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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.

Matching source sections

43 sections found. Current publication documents are listed before historical material.

-1.2cm TFPT — [formula in source] Audit, Cascade Bridge and Bootstrap\\[2mm] The seven [formula in source] slices as an audit raster, the old cascade as the same even-integer spine, the M\"obius self-consistency loop — and the thirty-two-step celestial/twistor route with the measure chain derived

E8 audit and bootstrap

arrows.meta,positioning,calc,fit,backgrounds,shapes.geometric,shapes.misc,decorations.pathmorphing,decorations.pathreplacing,patterns,angles,quotes,matrix =3.5em

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documents/tfpt_3_e8_audit_bootstrap/preamble.tex · lines 1 to 107

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Front matter / support

E8 audit and bootstrap

[formula in source] as an audit container, not a mystery: the seven maximal slices of [formula in source] as a falsification raster (every load-bearing number must appear in at least one projection), the bridge showing the old [formula in source] orbit cascade [formula in source] is the same even-integer spine as the compiler, and the M\"obius bootstrap in which [formula in source] and the `` [formula in source] '' i

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documents/tfpt_3_e8_audit_bootstrap/sections/001-part-the-e-8-secondary-branching-atlas.tex · lines 1 to 53

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The [formula in source] secondary-branching atlas

E8 audit and bootstrap

Purpose and discipline. This note does not introduce new physics. It builds an audit raster: the claim that every load-bearing TFPT number should appear in at least one [formula in source] branching projection. A number that appears in none is suspect; a number appearing in several independent projections becomes structurally strong. All arithmetic identities below are exact ; the physical readings are audit-level \

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documents/tfpt_3_e8_audit_bootstrap/sections/001-part-the-e-8-secondary-branching-atlas.tex · lines 54 to 63

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The compiler core (where this note sits)

E8 audit and bootstrap

The strongest current form of the theory is a five-layer compiler:

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documents/tfpt_3_e8_audit_bootstrap/sections/001-part-the-e-8-secondary-branching-atlas.tex · lines 64 to 86

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The [formula in source] anchor microcode

E8 audit and bootstrap

The parabolic anchor [formula in source] (splitting type of [formula in source] ) is a miniature compiler. Its power sums [formula in source] generate the discrete budget:

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documents/tfpt_3_e8_audit_bootstrap/sections/001-part-the-e-8-secondary-branching-atlas.tex · lines 87 to 183

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The residue and length matrices as spectral objects

E8 audit and bootstrap

With the residue matrix [formula in source] and the full word-length matrix [formula in source] ( [formula in source] the rank-one winding), [formula in source] the spectral invariants are pure compiler numbers (all verified): @lYlY@ Invariant of [formula in source] & value & Invariant of [formula in source] & value \\ [formula in source] & [formula in source] & [formula in source] & [formula in source] \\ [formula i

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documents/tfpt_3_e8_audit_bootstrap/sections/001-part-the-e-8-secondary-branching-atlas.tex · lines 184 to 211

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Bilinear anchor forms.

E8 audit and bootstrap

With [formula in source] and [formula in source] (all verified): @c|cc@ 2.5emc|cc@ [formula in source] & [formula in source] & [formula in source] & [formula in source] & [formula in source] & [formula in source] \\ [formula in source] & [formula in source] & [formula in source] & [formula in source] & [formula in source] & [formula in source] \\ [formula in source] & [formula in source] & [formula in source] & [form

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documents/tfpt_3_e8_audit_bootstrap/sections/001-part-the-e-8-secondary-branching-atlas.tex · lines 212 to 295

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The secondary branching atlas

E8 audit and bootstrap

Each maximal subalgebra of [formula in source] mirrors a TFPT module. The dimension identities are exact ; the readings are audit-level . The seven slices of [formula in source] are shown below: the same total cut seven ways, each cut a different TFPT module.

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documents/tfpt_3_e8_audit_bootstrap/sections/002-section-the-secondary-branching-atlas.tex · lines 1 to 149

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explicit file citation v170_diamond_slice_compression.py
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Group-theoretic audits (optional)

E8 audit and bootstrap

Weyl completion index. Over the main stabiliser, [formula in source] A group-theory machine-check, not physics: it quantifies the Weyl symmetry created beyond the [formula in source] stabiliser. \ (arithmetic) / \ (reading)

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documents/tfpt_3_e8_audit_bootstrap/sections/002-section-the-secondary-branching-atlas.tex · lines 150 to 379

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Front matter / support

E8 audit and bootstrap

The translator round ( QGEO.TRANSLATOR.01). The corpus RP anti-automorphism is found on the curve ( [formula in source] checks, [formula in source] \,s): pulling [formula in source] back along the compiler conjugation and composing with the J-adjoint gives an algebra automorphism [formula in source] — and [formula in source] is inner: the intertwiner space is one-dimensional, its generator [formula in source] is inve

