Scoped exclusion
Positive-only compression removes the required negative carrier sector
In the question: Historical: common source, state and event selection
Literal source interface of the archived definition; not a refutation of the algebraic 3+2 statement for a supplied P2 carrier. Likewise (2G−I)|Ran(G)=I: full boundary data alone do not create an internal marking.
Read the exact result, assumptions and evidence
Result
Pprim=C Pgap implies Ran(Pprim)⊂Ran(C). Thus (2C−I)|H_car=I for a carrier embedded there, and E_−=0. Every isometric pullback W into Ran(C) also yields W*(2C−I)W=I. The later 3+2 polarization does not follow this way. The general lemma CQ=Q ⇒ (2C−I)Q=Q is kernel-checked. A different carrier factor needs an explicit different map.
Required assumptions
- 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.
- Literal carrier embedding after positive compression
Read the archived phrase H_car after primitive admissibility compression literally as a subspace of Ran(Pprim)⊂Ran(C), then define internal polarization as (2C−I)|H_car. A different coefficient-factor interpretation instead requires its own embedding and internal involution.
Original evidence
- PROOF.txt lines 189–221
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/seam-full-collar-reconstruction-20261015/PROOF.txt
9f4effed34316798c6a35e1ac0ec2832cd3720180f476cb8747bb32359b56e6a
- 001-section-primitive-core-and-carrier-interface-handoff.tex lines 192–289
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
- 001-subsection-carrier-algebraic-normal-form.tex lines 172–283
Source checked at this snapshot
Original location and fingerprint
documents/archive--tfpt-45--source_extracts--02_carrier_source/sections/001-subsection-carrier-algebraic-normal-form.tex
fb846ac340cc9f8ea0aa6431598b624f2f744fa08b7d4cfdc081c358d1ea7cee
finding:positive-compression-erases-carrier-minus-sector