Chains that would benefit from synthesis
2026-10-01. These are writing opportunities, not new research priorities. No source note is merged or replaced. The catalog and dependency map already provide routing; a future synthesis earns a place by stating the strongest common conclusion and its remaining premise.
| Common question | Existing chain and what to summarize | Strongest supported conclusion | Remaining question / recommendation |
|---|---|---|---|
| What does a usable record cost? | newton-mark-floor → planck-gap-derivation → mark-cost-and-statistical-floor / planck-gap-probabilistic → record-costs-recoil → record-costs-disturbance → record-distance-path-length | Exact quantum error/recoil conjugacy; sharp Gaussian invariant-test benchmark; arbitrary instrument and Bures/path bounds with explicit body/apparatus resources | Independent positive action necessity and attainment remain open. The existing planck-gap-paper is already the synthesis; add a concise scope diagram when writing the book rather than another duplicate note |
| Which classical data permit reconstruction? | classical-readout-refinement → hidden-clock / preparation / energy ambiguities → one/two/three calibrations → full-pointer/full-clock/three-calibration recovery → fixed-coupling and calibration-tolerance | Fixed preparation and incomplete records create exact fibres; richer records and shrinking preparation errors can recover the body, with conditioning costs. No universal floor follows from the tested finite Hamiltonian designs | A composition-stable physical admissibility restriction remains missing. conservative-harmonic-receiver already consolidates R03–R33; build a short design/known-data/fibre/recovery table, not a second long apparatus notebook |
| Why did the old bridges fail? | blocking-step → blocking-criterion-monotone; flow-jacobian → flow-conjugation → lattice-truncation-uniform; large-field action/entropy → Agmon correction; finite-verification/what-would-unblock → reasons-to-stop | Strong-side criteria, exact smoothing, action costs and finite certificates supply different inputs; none of the tested bridges supplies controlled weak-side arrival with generated interactions | The present weak-side normalized insertion programme is the replacement. mass-gap-position and reasons-to-stop already synthesize diagnosis; the new obstruction map supplies missing retrieval, not another theorem |
| What exactly survives one insertion and many? | refinement-composition-and-limit → halving-atlas → series-parallel → compact-group midpoint/centre → order-t/small-field → Gaussian 4D composition/parallel log | Exact local identities, selected arbitrary-partition limits, and all-order weak-strip cluster/dressing results; perturbative logarithms conditional on matching | Stable nonlinear iteration and physical continuum/gap reconstruction remain open. A future “local law to iterated effective action” synthesis would materially improve understanding, because the atlas and theorem compendium still mix logical depths |
| What can a physical background preserve after recording? | necessity-unit-and-indeterminacy → newton-indeterminacy-routes → sed-zeta-radiation-link / sed-closure-under-recording | Radiation supplies a conditional calibration route; affine copies close at supplied cost, while complete records and nonlinear copies expose escapes; phase memory survives local-data collapse | A physical history rule and independently selected nonzero normalization remain open. Keep this as a mechanism chapter after a successful new result, rather than freezing another premise inventory now |
Any synthesis should link the earlier negative versions to their correcting notes and preserve design-specific assumptions. The current book map uses these chains without claiming the missing statements have been proved.