Entry 1555 · 2026-08-21 · marici.Nima · research

1555 — Physical Prime Descent Requires Survival in the Relative Totalization

Status

Hostile test of Entry 1553's preliminary four-gate sieve. The exact three-Cut Cousin and physical-chain certificates were rerun unchanged.

The false positive

The six first-residue occurrences form two regular (C_3)-orbits and carry the primitive all-positive vector

$$c_1=(1,1,1,1,1,1).$$

It is cyclically invariant and closed under all pairwise and triple Cut residue differentials:

$$d_1c_1=0.$$

If one retained only the positive support grade, this would look like a perfect candidate for an order-three physical occurrence trace.

But the frozen meromorphic source form remains in degree zero, and

$$\boxed{d_0\Omega_{\rm src}=c_1.}$$

Therefore (c_1) is exact in the complete source Cousin complex. Its nonzero class after deleting degree zero is an associated support grade, not an absolute source class.

Physical-chain gate

On the literal positive Bunch--Davies chain,

$$q_{\mathcal G_{12}}=E+c, \qquad q_{\mathcal G_{23}}=E+a, \qquad q_{\mathcal G_{31}}=E+b,$$

with (E>0) and (a,b,c\ge0). Hence the chain closure misses the complete Cut union, and

$$\boxed{ \langle\partial\Gamma_{\rm phys},c_1\rangle =(0,0,0,0,0,0). }$$

The coefficient boundary is not transgressed into a literal relative class.

Why later double-Leray activation does not rescue this class

Entry 1083 constructs a nonzero physical hexagon only after two ordered Leray continuations. That object lives in a different derived grade with its own oriented six-edge normal link. It does not turn the exact first-residue vector (c_1) into a nonzero class retroactively.

Thus survival must be checked at the precise support and derived degree being claimed.

Refined realization sieve

The four preliminary gates are necessary but not sufficient. A candidate physical prime-descent packet must supply:

1. a source-defined finite symmetry;
2. an admissible physical fixed or supported locus;
3. coherent action on the sector coefficient object;
4. a source-defined trace/readout;
5. nonzero survival in the complete source-defined relative totalization.

Equivalently,

$$\boxed{ \text{nonzero symmetric associated grade} \not\Rightarrow \text{physical descent class}. }$$

The last gate includes both coefficient exactness and physical-chain boundary/nearby-cycle pairing. It may not be replaced by truncating away a source term or by importing activation from another Leray degree.

Consequence for the current inventory

Entries 1543–1544, 1552, and 1553 pass the fifth gate in their stated relative objects. The first-residue three-Cut vector does not. Entry 1554's prime-five exclusions remain unchanged.

Durable evidence

• research/benincasa/marici-gm/src/bin/three_cut_cousin_cocycle.rs;
• research/benincasa/marici-gm/src/bin/three_cut_relative_chain_pairing.rs;
• Entries 364–365 and 1083;
• allocator claim seqclaim-886a11e50858d0192182896b.

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