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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.

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

-1.2cm TFPT — The Standard Model from the Compiler\\[2mm] The [formula in source] -ladder, the flavor block from parabolic transport, and the worked closures ( [formula in source] , quark [formula in source] , the gap, Starobinsky [formula in source] )

Standard Model and flavor structure

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_2_standard_model/preamble.tex · lines 1 to 94

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Front matter / support

Standard Model and flavor structure

The Standard Model as one [formula in source] -ladder mass formula (all masses, CKM, PMNS, neutrinos), the flavor matrix from parabolic transport on [formula in source] , the five worked closures ( [formula in source] , quark [formula in source] , the explicit mass gap, Starobinsky [formula in source] , the H2 splitting), and gravity/quantum gravity as the seam response (the Seam Response Grammar [formula in source]

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documents/tfpt_2_standard_model/sections/001-part-the-standard-model-in-one-master-formula.tex · lines 1 to 24

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The Standard Model in one master formula

Standard Model and flavor structure

In one sentence. The fermion spectrum — masses, Yukawa structure, CKM, the PMNS skeleton and the neutrinos — follows from one master formula with three ingredients: the seed [formula in source] , the carrier base [formula in source] and the residue matrix of the compiler. No free Yukawa exponents remain; the charged-lepton amplitudes are closed, the quark mass ratios are closed too (integer Pl\"ucker readouts, v49/ v

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documents/tfpt_2_standard_model/sections/001-part-the-standard-model-in-one-master-formula.tex · lines 25 to 36

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The principle: one master formula instead of many Yukawa numbers

Standard Model and flavor structure

In the source-layer construction each fermion mass arises through a Yukawa coupling [formula in source] built as a transport word-length [formula in source] on a hexagon ( [formula in source] ) times a holonomy amplitude. In the compiler picture this is one line:

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documents/tfpt_2_standard_model/sections/001-part-the-standard-model-in-one-master-formula.tex · lines 37 to 66

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explicit file citation v172_trace_anomaly_seed.py
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The seed [formula in source] as a decoder

Standard Model and flavor structure

A single seed drives four independent low-energy observables. This is the strongest compression of the flavor input:

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documents/tfpt_2_standard_model/sections/001-part-the-standard-model-in-one-master-formula.tex · lines 67 to 91

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The flavor residue matrix is the compiler signature

Standard Model and flavor structure

The core of the simplification: the word-length matrix [formula in source] splits into the residue matrix [formula in source] (the hexagon packets of the three sectors) and the winding matrix [formula in source] (one [formula in source] per first generation [formula in source] anchor). [formula in source] carries all the discrete flavor information — and its invariants are exclusively compiler numbers:

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documents/tfpt_2_standard_model/sections/001-part-the-standard-model-in-one-master-formula.tex · lines 92 to 216

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Charged leptons: completely closed in [formula in source]

Standard Model and flavor structure

For the leptons the hexagonal resolvent solves the amplitudes [formula in source] in closed form — only pure [formula in source] powers with rational carrier prefactors remain:

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documents/tfpt_2_standard_model/sections/001-part-the-standard-model-in-one-master-formula.tex · lines 217 to 314

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explicit file citation v21_solar_product_quark.py
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explicit file citation v220_cp_hexagonal_modulus.py
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Quarks: hierarchy from the same word-lengths

Standard Model and flavor structure

The quark sectors use the same master formula with [formula in source] , [formula in source] . Where two generations share the same word-length the mass ratio is pure transport amplitude; where they differ by [formula in source] a factor [formula in source] appears:

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documents/tfpt_2_standard_model/sections/002-section-quarks-hierarchy-from-the-same-word-lengths.tex · lines 1 to 164

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The Sheet Diamond and the Winding Line: masses and transport from one surface

Standard Model and flavor structure

The mass-power matrix and the transport word-length matrix are not two independent machines: they are the two sheet-readouts of one parabolic projection [formula in source] acting on the residue matrix [formula in source] . Collect the [formula in source] -orders [formula in source] of the nine charged fermions into the mass-power matrix with [formula in source] the sheet ( [formula in source] ) involution. Then, exa

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documents/tfpt_2_standard_model/sections/002-section-quarks-hierarchy-from-the-same-word-lengths.tex · lines 165 to 183

