Notes

Auxiliary results, expanded proofs, and working ideas.

These notes collect auxiliary results, expanded proofs, examples, and conceptual connections that complement my papers. Some also record independent proofs of known results; sources and novelty claims are indicated within each note.

Research use. If your research substantially uses a result, proof method, construction, or conceptual framework developed here, please cite the relevant note, preferably its exact version and the relevant proposition or section. An acknowledgement of broader conceptual influence is also appreciated.

Review status. Unless explicitly stated otherwise, these are working research notes that have not undergone peer review or independent verification. They may contain errors, gaps, or unstated assumptions. Please check the arguments and dependencies before relying on them. Corrections and comments are welcome.

N0007 — Exact norms and evaluator-only Hahn-Banach inputs

N0007 · version 0.1 · updated 2026-09-10

Proof: Draft Review: Not externally reviewed Contribution: Follow-up deductions; not an omitted draft section

Hahn-BanachComputable analysisWeihrauch reducibilityRepresentationsNorm information

Norm recovery in the limit, a precise upper-bound bridge to the retained proofs, and a finite-dimensional obstruction.

N0006 — Transporting Hahn-Banach instances and extracting separators

N0006 · version 0.2 · updated 2026-09-10

Proof: Draft Review: Not externally reviewed Contribution: Expanded known reduction; general transport and scope clarification

Hahn-BanachComputable analysisWeihrauch reducibility

Unknown-norm transport, the retained norm-one forcing construction, and the lower bound for the literal exact-norm problem.

N0005 — Uniform block isometries without sign tests

N0005 · version 0.1 · updated 2026-09-10

Proof: Draft Review: Not externally reviewed Contribution: Expanded isometry proof and explicit formulas

Hahn-BanachComputable analysisWeihrauch reducibilityIsometries

A branch-free block formula, explicit inverse and complete Cauchy-name conversion for the varying gadget space.

N0004 — A uniform Hahn-Banach extension loop: states and decoding

N0004 · version 0.2 · updated 2026-09-10

Proof: Draft Review: Not externally reviewed Contribution: Expanded loop proof; exact-oracle follow-up marked

Hahn-BanachComputable analysisWeihrauch reducibilityInfinite loops

The original norm-one state decoder, a general-bound version, and iteration of the literal exact-norm one-step oracle.

N0003 — Interval choice through a fixed tree and a fixed hyperplane of the sequence space

N0003 · version 0.2 · updated 2026-09-10

Proof: Draft Review: Not externally reviewed

Hahn-BanachComputable analysisWeihrauch reducibilityLipschitz-free spaces

The retained tree/free-space reconstruction with fixed located hyperplane, exact norm-one witnesses, and lower reductions to the literal problem.

N0002 — Effective one-step Hahn-Banach intervals

N0002 · version 0.2 · updated 2026-09-10

Proof: Draft Review: Not externally reviewed Contribution: Expanded known proof; supplied-bound generalization

Hahn-BanachComputable analysisWeihrauch reducibility

The direct certificate proof, a functional realizer, and the precise supplied-bound and exact-norm specializations.

N0001 — Hahn-Banach working notes: scope and reading map

N0001 · version 0.2 · updated 2026-09-10

Proof: Expository overview Review: Not externally reviewed Contribution: Exposition and provenance

Hahn-BanachComputable analysisWeihrauch reducibility

The paper's evaluator-only convention, its norm-one restrictions, and a reading map for the retained proofs and the norm-information follow-up.

Dependency map

An arrow A → B means that B lists A as a prerequisite. Conceptual similarity is not a proof dependency.

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