The Epistemic Vertical

The revision of 2026-10-03 withdraws the former verdict that all structural gaps are closed. The mathematical kernel and premises specify the current scopes. Coinciding numbers and finite machine checks do not transfer a proof between levels.

Three application domains

Domain	Correct object	Additional input
Universe and physics	A specified site, sheaves, chosen fields and joint-state spaces	Physical identification, scale, matter module, preparation, and clocks
Subject and dynamics	Augmented state record, feedback family, capability gates	Experiential extension, observation law, and phenomenal interpretation
Foundations of mathematics	An explicit algebra, grading, code, or doctrine with stated axioms	A comparison map and verification of those axioms for each new object

No row derives every other row. Agreement of Fano geometry in two constructions establishes a common finite object only after an explicit isomorphism; it does not establish identical physical causes or cognitive levels.

Transfer obligations

A transfer requires:

1. Typed domains, codomains, and a transfer map.
2. Verification of the source theorem's hypotheses.
3. Preservation of the structure and observables actually used.
4. A distinction between isomorphism, embedding, reduction, and selected aggregation.
5. Independent verification of the physical or phenomenal bridge.

The joint space of two seven-axis holons has dimension 49; a seven-dimensional aggregate discards information. A higher hierarchy is not determined by a finite matrix or attenuation factor. Perfect single-error binary diagnosis gives a conditional bound $N\ge7$, permits length 15, and does not imply a normed division algebra.

Open obligations

Obligation	Current scope
Physical selection of seven axes	[P/H]; exact code and representation bounds require their own hypotheses
Reconstruction uniqueness	[H] strong comparison (RI); measurement requires observation-law identifiability
Terminal self-model of the Universe	Requires a carrier, clock extension, and dynamics; the terminal sheaf selects no numerical anchor
Universal depth-three ceiling	Withdrawn; a selected SAD score and coding ladder do not bound general cognitive depth
Natural realization of a Fano doctrine	Proofs inside a chosen octonionic construction are relative to that construction; independent realization is tested separately
Experience from structure	[P/I]; a numerical criterion does not derive phenomenal identification
Physical spacetime and matter	[H/I] module, field, and clock bridges; finite algebraic computations do not replace them

Numerical agreements

An agreement of seven, attenuation $1/3$, a score ceiling, or a group dimension becomes structural only through an explicit map of derivations. Twenty-one complex matrix pairs are not automatically twenty-one independent addresses, $\dim G_2=14$ is not automatically fourteen control degrees of freedom, and two values of three do not identify their hierarchies.

Independent inputs

The assertion that exactly two inputs remain and everything else is a theorem is withdrawn. Beyond the quantum formalism and phenomenal identification, the site and metric, dimension and frame, dynamical family, controls and preparation, clocks, experiential extension and readout, observation law, and physical module bridges are specified. Independence or equivalence requires a model or proof; sentence count does not measure independent assumptions.

Consistency discipline

Each result has one current status and an explicit source. A historical closure verdict is not a proof premise. Changed assumptions propagate to dependent pages in both locales. Status checks, site builds, and numerical witnesses verify their stated properties; they are not formal verification of the whole corpus.

General audit promises are replaced by checkable obligations. The status registry records current results, and the identifiability protocol states when measurements can test them independently.