Established in scope
Whole variable-mark class and primitive local selector
In the question: Automatic joint origin hypotheses and source responses
Conditional existence/selection theorem in the declared standard D/A metric. Not classification of all glues or physical sources; not derivation of local primitive insertion from unit topological winding. Retain known four-mark/three/five,E8 and later origin results. Higher ranks without the added condition remain possible; no new universal F1 prerequisite. Assuming the E8 source to derive E8 would be circular. The whole variable family gives a conditional converse; first check whether original theorems already supply the matching pairing/insertion.
Read the exact result, assumptions and evidence
Result
The stated standard class admits an even unimodular completion iff n=4r²,r>=1,of index4r. Necessity uses determinant4n and rank2n divisible8;sufficiency uses (spinor_D,rλ1_A) of order4r and norm2r². Full HNF Gram constructions at n4,16,36 are exactly even integral and determinant1. Any such completion containing an actually local primitive A discriminant projection forces n|4r,hence r1,n4,without minimality. The proof needs neither cyclic H nor injective component projections. The original marked n4 compiler already contains this primitive class: its actual g=(1/2)^8 projects to an order4 class modulo A3=D3. This is reused, not declared a new global source gap. The established compensated charged-source quarter action retains the inverse internal glue character.
Required assumptions
- Declared joint standard lattice class with variable mark count
n>=3; L0=D_(n+1)⊕A_(n−1) with standard positive root norm2. Seek an even unimodular overlattice of the same rank2n. Primitive family projection means an actually local charge in L whose image generates A*/A=Z_n; topological winding, external defect or module alone does not suffice. Neither the metric/D-A realization nor the local primitive insertion is presumed derived 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
- GENESIS-SYNTHESIS-20261102.txt lines 1–177
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/seam-positive-kernel-search-20261015/GENESIS-SYNTHESIS-20261102.txt
5b86ff944370aa4fbf65ff712b92b581dfa1a1b80cccd6c928217e63057961b0
- genesis_checks.py lines 1–120
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/seam-positive-kernel-search-20261015/genesis_checks.py
fc1160300289b57659af1d10d21269b0c4ca3e2d9dcef9ba68872fe10df38d06
- PRIMITIVE-SOURCE-APPLICATION-20261102.txt lines 1–32
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/seam-positive-kernel-search-20261015/PRIMITIVE-SOURCE-APPLICATION-20261102.txt
6faa73ece2c1a60b674ad5788d31d76f0f6f9f79d298af12560cc19a1392e555
- LATTICE-AND-SOURCE-FRAME.txt lines 100–171
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/canonical-seam-fermionization-20261025/LATTICE-AND-SOURCE-FRAME.txt
77e0687412cb79bf1d51d079946484b6e8be337adf8a72a85bf2e6079b045ae7
- SOURCE-CHARGE-GLUE-QUARTER-IDENTITY.txt lines 10–92
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/bracket_process_origin_20261028/original/SOURCE-CHARGE-GLUE-QUARTER-IDENTITY.txt
adbf414bf1105de1087740b3bd1707e9f0dcfe7504eb0da4467a0e01a2289b9c
finding:r101-variable-mark-completion-and-primitive-local-selector