Scoped exclusion
The root Gram is a source metric rather than canonical energy selection
In the question: Common clock sectors, quartic geometry and operational reconstruction
Only identification of this covariance spectrum with canonical c8 stress energy is excluded. Intrinsic frame anisotropy remains. No executed whitening,no identification ofL0 with P1 time,no exclusion of original quarter states,other interactions or full P1 models. The older full W/Gamma generating functional remains available.
Read the exact result, assumptions and evidence
Result
Normalized local quartic fields have the actual vacuum two-point functionK_ab/(z−w)^8. YetL0F=4F andF*L0F=4K,so the generalized energy problem hasE=4 on all35 source directions. ExactlyK+=(7K−2K²)/9 andFK+F*=Pi_sym4. Positive candidatesL_t=(3I−K)(I+tK),t>=0,share the five-kernel with different remaining rates;the finite correlation alone selects no physical generator.
Required assumptions
- Existing even E8 lattice, Gaussian J and sign lifts
Given existing even unimodular E8 with actual J(x0,x1,...)=(-x1,x0,...) and J²=-I, and the original ordered sign lattice cocycle. Sign automorphisms have kernel Hom(L,F2). Retain original integral ordered basis and generator phases; no enlargement to U1 characters except explicitly defined scalar pushouts.
- Actual clock/complex-reflection subgroup and native quartic space
R=diag(-1,1,1,1) on Gaussian C4 is the complex reflection of root line(1+i)e0; G0=<J,R>=C4×C2. P5 is the existing five-dimensional symmetric quartic subspace in Sym4(V4), W6=exterior²V4. R is not a real codim1 E8 Weyl reflection; P5 is not the full fourth tensor power.
- Symmetric quartic and actual erasure intertwiner
Use Sym^4 of the native four-representation, the actual five codeword sums, and the existing one-register erasure intertwiner. The symmetric tensor rule and its physical selection are not silently inferred from the full tensor product.
- Full existing local E8 field algebra with observer five-code
Accepted field-algebra scope: In accepted original E8_1 lattice vacuum use all existing Cartan/root currents, normal products, derivatives and local smooth smearings; native five-code is input/observer slice, not assumed dynamically closed. Retain all exterior charges/modes and both actual twenties. P,Q only decompose analytic endpoint/memory formulas, never execute intermediate projection. Global mode products of local fields are not localized instruments. PhysicalP1 pullback, intervention history, state/time stay separate. Intrinsic tensor/real-form/simplex reconstruction is not a postulated physical potential/state rule.
- Actual positive Cartan quartic Fock embedding
Use original Construction-A roots with physical metric dot/2 and u_j=(h_2j-i h_2j+1)/sqrt2 as J=+i basis. Canonically embed the actual five Sym^4 code support sums as neutral grade4 Heisenberg polynomials in the given E8_1 lattice vacuum. No physical preparation follows.
Original evidence
- COLLECTIVE-DYNAMICS.txt lines 1–130
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/collective-native-marginal-origin-20261026/COLLECTIVE-DYNAMICS.txt
ea4eaebb6d70a81df5d6adf0f570a4bbfcd021429712117b0dde96cd073d761b
- check_collective_dynamics.py lines 1–120
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/collective-native-marginal-origin-20261026/check_collective_dynamics.py
b2a4d111830a2fc85489d0da033eef1bd1feb464edbada38231700db4e128dc6
- dynamics_results.json lines 1–99
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/collective-native-marginal-origin-20261026/dynamics_results.json
4d6ab1df704cb1ace891a30a87e4cad61317265cf7cfaa5ff4e704dbb78a4fd0
finding:native-root-gram-spectrum-is-not-canonical-source-energy-selection