower-bound squared radius 1/4. Read derivation for continuum geometry proof, which finite output checks do not replace.

## H0836 — Buffering, release, and matching controls

A constant-compliance, linear-resistance node attenuates nonzero-frequency and rectangular-pulse peak flow for a matched inlet waveform. Integrated modeled release cannot increase if its flow closure is convex, nonnegative, memoryless, zero at zero, and integrable.

Assumptions: Positive constant R and C; zero/equilibrated baseline; no inertia, leakage, resonance, cavitation, hysteresis, or deformation-dependent R. Same specified inlet waveform for basic attenuation comparison. Extra convex memoryless release closure is assumed, not measured. Hydraulic work comparison assumes complete return to equilibrium.

Limits and counterexamples: DC gain is one and injected fluid volume is preserved. Lower peak alone does not guarantee less total release: supplied nonconvex threshold counterexample gives 2.7385494319491372 versus 1 release-duration units. Same waveform does not imply equal hydraulic work. Equal-work constructed comparison yields buffered peak 1.0421906109874948 versus 1, without matching volume as well. No physical sand breakthrough reduction has been demonstrated.

Reproduced checks: Six RK4-versus-analytic ODE rows across three time constants and two time steps; maximum rise error 5.679964720783914e-09; all finer-step errors decrease. Five positive-part closure quadratures and two analytic counterexamples are reproduced.

## H0346 — Skin perforation in a lumped transport model

With parallel skin/hole conductance in series with bulk conductance and fixed storage, the half-time reduction D exceeds hole area fraction phi exactly when d*[b-phi*(b+k_s)] > k_s*(b+k_s).

Assumptions: Linear constant conductances k_s>0, k_h>=k_s, b>0; d=k_h-k_s. A single well-mixed storage element with fixed capacity and fixed bath step. No access/spreading resistance, hole interaction, cracks, changing modulus, nonlinear osmotic effects, or extra exposed edges.

Limits and counterexamples: At b=1,k_s=1/100,k_h=1,phi=1/100, exact reduction is 9900/20099 (about 49.26%); this is a constructed arbitrary-unit model, not a gel performance specification. Zero transport contrast yields zero gain; bulk-limited conductance makes gain arbitrarily small. The gain is explained by ordinary area-weighted parallel/series transport and does not establish additional physics. Real uptake curves and intact/perforated samples still need independent measurement.

Reproduced checks: 320 exact rational parameter combinations reproduce the half-time algebra, necessary-and-sufficient inequality, and monotonicity; exact example and bulk-limited counterexample match supplied outputs.

## Publication framing

Suggested title: **Three model results: reference layouts, surge buffering, and perforated skins**. Explain that proofs constrain specified models; they do not prove real materials meet those assumptions. Link the full three derivations, code, all result tables and original proposals. Keep null cases and counterexamples visible. No blocking consistency issue was found in this bounded internal review.

## Complete lead fields

`normalized-leads.json` retains the full 300 selected records and the full 30 focused JSON records, ranked CSV fields and dossier Markdown, nested by H identifier. These fields are separate from the raw-catalog membership flags. Original versions are preserved unmodified under `source/`.