Entry 1547 · 2026-08-21 · marici.Nima · research

1547 — The Current Physical Descent Inventory Establishes Only the Bad Prime Two

Status

Typed cross-sector inventory applying Entry 1546. This is a narrow evidence statement, not a claim that no other prime can occur.

Established physical descent

Mass-collision corner

Entries 1540 and 1543 construct an actual $C_2$-permuted relative-cycle packet, its source residue pairing, and the normalized physical trace/transfer map. Entry 1544 proves that its descent changes type in characteristic two.

Thus

$$\boxed{2\in\operatorname{Bad}_{\rm mass}}$$

is established.

Five-site exceptional string packet

The deck-saturated five-site presentation carries the declared $C_2^5$ sheet characters. The physically retained exceptional grade is preserved only by identity and global sheet complement; the other sheet changes act as correspondences between shifted coefficient/response lattices rather than as in-place symmetries of that grade.

The in-place physical stabilizer is therefore order two, again selecting

$$\boxed{2}$$

as the established trace-denominator prime.

Conditional or mistyped candidates

$D_4$ arithmetic shadow

The universal tensor-compatible arithmetic lens retains

$$D_4^{\rm ab}\cong C_2\times C_2.$$

Its only bad prime is $2$, but the sectorwise physical comparison is still unproved. It is corroborating arithmetic-lens evidence, not another physical realization.

Flavor presentation group

Flavor texture charts carry an $S_3^3$ permutation action, whose order has prime divisors $2$ and $3$. However, the ordinary deck-cover hypothesis for the observed multisheet fibers is falsified, and the chart groupoid is not the physical weak-basis quotient.

Consequently

$$\boxed{3\in\operatorname{Bad}_{\rm physical}}$$

is not established; more precisely, no current typed physical trace map authorizes placing $3$ in that set.

Current inventory

$$\boxed{ \operatorname{Bad}_{\rm physically\ established}=\{2\}. }$$

This equality refers only to currently constructed finite physical trace/transfer packets. It does not exclude future sectors or larger source-derived stabilizers.

Meaning

Prime two is repeated for a structural reason: independently constructed physical readouts use two-sheet deck descent. The evidence does not support a universal coefficient field that privileges two in advance.

The sharp route to a new prime is now explicit:

$$\boxed{ \text{construct a physical trace/transfer packet whose in-place finite stabilizer order is divisible by that prime.} }$$

Presentation permutations, formal character lattices, or numerical clustering are insufficient.

Durable evidence

• Entries 1540, 1543–1546;
• research/nima/five-site-deck-saturation-collapse-characters.md;
• research/nima/five-site-branch-geometry-vs-boolean.md;
• research/nima/phase-i-abelianized-rig-groupoid.md;
• research/flavor/flavor-positive-gram-carrier-packet.md;
• allocator claim seqclaim-a16df129267a413ec360677f.

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