How to Read the Six-Paper Stack

The stack is designed to be read in order. Each paper proves one step and hands a typed interface to the next; nothing downstream claims more than upstream results license.

Paper 1 — the distinction

Fix a realization/readout map $\rho: \mathcal{C} \to S$ from complete realization packages to bounded readouts. Two relations must be kept apart: the quotient presentation $S \cong \mathcal{C}/\sim_\rho$, which always holds for $S = \mathrm{Img}(\rho)$, and realization-structure equivalence, which requires admissible faithful recovery. Paper 1 proves these come apart, and pins down exactly when — including an equivariant no-selector theorem and explicit exception classes.

Theorem — Readout Non-Equivalence (informal)

If no admissible realization-faithful section of $\rho$ exists, the readout domain is not realization-structure equivalent to the package domain, even though it is an exact quotient of it.

Paper 2 — the brake

It is a recurring error to read Paper 1 as "readout loss is automatically a problem." Paper 2 proves the precise extra condition needed: a certified active failure of an essential public closure slot, with no checked repair or public surrogate. Without that certificate, no obstruction claim is licensed.

Paper 3 — conditional canonicality

Given a certified completion need, when is a proposed completion the completion? Exactly when it is a certified initial object in the public admissible completion category:

$\mathrm{CCO}_{\mathrm{pub}} = \mathrm{Init}\left(\mathbf{Comp}_{\mathrm{pub}}\right)$

A canonicality criterion, not an existence theorem: completion need does not imply canonical completion.

Paper 4 — from object to artifact

A canonical completion object is still not a public artifact. Paper 4 defines the down-compiler — total, deterministic, route-legal, gate-cleared, residue-aware — and proves it emits exactly one statused output from an eight-member codomain that includes declared failure and residue outputs.

Paper 5 — the runtime

Paper 5 supplies the calculus that governs public claims after compilation: routes, status algebra, residue algebra, the equation-artifact grammar, claim licensing, dry-test audit, downgrade logic, and forbidden-promotion discipline. Its claim-cap theorems bound every emitted output.

Paper 6 — the synthesis

The capstone composes the five upstream interfaces into a single typed synthesis object and proves the Scoped Shadow Fixed-Point Law-Packet Theorem. That theorem is the precise, bounded sense in which the historical "Everything Equation" survives:

$L \;=\; \Omega_{T1}\,\Delta\,\partial\,[\,L\,]$

Licensed only as a scoped, residue-visible, status-certified, claim-bounded closure-fixed law packet — not as source-level equality or a solved theory of everything.