Research #8 complete preprint and reproducibility release, prepared 17 October 2026. Start with the two focused eight-page papers: The Exact Price of a Pilot Dimension for a Fresh Binary Superposition, then A Global Phase-Adversarial Hierarchy for Every Square-QAM Order. Research_8_Complete_Guide.md explains reading order, scope, validation and preserved history. Research_8_Complete_Release.zip contains the full proof-audit editorial edition: 206 files including its 205-entry SHA-256 manifest, both current PDFs and editable sources, proofs, exact certificates, software, figures, saved experiments, audit notes, source comparisons and earlier releases.
Pilot-dimension result. Two independently Haar-phased users acquire deterministic linear same-carrier pilots before fresh centered-binary payload bits arrive, then transmit one simultaneous complex payload coordinate. All pilot/payload waveform energy is charged and any measurable nonlinear receiver is admitted. The claimed exact unit squared-label-support-gap energy is 5/2+sqrt(2) for one complex pilot and 29/8 for two or more; no pilots leave all four label laws identical. For independent one-round blocks with iid CN(0,N0) noise, the claimed sharp leading per-block coefficients are 10+4sqrt(2) and 29/2 times N0 ln N. An explicit phase-strip Gaussian-mixture converse and rank-compressed gamma-tail achievability supply finite-block bounds and a non-sharp logarithmic bracket. These are not exact finite-N Bayes-optimal energy formulas. A constant-work one-pilot nearest-support decoder and a phase-integrated one-angle Bayesian implementation are supplied. Arbitrary nonlinear or feedback-adaptive transmitter acquisition is not optimized.
All-order QAM result. Under unit squared-amplitude normalization, the manuscript claims the unique optimal geometric hierarchy, up to permutation, for every square-QAM radix m>=2 and finite user count K, with ratio alpha=1+(m-1)sqrt(2) and worst-phase distance delta/sqrt(sum from h=0 to K-1 of alpha^(2h)). The objective compares label tuples at a common phase state; it is not unknown-phase Bayesian identifiability. Exact rational certificates cover m=2,...,16 and an analytic Farey radial-chain obstruction handles m>=17, followed by an all-user joint-moment induction. The current scalar bound is 601/1000 and covering product 4403527/4480000<1. The finite checkers do not formally verify the complete infinite analytic argument.
Relationship to prior research. Research 4 already establishes the all-user 16-QAM theorem and supplies the radial and aggregate-induction framework. Research 8 reproduces that special-case optimum; its claimed extension concerns all square-QAM orders. The pilot work extends the Research 7/8 phase-acquisition programme. Researches 1-7 are linked as related works, with substantive overlap and primary-literature comparisons disclosed. Historical priority remains unresolved.
Finite-SNR evidence and physical limits. The release includes training-selected ordinary-pilot candidates, 8192 independent held-out trials per design/budget with shared underlying trials across comparisons, numerical phase integration checks, matched waveform-energy accounting and simultaneous confidence intervals. Stronger two-pilot baselines reverse several earlier apparent harmonic advantages. The calibrated-harmonic construction uses extra frequency and observation resources. These are model simulations, not measured RF performance, device-energy savings or proof of a deployed one-coordinate deadline.
Completeness and verification. Current papers, LaTeX sources, exact certificates, independent checkers, constructive collision witnesses, Bayesian and nearest-support receivers, raw/summarized data, graphs, confidence calculations, finite-block bounds, claim ledger, corrected reconstruction guide and an unexecuted physical-validation plan are included. Original v6 and preceding Codex releases are preserved as labeled history; earlier superseded assertions do not override current papers. Fresh extraction verifies all 205 file hashes before and after the standard checks. Optional scientific-mode checks passed in the preceding proof-audit edition; the editorial revision changes navigation only.
AI and review status. Google Gemini and OpenAI ChatGPT/Codex substantially assisted derivation, proof development, writing, literature comparisons, software and verification. All model-assisted audits remain internal. No independent human specialist proof certification, exhaustive priority review or physical validation has been established. Public review is requested to identify failed steps, counterexamples and matching prior results. This record is a preprint, not an accepted journal publication.
Rights and provenance. No additional reuse license is asserted; preserved components retain their existing terms. Private correspondence, portal account details, credentials, installed dependencies and third-party full-text caches are excluded.