Expositions · Premise notes · PRM-026
PRM-026 · Det² selector object (historical; retired as a selector of AX6_pol)
Register page /premises/PRM-026/ · kind POSTULATE · claims declared to rest on it today: none
Drafted by the house under R81 — no drafting lane wrote this note; every quote was matched against the suite TeX at its locator. What a premise note is.
← PRM-025
Premise
House-drafted note (R81-D5, S327j). R81 registered this historical row so that the two objects printed under the one label AX6 stay distinct: PRM-006 is AX6_pol; this row is the Det² object. No drafting lane wrote this note: the house drafted it from its reading of every line of the suite TeX that names the Det² object, at S327j. Every quote was matched against the TeX at its locator. No lane has reviewed this note.
Registered from the suite: p4_higgs_ewsb.tex:353-355 (PDF p.73), register quality HOUSE_TRANSCRIBED, located status HISTORICAL:
The Det² object is the degree-six selector cos(6ψ) = ½ with its 50° branch
The TeX at those lines: The \textbf{Det$^2$ object} is the degree-six selector $\cos(6\psi)=\tfrac12$ with its $50^\circ$ branch
What kind of premise this is
Register kind: POSTULATE, located status HISTORICAL. In print the object is a retired selector, not a live premise: Paper 4 retires it as a selector of AX6_pol (p4_higgs_ewsb.tex:356-358), and the Appendix X input ledger lists it as a distinct object, retired (appendix_x_zero_parameter_input_ledger.tex:90). It is registered so that an earlier statement of "AX6" as cos 6ψ⋆ = ½ is read as this object and not as AX6_pol (p4_higgs_ewsb.tex:366-369). Source status words: a distinct, retired selector (Rev32.2) (p7_precision_tests_falsification.tex:54).
Where the suite invokes it
A house census, not a lane draft: every line of the suite TeX that names Det$^2$ or Det^2 (TeX comment lines excluded) falls inside one of the 9 passages below (DISCHARGED 4, MENTIONED 1, STATED 4), except appendix_a_lagrangian_derivation.tex:295 — the term λ₆ Det² of the potential V: the square of the cubic norm, not the selector object; appendix_a_lagrangian_derivation.tex:297 — the same potential term, with an external Z₂ imposed: not the selector object. Pages refer to the sealed Rev32.7 page-delimited text.
| # | locator | quote (verbatim, TeX source) | role | argument |
|---|---|---|---|---|
| 1 | p1_peirce_gauge_group.tex:51PDF p.23 | the degree-six Det$^2$ object $\cos(6\psi)=\tfrac12$ once printed under the same name is a distinct, retired selector | DISCHARGED | Paper 1: the object once printed under the name AX6 is a distinct, retired selector |
| 2 | p4_higgs_ewsb.tex:353-354PDF p.73 | The \textbf{Det$^2$ object} is the degree-six selector $\cos(6\psi)=\tfrac12$ with its $50^\circ$ branch | STATED | Paper 4 (Rev32.2): the Det-squared object named and defined |
| 3 | p4_higgs_ewsb.tex:354-355PDF p.73 | it is \emph{not} a solution of AX6$_{\rm pol}$ ($\tan^250^\circ=1.4203\ne2.1771$) | STATED | Not a solution of AX6_pol; gives 0.3099 under the weak-angle readout |
| 4 | p4_higgs_ewsb.tex:356PDF p.73 | is the sole object of A667's degree-three Galois argument | STATED | A667's degree-three Galois argument applies to this object only |
| 5 | p4_higgs_ewsb.tex:356-358PDF p.73 | The Det$^2$ object is therefore \textbf{retired as a selector of AX6$_{\rm pol}$} | DISCHARGED | Retired as a selector of AX6_pol; A667 remains correct for the 50 degree object only |
| 6 | p4_higgs_ewsb.tex:366-369PDF p.73 | Any earlier statement of ``AX6'' as $\cos(6\psi_\star)=\tfrac12$ with $\psi_\star=50^\circ$ refers to the Det$^2$ object. | STATED | Binding vocabulary (footnote): an earlier AX6 printed as cos 6psi* = 1/2 refers to this object |
| 7 | p7_precision_tests_falsification.tex:54PDF p.110 | the Det$^2$ object $\cos(6\psi)=\tfrac12$ is a distinct, retired selector (Rev32.2) | DISCHARGED | Falsification map, AX6_pol row: the Det-squared object is a distinct, retired selector |
| 8 | appendix_a_lagrangian_derivation.tex:373PDF p.143 | the Det$^2$ selector $\cos(6\psi)=\tfrac12$ is a different object | MENTIONED | Appendix A psi_pol frontier: the Det-squared selector is a different object from AX6_pol |
| 9 | appendix_x_zero_parameter_input_ledger.tex:90PDF p.323 | The Det$^2$ object $\cos(6\psi)=\tfrac12$ ($50^\circ$) is a distinct object, retired as a selector of AX6$_{\rm pol}$ | DISCHARGED | Input ledger, weak-angle selector row: a distinct object, retired; A667's degree argument applies to it only |
House reading notes:
p4_higgs_ewsb.tex:353-354— The registered statement (PRM-026 PRIMARY).p4_higgs_ewsb.tex:356-358— The registered DISCHARGED occurrence (PRM-026 SECONDARY).
Arguments that rest on it
NO RECORD declared. Under R82-d the PI ruled no edges for PRM-026: LIB2-249 (retired) is about this object, and its result does not rest on it.
What breaks without it
Nothing current, in print: the object is retired as a selector, and A667's degree-three argument applies to it only, so A667 does not constrain AX6_pol (p4_higgs_ewsb.tex:356-358). What the separate row protects is the reading: with one row for both objects, an argument about this object could be read as an argument about AX6_pol. NOT ASSESSED beyond the printed disposition.
Registrar sync
Registrar state after R76, R78 and R82 (S327j, master 0e1418ad6501767d). Declared today: none (UNKNOWN, not INDEPENDENT). R82-d (PI, S327j): no edges for this premise.
Tier and what this does not show
A premise is not a result, and invocation count is not importance. A historical row is registered for the record, not as a live input. The roles above are house readings. No record or premise is upgraded, downgraded, or edited.
Sources
TeX: p1_peirce_gauge_group.tex:51; p4_higgs_ewsb.tex:353-354; p4_higgs_ewsb.tex:354-355; p4_higgs_ewsb.tex:356; p4_higgs_ewsb.tex:356-358; p4_higgs_ewsb.tex:366-369; p7_precision_tests_falsification.tex:54; appendix_a_lagrangian_derivation.tex:373; appendix_x_zero_parameter_input_ledger.tex:90.
Register: PRM_REGISTER_S312.jsonl row PRM-026 (R81-D5). Ruling: Trackers/RULING_R81_S327_PREMISE_REGISTER.md.
← PRM-025
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