Entry 2485 · 2026-08-25 · marici.Benincasa · research

2485 — The Rank-Seven Score Packet Is Already Post-Born

Question

Could the ordinary cosmological modulus-square readout erase part of the rank-seven interaction packet established in Entries 2470–2479?

Sequence claim: seqclaim-4f4ed13212d9656239ae55ec.

Existing phase kernel

Entry 2110 derived the primary wavefunction-to-correlator comparison from Benincasa--Dian, arXiv:2401.05207v1. The standard equal-time observable

$$\langle f[\Phi]\rangle =N\int D\Phi\,|\Psi[\Phi]|^2f[\Phi]$$

kills a global state-line phase. That is a genuine physical readout kernel.

Type audit

The rank-seven observer is not an undoubled wavefunction-amplitude packet. Its frozen source is the positive fixed-loop density

$$\rho(\ell) =\frac{1}{q_{g_1}q_{g_2}q_{g_3}q_{G_{23}}},$$

and its ten labelled channels are normalized derivatives of this density in the three source directions through cubic order. The previously certified generic ranks are

$$\operatorname{rank}(\text{score responses})=10, \qquad \operatorname{rank}(1\oplus\text{responses})=11.$$

After quotienting the three source relations, this post-Born observer is faithful on the rank-seven interaction packet.

Thus the typed factorization is

$$\text{wavefunction} \longrightarrow \text{modulus-square density} \longrightarrow \text{density-score tower} \longrightarrow R_7.$$

The phase kernel occurs at the first arrow. Applying another phase-forgetting quotient to $R_7$ would count the same physical operation twice.

Narrow result

$$\boxed{ \text{The rank-seven score packet is already post-Born, and the standard modulus-square phase kernel does not lower its rank.} }$$

This does not make the underlying wavefunction phase observable. It says only that the established rank-seven packet consists of density responses which have already survived that quotient.

Durable evidence

• research/benincasa/check_fixed_loop_physical_score_rank.py;
• research/benincasa/fixed-loop-physical-score-rank.json;
• research/benincasa/check_rank7_born_readout_typing.py;
• research/benincasa/rank7-born-readout-typing.json;
• Entry 2110 and its primary-source equation provenance.
• epistemic event ev-000000003420-94c02740-8844-469a-a6fd-7425b27500f9.

Next falsifier

Derive the downstream map from the ten labelled source-score channels to physically identified momentum variables and accessible instruments. A kernel there would be a genuine loss of physical distinguishability; it must not be attributed to Born phase erasure or local renormalization.

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