TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/native-observation-arity-20261025/NATIVE-OBSERVATION-ARITY.txt
Original file SHA-256: 3beb984ed44fdc1c9aab40626fc19357aaa5a0a15dcaa57259f6d71e487e5b39
Inclusive original lines: 201-246
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.

000201 | informative term on Sym^3 are consequences of full G31 covariance.  They are
000202 | not an extra bosonic-sector choice for this POVM classification.
000203 | 
000204 | Each E_a has eigenvalues 5/6 on its Ovoid ray and zero on the orthogonal
000205 | four-space.  The two eigenvalues of the bracket are therefore
000206 | 
000207 |     (1+4t)/6, with multiplicity 1,
000208 |     (1-t)/6,  with multiplicity 4.
000209 | 
000210 | Positivity is equivalent to
000211 | 
000212 |     -1/4 <= t <= 1.
000213 | 
000214 | At t=1 this is the existing rank-four readout on the twenty-dimensional
000215 | carrier.  At t=0 it is uniform.  At t=-1/4 the Ovoid ray is excluded and the
000216 | carrier effect has rank 16.
000217 | 
000218 | The checker constructs t=1 as six actual 64 by 64 matrices.  They sum to I64,
000219 | each has rank 48 and spectrum
000220 | 
000221 |     5/6 with multiplicity 4,
000222 |     1/6 with multiplicity 44,
000223 |     0   with multiplicity 16.
000224 | 
000225 | All 60 times 6 covariance identities are certified exactly in factored form:
000226 | the checker verifies the decoder intertwiner, all six H5 effect identities,
000227 | and invariance of Pi20 for each of the sixty roots.  Multiplying these three
000228 | identities gives the displayed 64 dimensional covariance identity.  Hence
000229 | n=3 is attainable, while n=1 and n=2 are excluded, proving minimality.
000230 | 
000231 | Boundary
000232 | --------
000233 | 
000234 | The theorem classifies the finite native covariant effects on the full space
000235 | at the first allowed tensor stage.  It does not select a physical tensor
000236 | stage, a copying process, or the parameter t.  It also does not derive Nfam or
000237 | a P1 source.
000238 | 
000239 | Run
000240 | ---
000241 | 
000242 |     python3 experiments/theory-contracts/native-observation-arity-20261025/native_observation_arity.py
000243 |     python3 -OO experiments/theory-contracts/native-observation-arity-20261025/native_observation_arity.py
000244 | 
000245 | Both executions use exact arithmetic and write
000246 | native_observation_arity_results.json.