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Front matter / support

Standard Model and flavor structure

The whole flavor algebra lives on a single two-parameter operator surface, [formula in source] with the two global invariants [formula in source] The mass-transport pencil [formula in source] is the cut [formula in source] , on which the anchor-block determinant factorises as [formula in source] — the master cover of the operator-pencil sections below (unique up to M\"obius reparametrisation, v85_master_cover.py). Th

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documents/tfpt_2_standard_model/sections/003-source.tex · lines 1 to 447

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Front matter / support

Standard Model and flavor structure

is a binary internal compiler \ ( v410_sheet_generator_binary.py)] The sheet axis [formula in source] is not only the rank- [formula in source] direction of the cross — its iterates print the binary carrier spine. The closed form (proved by the inductive step [formula in source] ) [formula in source] gives [formula in source] — the [formula in source] exponents, then [formula in source] , [formula in source] and [for

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documents/tfpt_2_standard_model/sections/004-source.tex · lines 1 to 388

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Front matter / support

Standard Model and flavor structure

The ``which sheet does parity select'' question above had a blocker: no independently motivated sector [formula in source] sheet map. The cover supplies one itself. At each branch point the anchor block is rank one, with canonical integer kernels: [formula in source] — at the carrier point the block annihilates the democratic vector itself. Collapse lemma : rank one forces [formula in source] , hence proportional to

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Closing the audit gates: is [formula in source] , [formula in source] , [formula in source] derived or imported?

Standard Model and flavor structure

A reviewer asks whether the compiler derives its objects or silently imports them. We answer the three flavor/EM gates explicitly ( v13_open_gates.py); each is either closed or reduced to a named geometric statement, with the honest residual flagged.

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Mixing: CKM and PMNS from holonomy

Standard Model and flavor structure

@p3.0cmp6.0cmcc@ Quantity & Formula & Prediction & PDG \\ [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] (leading, ) & [formula in source] rad & [formula in s

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Downstream flavor readout: the rare kaons [formula in source]

Standard Model and flavor structure

The closed CKM point is not an end state — it feeds the theoretically cleanest flavor-changing neutral-current probe, the rare decays [formula in source] and [formula in source] . These are not a new compiler power: the only TFPT-specific content is the CKM point above; the short-distance loop functions ( [formula in source] , [formula in source] , [formula in source] , [formula in source] , Brod–Gorbahn–Stamou) are

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Honest note on the search.

Standard Model and flavor structure

A generic ``spine-ratio'' scan ( [formula in source] , [formula in source] , the [formula in source] ratios, [formula in source] , [formula in source] ) finds [formula in source] hits abundantly — which is weak evidence, since [formula in source] numbers are densely covered by ratios of [formula in source] . We therefore count only named invariants (like [formula in source] or the exact endpoints), not generic ratios

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Neutrinos

Standard Model and flavor structure

The neutrino sector is the Majorana branch of the same construction: [formula in source] . @p3.6cmp5.2cmc@ Quantity & Origin & Value \\ [formula in source] & [formula in source] (UV), closure [formula in source] & [formula in source] \\ [formula in source] & primary (freeze): [formula in source] (seed, [formula in source] ); two derived variants in the named box & [formula in source] (NuFIT 6.0 [formula in source] )

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How the legacy layers simplify (bridge map)

Standard Model and flavor structure

@p0.7cmp3.5cmY@ layer & before & in the compiler picture \\ 1 & boundary [formula in source] & axiom (P1), unchanged; hardenable via Calder\'on/Lean \\ 2 & carrier, [formula in source] , [formula in source] , [formula in source] , [formula in source] & all one Pascal row [formula in source] on [formula in source] ; [formula in source] is the [formula in source] half-spinor \\ 3 & EM fixed point [formula in source] fl

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Is the entire Standard Model thereby derived?

Standard Model and flavor structure

Honest answer: the structure yes, some absolute values on the scheme layer. Three layers:

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Closure status of the five former open questions

Standard Model and flavor structure

For each question the entry is typed honestly as closed, reduced or conditional: the proof chain isolating one sharply named remainder — and, where possible, a reduction that makes the problem smaller than previously thought. This is a resolution map, not a claim that all five are fully solved.

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