Sealed or Leaky Section 13

Assumptions and result status

Jeremy Rodgers · Independent Researcher · Version 3.1
doi:10.5281/zenodo.23077474

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Section 14 of 17

13 Assumptions and result status

The following register distinguishes mathematical representation premises from physical preparation and access premises. Each is needed only for the results that invoke it.

Premise	Content	Contribution and limit
Tetralemma premises	(SO), (D), (MI), (NS) of Section 2.1; (QT) optional.	Exclude completeness of each specified admissible classical readout. (D) supplies (SO); only (D), (MI), (NS) are separately necessary within that class.
Certification imports	Sequential likelihood model; entropy production and soundness of [28]; correct-dimension continuity [29].	Keep classical isolated side information, independent seed and explicit pass probability. The observed pass does not establish that probability or universal independence.
Operational closure	Complete causal record laws; alternative class contains their identity-readout surrogate.	Gives non-identifiability only in that closed class. It does not establish a physical source ontology or a finite Markov surrogate.
Ontic preparation model	Common measurement responses, convex-linear preparation randomization, specified trine data.	Forces distinctions between ontic preparation laws. It does not assume or prove incompleteness of a pure ray as an individual state.
POVM domain	All pure states and finite proper ensembles, one fixed experiment, common apparatus and mixture rule.	Gives exact and quantitative eventwise sealing tests. A nonquadratic event still needs a physically allowed reader.
Deterministic completion	Future record is a function of the complete initial state; readout-conditioned randomness is nondegenerate.	Requires unresolved initial information. Universal determinism itself is an additional premise.
Pilot constitution	Specified sector graph, P3 coherent apparatus catalogue, exporter and service rules; basis-ready census and zero residues; independent symmetric gas preparation.	Produces finite retained-record predictions. These microscopic rules are not consequences of observed quantum statistics.
Pilot controls	Driven coherent pulses and holds; included memory; common preparation law; quantified finite gas and drainage budgets.	Supplies ordinary stored bits. Autonomous timing to $o(1/N)$ and a relativistic implementation remain unproved.
Undrained limit	One monotone edge, initially empty stock, $w\in C^2$ , $1-w\ge c>0$ , $\mu_N\to\infty$ , $\mu_N/N\to0$ , $\mu_N\delta_{\rm g}\to0$ .	Proves an endpoint asymptotic. General graphs, reversals and a retained reader at this accuracy require further work.
Deterministic CHSH	Common setting-independent initial law; Alice's record precedes and is independent of Bob's later intervention; equilibrium marginal independence; $S>2$ .	Forces setting-dependent ontic response and permits mathematical signalling reweightings. Their physical preparation is not supplied.
Massive construction	Driven semibounded oscillator and internal-key Hamiltonians, guidance, complete equilibrium, retained stationary Alice record.	Gives finite noisy $S>2$ within the massive constitution. It is not a construction of nonequilibrium preparation.
Repetition	Available resets, independent trials, common laws and an implementable test.	Amplifies an operational gap. It cannot amplify an inaccessible ontic distinction into an observable one.

Result	Quantitative conclusion	Status
No-signalling guessing, Lemma 2.3	$\max_aP(a\mid x)\le3/2-S/4$ .	Proved; coincides with [22].
Hidden information, Theorem 2.4	$H_{\min}(Z\mid T)\ge\fNS(S)$ ; $H(Z\mid T)\ge(S-2)/2$ ; also $\fQ$ under (QT).	Proved; conditional on the four premises.
Tetralemma, Theorem 2.7	Exclusion; (D), (MI), (NS) separately necessary within (SO).	Proved; branching outside the scalar-outcome class.
Three-branch form, Proposition 2.8	False.	Proved.
Extracted-string translation, Corollary 3.8	Passing-ensemble Shannon bound $>1024-1.1\times10^{-9}$ ; unsmoothed min-entropy only $>39.86$ .	Conditional on B-admissibility, deterministic response, seed and $\pi\ge\kappa$ .
Raw-certificate translation, Corollary 3.10	Passing-ensemble Shannon and deletion-smoothed bounds $>1304.97$ ; unsmoothed $>39.93$ .	Published aggregate parameters; no extractor or source–setting independence needed.
Threshold test, Lemma 3.12	Complete deterministic B-admissible models have pass probability $\le v^{-1}$ .	Conditional frequentist bound; no lower bound on pass probability required.
Trine preparation bounds, Theorems 8.1, 8.3	Pairwise $1/4$ ; three-distance sum $1/2$ ; robust bounds $1/4-4\epsilon$ and $1/2-13\epsilon/2$ , truncated at zero.	Proved and sharp for the ideal finite table. Ontic-law distances.
Quantitative POVM, Theorem 9.2	$\Gamma(h)=2d(h)$ ; a witness uses at most $d^2+1$ pure-state occurrences.	Proved; eventwise and conditional on access.
Readout simulation, Theorem 5.2	An accessible gap $\delta$ forces worst-case error at least $\delta/2$ .	Proved; does not identify a unique completion.
Retained pilot preparation, Theorem 11.5	Gap at least $1/(2N)-2\epsilon_N$ on the specified window, $N\ge2$ .	Controlled finite-time lower bound; ideal floor coefficient is exact.
Retained pilot setting, Theorem 11.7	Gap at least $1/N-2\epsilon_N^{AB}$ on the specified window, $N\ge3$ .	Controlled finite nonrelativistic model prediction.
Undrained endpoint, Theorem 11.10	$\mu_N(P_X-P_Z)\to5\sqrt3g/(6\kappa)$ .	Proved in the specified asymptotic regime; retained-reader gap open.
Initial-residue repair, Proposition 11.9	No single independent residue law restores all monotone and return Born means.	Proved obstruction for the unchanged reset exporter; census scope.
CHSH reweighting, Theorem 12.1	Union mass $\ge(S-2)/2$ ; signal budget $\min\{2d,d+\kappa/2,1\}$ for $\kappa>0$ .	Sharp mathematical bounds; reweighting accessibility separate.
Accessible sealing, Theorem 7.1	$d_{\mathcal F_1}(\Phi_P,\Phi_Q)=d_{\Phi^*\mathcal F_1}(P,Q)$ .	Access-relative; complete-law conservation does not imply operational conservation.