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documents/tfpt_3_e8_audit_bootstrap/sections/003-source.tex · lines 1 to 380

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explicit file citation v609_translator_factorization.py
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Front matter / support

E8 audit and bootstrap

The interacting Klein–Landau semigroup ( WOIT.GAMMA.SEMI.01). The gamma net-dynamics slice ( [formula in source] checks, [formula in source] \,s). At [formula in source] the v524 Klein–Landau pattern reproduces exactly at [formula in source] on the admissible cut: all seven steps [formula in source] Hermitian (domain dims [formula in source] ), even steps PD, odd steps [formula in source] indefinite with exactly zero

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documents/tfpt_3_e8_audit_bootstrap/sections/004-source.tex · lines 1 to 373

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explicit file citation v645_klein_rp.py
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explicit file citation v624_external_lattice_audit.py
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Front matter / support

E8 audit and bootstrap

The ST31 degree- [formula in source] / [formula in source] round ( E8.ST31DEG.01). The regular clocks of [formula in source] against the compiler clock ( [formula in source] checks, [formula in source] \,s, exact arithmetic). The regular [formula in source] -clock: an explicit [formula in source] with free census [formula in source] and [formula in source] (Springer); exact center relations [formula in source] and [f

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documents/tfpt_3_e8_audit_bootstrap/sections/005-source.tex · lines 1 to 392

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Front matter / support

E8 audit and bootstrap

The [formula in source] torsor closure ( VGEO.TORSOR.01). The calibration/scale-torsor audit of the [formula in source] interface ( [formula in source] checks, [formula in source] \,s; verdict torsor closure pass). The interface is a well-defined [formula in source] scale torsor: complete export table [formula in source] ; dimension matrix rank [formula in source] (conditional [A] on the flavor block, named); all con

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Front matter / support

E8 audit and bootstrap

The transition-bus torsor ( E8.TRANSITIONBUS.01). One probe ( [formula in source] ; verdict transition-bus-torsor). The [formula in source] roots are [formula in source] disjoint coordinate [formula in source] -frames over [formula in source] ; on [formula in source] the [formula in source] root pairs are exactly the [formula in source] [formula in source] points of the plus-type quadratic space, and each class fiber

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documents/tfpt_3_e8_audit_bootstrap/sections/007-source.tex · lines 1 to 380

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explicit file citation v807_lorentz_nullselector.py
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Front matter / support

E8 audit and bootstrap

The P1 index-KMS identity ( P1.INDEX.KMS.01). One probe ( [formula in source] incl.\ the [formula in source] must-fire controls; verdict p1-identity-closed). The closed normalization identity [formula in source] is exact in formal arithmetic, with each factor independently sourced: the Jones index [formula in source] is a [formula in source] -free theorem (zero occurrences of [formula in source] in all four sources,

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Front matter / support

E8 audit and bootstrap

The Wick functor arc ( SEAM.CFIN. WICKFUNCTOR.01 [O]). Three probes ( [formula in source] ; wickfunctor-partial, wickmix-measured (wickmix-obstructed), wickblock-measured (blockfunctor-constructed / seam-diagonal); embedded byte-exact; exact integer/rational/symbolic in every decision typed proved or symbolic). The six compiler roles exist in the deployed seam ( [formula in source] slot pairs [formula in source] the

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Further audit lemmas (machine-verified this round)

E8 audit and bootstrap

Five more exact identities tie the flavor matrices and the [formula in source] exponents to the compiler. All checked with exact integer arithmetic.

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What this changes, and what stays open

E8 audit and bootstrap

[formula in source] is one container whose maximal subalgebras each project a different TFPT module:

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The [formula in source] cascade bridge

E8 audit and bootstrap

The connection in one sentence. The old E [formula in source] cascade (Paper V1.06: the nilpotent-orbit chain [formula in source] , [formula in source] ) and the new compiler/atlas are the same even-integer [formula in source] spine, read three ways: the cascade orders the numbers [formula in source] as a scale ladder, the atlas reads them as [formula in source] subalgebra branchings, and the compiler generates them

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The old cascade, recalled

E8 audit and bootstrap

Paper V1.06 builds a deterministic scale ladder from the nilpotent orbits of [formula in source] . With centralizer dimension [formula in source] and the Hasse chain restricted to [formula in source] , a unique maximal chain runs from [formula in source] ( [formula in source] ) down to the regular orbit ( [formula in source] ): [formula in source] The cascade arithmetic (endpoints, exponent rungs, IR-tail product, va

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

cross reference join YukawaTrilinearForm.lean
TeX and evidence source explicitly name the same Python identifier; statement equivalence not inferred
explicit file citation v5_e8_cascade.py
literal source filename/path in TeX
cross reference join CalderonInterface.lean
TeX and evidence source explicitly name the same Python identifier; statement equivalence not inferred

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.

Complete structured registry How source relations are recorded Knowledge and evidence coverage