Established in scope
One primitive integral charge forces the entire E8 completion
In the question: Automatic joint origin hypotheses and source responses
Weaker premises thanR101,not new fourmark/E8 construction or physical origin. Originalv983 already contains the generator. Standard normalization and actual local primitive insertion remain inputs. Nonprimitive n16,scaled n5 and diagonal doubled braiding class are actual countercontrols. Full doubled locality does not imply positive one-sided integrality;keep braiding,Hilbert norm and energy distinct.
Read the exact result, assumptions and evidence
Result
On the entire standard class,4d² is integral and a²=−b²/n modZ. Integralv² forces n|4b²,primitivity hence n4. D5 spinor5/4 and A3 class3/4 force even norm,index4 and determinant1;any further integral extension lies in the selfdual sublattice,so L is exactlyE8. Evenness,selfduality,minimality follow. Two marked inverse-paired glues remain. Exact replay of11216 primitive representatives n3..96 and actual countercontrols passed;the general proof is the denominator argument.
Required assumptions
- Integral standard pairing with primitive family class
n>=3,L0=D_(n+1)⊕A_(n−1) with standard positive root norm2. L is any integral overlattice in the same space,containing v whose A discriminant projection bλ1 is primitive,gcd(b,n)=1. Do not assume evenness,unimodularity,rank8 or minimality. Standard pairing and actual local insertion are candidate premises,not automatic P1 or double-cover consequences.
- 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
- PRIMITIVE-INTEGRAL-COMPLETION-20261102.txt lines 1–148
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/seam-positive-kernel-search-20261015/PRIMITIVE-INTEGRAL-COMPLETION-20261102.txt
695a3249781bc7f6c46e091a0faec0c8eda384a9cf64c6d67f501d5ddf10c0e6
- integral_origin_checks.py lines 1–157
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/seam-positive-kernel-search-20261015/integral_origin_checks.py
7a4c677afaa4ef72c450e0febd720c18ed4e4d7e2df405ca70f9e84f789b56d2
- v983_simple_current_generator.py lines 1–63
Source checked at this snapshot
Original location and fingerprint
verification/v983_simple_current_generator.py
769a9c5cb5e6518d8d2a445d347150f5ce0d1410c95db263ca2db72466e176c8
finding:r102-primitive-integral-charge-forces-entire-e8-completion