TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/seam-full-collar-reconstruction-20261015/PROOF.txt
Original file SHA-256: 9f4effed34316798c6a35e1ac0ec2832cd3720180f476cb8747bb32359b56e6a
Inclusive original lines: 189-221
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
Conversation metadata and personal execution details are omitted where indicated.

000189 | 8. The original positive-only compression destroys the proposed carrier marking
000190 | 
000191 | A second, independent typing failure occurs before the finite carrier theorem.
000192 | In 01_boundary_kernel_source.tex:204-207 the seam selector is
000193 | P_Seam,+=(I+F)/2=C. Lines 249-261 state Pprim=C Pprim,gap, hence
000194 | Ran(Pprim) is contained in Ran(C), even without assuming the factors commute.
000195 | Lines 274-283 select H_car after primitive admissibility compression and define
000196 | epsilon_car=F|H_car. Read literally as H_car subset Ran(Pprim), this implies
000197 | epsilon_car=+I, E_-=0 and E_+=H_car. Indeed C v=v implies (2C-I)v=v.
000198 | Equivalently, for any carrier projection Q with C Q=Q, (2C-I)Q=Q.
000199 | An isometric pullback W with image in Ran(C) cannot fix this: W*F W=I.
000200 | 
000201 | But 02_carrier_source.tex:174-180 defines P3=(I-epsilon_car)/2 and
000202 | P2=(I+epsilon_car)/2, and lines 235-283 require dim E3=3 and dim E2=2.
000203 | The stated positive-only restriction therefore cannot supply the claimed 3+2
000204 | marking. This is a contradiction in the literal source-to-carrier construction,
000205 | not a refutation of the abstract P2 interface or its conditional 3+2 algebra.
000206 | If H_car instead means a separate coefficient factor BEFORE state compression,
000207 | the displayed restriction has a different type and needs its actual embedding
000208 | and internal involution. The cited definition supplies neither map.
000209 | 
000210 | The repair must retain the full field space and the marking action before any
000211 | state/admissibility projection. A state covariance is not an internal carrier
000212 | grading. In particular, the full two-face route is NOT sufficient if one again
000213 | sets epsilon_car=(2G-I)|Ran(G); that restriction is identically +I as well.
000214 | G is to be retained as operator data on both labeled faces, with the local field
000215 | algebra and source marking, not used to discard one grading and later recreate it.
000216 | No arbitrary 3+2 matrix or five selected modes are inserted as a purported repair.
000217 | This identifies a concrete reason why the previous carrier reconstruction cannot
000218 | close its own missing marking map, and specifies the information it must preserve.
000219 | The executable carrier audit checks an explicitly supplied isometric embedding W
000220 | and claimed involution E against (2G-I)W=W E. It validates a supplied dictionary;
000221 | it does not derive W or E, and a positive-only image cannot carry a negative E sector.