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Search the paper sections, open their original context and follow the checks they actually cite. The knowledge atlas explains the result; this library locates its source.

2026-06-21 (the golden ratio made precise: the [formula in source] atoms are the affine- [formula in source] network spectral angles, [formula in source] the [formula in source] signature: v313)

Research changelog · TFPT — Introduction and reading guide

v313_golden_atoms_spectral.py ( GOLD.ATOMS.01, / ). A follow-up to v312's observation, made exact. \ the affine- [formula in source] adjacency characteristic polynomial factors as [formula in source] , so the golden minimal polynomial [formula in source] divides it and [formula in source] is an exact eigenvalue; \ the non-trivial eigenvalues are [formula in source] for exactly [formula in source] ( [formula in source

Opening source excerpt. Formulas and the full argument remain in the original document.

Source location and explicit evidence links

documents/changelog/sections/017-source.tex · lines 1 to 18

These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.

  • explicit script identifier v312_hypergraph_substrate.py

    literal short identifier uniquely resolves in local script registry

  • cross reference join tfpt_readouts.wl

    TeX and evidence source explicitly name the same Python identifier; statement equivalence not inferred

  • cross reference join tfpt_readouts.wl

    TeX and evidence source explicitly name the same Python identifier; statement equivalence not inferred

  • explicit file citation v313_golden_atoms_spectral.py

    literal source filename/path in TeX

  • cross reference join KronheimerMarks.lean

    TeX and evidence source explicitly name the same Python identifier; statement equivalence not inferred

  • cross reference join tfpt_readouts_extension.wl

    TeX and evidence source explicitly name the same Python identifier; statement equivalence not inferred

  • cross reference join tfpt_readouts_extension.wl

    TeX and evidence source explicitly name the same Python identifier; statement equivalence not inferred

  • explicit script identifier v63_seam_engineering_index.py

    literal short identifier uniquely resolves in local script registry

  • explicit script identifier v305_witness_independence.py

    literal short identifier uniquely resolves in local script registry

  • explicit claim identifier status_ledger.csv

    exact local ledger claim identifier

  • explicit script identifier v76_gmetric_reduction.py

    literal short identifier uniquely resolves in local script registry

  • cross reference join tfpt_readouts_extension.wl

    TeX and evidence source explicitly name the same Python identifier; statement equivalence not inferred

  • explicit script identifier v313_golden_atoms_spectral.py

    literal short identifier uniquely resolves in local script registry

What this source index covers

The public registry includes 116 document views, 6,693 section records and 985 physical LaTeX sources. Active publication documents, research material and archives retain their recorded roles. This is source navigation, not a new semantic review or proof run.