# Continuation checkpoint: effective reaction models and finite numerical evidence

9 October 2026. Previous turn: random-SAT research and software progress, pushed/deployed at `29d33e8547f555e6be59af062d3c4b7f67906bba`. This turn: progress through two selected family-149 manuscripts, a bounded model audit, independent graph/algebra controls and conventional numerical comparisons. The full perpetual goal stays active; no completion or blocked audit applies.

## Findings that change the opportunity

The newer mass-action paper asserts one eventual compact convex absorber per fixed positive stoichiometric class and positive fixed rates; entry time can depend on initial state. Selected formal scope covers older initial-state-dependent all-time bounds. The affine construction uses finite slopes and compactness-based thresholds; no practical numerical absorber, entry time or full source proof was obtained. Parts of the affine induction/gluing remain unread; precise extents are recorded.

The prototype normalizes explicit rate conventions, zero-rate reactions, self-loops and parallel reactions before checking the effective complex graph. Supplied nonnegative conservation vectors can give exact coordinate upper bounds. Exact face inequalities can certify supplied positive invariant rectangles; an initial state outside a valid rectangle receives no all-time or entry-time claim. No SBML/Catalyst import, unit bridge, physical process or stochastic extension is verified.

The A<->2A fixture shows identical nominal rates produce equilibria one versus two under different factorial conventions. Setting the reverse rate to zero leaves two drawn arrows but yields the unbounded equation A'=A. A coarse explicit Euler step can produce a negative value even when the continuous model has an independently verified positive invariant interval. These distinct errors must not be conflated with source-theorem validity.

## Evidence and current editions

- [Report](../prototypes/reaction-network-2026-10-09-v1/report.md), [comparison figure](../prototypes/reaction-network-2026-10-09-v1/model-convention-and-bounds.png), [fixture summary](../prototypes/reaction-network-2026-10-09-v1/summary.json).
- [702 finite controls](../snapshots/2026-10-08-baseline/reaction-network-validation-2026-10-09-v1.json): all 64 directed edge subsets on three complexes, sixty stored generated models, eleven named fixtures and parser/output preservation. NetworkX 3.4.2 and SymPy 1.13.1 provide independent graph/algebra comparisons.
- [Eleven numerical controls](../snapshots/2026-10-08-baseline/reaction-simulation-validation-2026-10-09-v1.json): SciPy 1.18.1 DOP853 matches eight logistic analytic cases with maximum observed error below 6.29e-11; sampled dimer mass drift is below 3.56e-15. These are floating diagnostics, not validated enclosures. Total new controls: 713, all passing.
- A transcribed public Catalyst tutorial graph has eight species, seven complexes, rank five and two linkage classes. It fails weak reversibility yet admits a checked positive conservation vector giving finite coordinate upper bounds. Rates/initial states were chosen for the experiment; it is not a customer model. Julia and libSBML were absent; no package installation or live Catalyst execution occurred.
- [Manifest](../prototypes/reaction-network-artifact-manifest-2026-10-09-v1.json): 34 files, including five inert tooling copies, and eleven source hashes. [Ledger v19](manuscript-ledger-2026-10-09-v19.json): 53 selected-section manuscripts, 158 source hashes and 666 pending/earlier-not-imported. Four PDF pages visually inspected.
- [Dossier 013 v2](../opportunities/013-reaction-network-assurance/2026-10-09-v2.md), [catalog v31](../opportunities/CATALOG-2026-10-09-v31.md), [directory v26](../FAMILY-ASSESSMENTS-2026-10-09-v26.md), [coverage v31](coverage-2026-10-09-v31.json).
- [42 utilities v28](../PROTOTYPES-2026-10-09-v28.md), [priorities v28](../COMMERCIAL-PRIORITIES-2026-10-09-v28.md), [feasibility v26](../FEASIBILITY-2026-10-09-v26.md): 32,820 controls in 67 reports. Facility planning remains first; reaction assurance stays low confidence until a useful real import path and recurring buyer problem are validated.

## Publication and continuation

[Integrity v31](integrity-2026-10-09-v31.json) passed with zero issues: 32,820 controls, 162 current Python syntax checks, 1,553 local links, 158 reading-source hashes and all 34 new artifact/eleven source hashes. The subsequent build checks all rendered routes.

Check rendered routes, then push normally to strykesg/mathideas and verify Dokploy application `6yFD3JCmfp0uZcCuJGex2` serves the new report, figure, exact certificate and manifest bytes. No deletion, force push, outreach, purchases or paid compute occurred.

The [02:56:08 UTC upstream check](upstream-check-2026-10-09-v3.json) still governs cadence: no repeat before 03:56:08 UTC without a signal. Source remains at `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. The existing hourly heartbeat stays active while the app/host are available.

Continue substantive manuscript reviews, such as tensor-network representation/compute feasibility or inverse-problem identifiability, and practical first-product gaps. Stronger independently checked facility-capacity bounds and standard-browser export completion remain open. Real buyer studies require permissioned data; no customer validation is inferred from these technical fixtures.