Conditional result
Positive quartic shape conditionally selects3+2; boundedness alone does not fix its sign
In the question: Historical: common source, state and event selection
Exact conditional internal shape selector and scoped control. No P1-derived field/potential, complete TFPT dynamical uniqueness, physical Higgs/gauge identification or T1–T8 closure.
Read the exact result, assumptions and evidence
Result
For every traceless Hermitian rank-five endomorphism with trX²=1, globally7/30≤trX⁴≤13/20. Exhaustive stationary-spectrum classification gives equality below only at2+3 and above at1+4. The even conjugation-invariant bounded-below controls -t+t²±trX⁴ therefore favor different splits, without an inserted preferred direction. The primitive spectral functional differentiates a supplied deformation; a positive profile does not imply a positive fourth-order shape term. Original X, trace constraint, deformation and sign remain to be derived.
Required assumptions
- Unmarked traceless Hermitian five-dimensional endomorphism
The diagnostic grants X=X* on an unmarked complex rank-five carrier, trX=0 and trX²=1 for shape classification. It studies trX⁴ or -t+t²±trX⁴, t=trX². Field, trace constraint, contraction, sign, even symmetry and dynamics are not derived here from P1.
- Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
Original evidence
- PROCESS_RECONSTRUCTION.txt lines 122–213
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/seam-joint-source-origin-audit-20261016/PROCESS_RECONSTRUCTION.txt
daaf8a80f62be064a2bbc53f17b00f40d329929d2c29b14793ddaa1ead04cea6
- process_reconstruction.py lines 45–88
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/seam-joint-source-origin-audit-20261016/process_reconstruction.py
2398a46a57942ff8fc54f8735101dc1f271cd748eb25f85595bfed5308e75ad5
- 001-section-primitive-core-and-carrier-interface-handoff.tex lines 302–343
Source checked at this snapshot
Original location and fingerprint
documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/sections/001-section-primitive-core-and-carrier-interface-handoff.tex
7d6e673d99c29d950dc601283cd51c1cc0b113567eeb79c8396fec9c82a02c79
finding:quartic-shape-selects-32-only-with-source-sign