TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/compiler-correlated-event-clock-20260919/PROOF.txt
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Inclusive original lines: 201-275
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
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000201 |   Phi_recorded(z)=z J20 [3I-z(2I+S20)]^(-1).
000202 | Population factor: z/(15-12z) times A.
000203 | Disjoint coherence factor: +/-z/(15-10z) times transpose.
000204 | For six accepts:
000205 |   count PGF=[z/(5-4z)]^6; E[N]=30; Var[N]=120.
000206 | The terminal channel has the Petersen and 1/15625 coherence attenuations,
000207 | but six accepts now consume thirty original events on average, not ten or
000208 | six. This distinction is essential when transporting the geometric phase.
000209 | 
000210 | 6. RELATION TO THE PRIOR QUARTIC/E8 LIFT AND ACTUAL TFPT CLOCK
000211 | 
000212 | Contract .12: tilde r=exp(-i*pi/4)r. Therefore on Sym2,
000213 | tilde U=-i U. For a word with N total executed events the paired scalar
000214 | is (-i)^N and the fundamental scalar is exp(-i*pi*N/4). Each homogeneous
000215 | CP history K rho K^dagger loses this scalar; at fixed coherent word length
000216 | it is only a common global phase. The new construction retains relative
000217 | Bell phases but does not by itself observe the alternative central lift.
000218 | 
000219 | N modulo8 can be retained exactly in the same classical history. If
000220 | Phi(z)^6=sum_N z^N E_N, its residue-class maps are
000221 |   Psi_a=(1/8) sum_{k=0}^7 exp(-2*pi*i*k*a/8) Phi(exp(2*pi*i*k/8))^6.
000222 | They are CP because they equal sums of the CP coefficient maps E_N over
000223 | N congruent to a modulo8. At a complex counting argument Phi(z) is generally
000224 | not a CP map; this Fourier formula does not restore coherences between N
000225 | histories or construct a phase-sensitive observable. A physical reference
000226 | path or charged offdiagonal sector remains necessary for that purpose.
000227 | 
000228 | The native deployed clock in v808.p4_transport is a THREE-dimensional
000229 | cusp quotient. Its v486 positive sixth root is
000230 |   M=[[1,0,0],[0,1/2,1/6],[0,1/6,1/2]], spec={1,2/3,1/3}.
000231 | Petersen's three-shell quotient has spec={1,-2/3,1/3}. Sixth powers match
000232 | spectrally, whereas one-step spectra do not. The Bell10 multiplicities
000233 | 1+5+4 are explicitly [H neu] in v808. A native physical intertwiner and
000234 | clock/readout identification do not follow merely from these rates.
000235 | 
000236 | Similarly, matching ten rays is not a linear identification of the Bell
000237 | memory Sym2(C4) with Lambda2 of the native quartic-five carrier. For the
000238 | source Pauli g=diag(1,1,-1,-1), the product of the two axis reflections in
000239 | coordinates2 and3, detg=1 and R4(g)=I5 on the actual quartic
000240 | basis of .12. Thus tr Lambda2 R4(g)=10, but tr Sym2(g)=2 (six plus and four
000241 | minus eigenvectors). No invertible linear intertwiner exists for these
000242 | actions. The equivariant ray/duad correspondence remains valid.
000243 | 
000244 | The underlying unobserved two-register channel is a mixture of product
000245 | unitaries with shared classical randomness. From a separable A:B input
000246 | it cannot create A:B entanglement. This does not prohibit initially Bell-
000247 | entangled states, quantum memory coherences, entanglement of a coherent
000248 | record/MPS, or postselected operations. Shared source correlation alone
000249 | must not be called a derived fundamental interaction.
000250 | 
000251 | 7. DECISIVE REMAINING ORIGIN QUESTION
000252 | 
000253 | The finite construction now carries source response, actual intervening
000254 | events, relational readout and primitive-count bookkeeping together.
000255 | The remaining origin test is specific: Does the native TFPT seam provide
000256 | this shared-event instrument and a physical record/reference observable
000257 | whose evolution is the tracked F above, and does that observable implement
000258 | the deployed cusp clock? The shared label, iid weights, outer mark, record
000259 | algebra and adaptive readout are explicit premises here. They are not
000260 | derived merely by constructing a working process.
000261 | 
000262 | Until that source/state/operator mapping is derived, this contract does not
000263 | select physical time, derive local charged currents, establish chiral
000264 | matter, reconstruct 3+1 spacetime or gravity, or solve all T1-T8. These are
000265 | the original objective; the finite common-process theorem is evidence on
000266 | one necessary connection rather than a substitute endpoint.
000267 | 
000268 | REPLAY
000269 | 
000270 |   python3 -B experiments/theory-contracts/compiler-correlated-event-clock-20260919/checker.py
000271 |   python3 -B -OO experiments/theory-contracts/compiler-correlated-event-clock-20260919/checker.py --out /tmp/tfpt-correlated-replay.json
000272 | 
000273 | No assert statements are used. Validation records are deterministic. The
000274 | source reconstruction and the history-frame algebra also received an
000275 | independent bounded matrix review, preserved with this contract.