# Agent Report — Denominator Gate Transfer Matrix

timestamp: 2026-05-07 09:01 UTC
category: gate_transferability_matrix
verdict: operator
observables_registry: 1.0.0-2026-05-06
observables_used: [SR, SR2, L1, L2, triple_var]
tool: tools/exp_denominator_gate_transfer_matrix.py
data: tools/data/denominator_gate_transfer_matrix.json

## Claim Under Test

Verificato dal campo vivo: il cycle 0803 ha mostrato che il denominator gate
trasferisce da BOUNDARY a DUALITA come operatore, ma non trasferisce la
coordinata locale GUE/Poisson.

Domanda di questo cycle: applicato a 4 perimetri non-BOUNDARY con poli
coerente/illusorio a distribuzione marginale preservata, quali parti del gate
trasferiscono e quali restano locali?

Perimetri:

- `DUALITA_golden`: sequenza Beatty aurea coerente vs permutazione illusoria.
- `R_periodic_triad`: pattern periodico a 6 fasi vs permutazione illusoria.
- `T_markov_alternating`: catena alternante low/high vs permutazione illusoria.
- `E_ar1_continuity`: continuita AR(1) positiva vs permutazione illusoria.

Parametri verificati: `n_gaps=4096`, `n_replicates=20`, `n_beta=11`,
`n_baseline=32`, `z_min=2.0`, `seed=202605070901`.

## Deposito Numerico

| perimeter | coherent one-sided observables | stable_count coherent | stable_count illusory | endpoint distance gated | ambiguous beta gated |
|---|---:|---:|---:|---:|---:|
| DUALITA_golden | SR, L1, triple_var | 3.00 | 0.25 | 3.418 | 0.30 |
| R_periodic_triad | SR, SR2, L1, L2, triple_var | 5.00 | 0.25 | 4.400 | 0.30 |
| T_markov_alternating | SR, SR2, L1, L2, triple_var | 5.00 | 0.05 | 4.412 | 0.30 |
| E_ar1_continuity | SR, SR2, L1, L2, triple_var | 5.00 | 0.60 | 4.394 | 0.30 |

Endpoint-stable observables: `[]` in all 4 perimeters.

Verificato: no observable is stable at both coherent and illusory endpoints.
The denominator gate is not a two-sided endpoint support. It is one-sided
support for generated order.

## Risultato

1. The gate transfers as one-sided coherence support.

   In all 4 non-BOUNDARY perimeters, the coherent endpoint carries denominator
   support and the illusory endpoint loses it. `DUALITA_golden` transfers on
   `SR`, `L1`, `triple_var`; the three other perimeters transfer on all five
   canonical observables.

2. The both-endpoint stable set collapses everywhere.

   `endpoint_stable_observables: []` is not a failure of the test. It is the
   structural content: the gate does not name "two classes with stable
   denominators"; it names the side where order survives its own shuffle null.

3. The beta 0.30 ambiguity layer transfers as protocol coordinate, not as
   BOUNDARY coordinate.

   The ambiguous gated layer is beta `0.30` in all 4 perimeters. This is not a
   GUE/Poisson layer. It is the coordinate created by the replacement protocol:
   enough positions are illusory to place the layer near the endpoint bisector,
   while enough coherent order remains to keep large z support.

4. DUALITA is narrower than the other perimeters.

   `DUALITA_golden` has one-sided support on 3/5 observables. `SR2` and `L2`
   stay near shuffle at the coherent endpoint (`z_mean` about `0.12`). The
   DUALITA gate transfers, but only through lag-1 and triple aggregation in this
   synthetic perimeter.

## Consecutio

The next word is not `boundary_layer`. The correct category is:

`order_denominator_gate`

Definition: an original-vs-shuffle denominator gate where support is expected
on the coherent/generated side, endpoint-stable observables may be empty, and
the layer coordinate belongs to the perturbation protocol unless anchored to a
domain-specific semantic axis.

This extends the 0803 result:

- 0803: BOUNDARY denominator gate transfers to DUALITA, BOUNDARY coordinate does not.
- 0901: across 4 non-BOUNDARY perimeters, the transferable object is one-sided
  order support; beta ambiguity is a protocol fold, not domain ontology.

## Self-Audit: 5 Lenti

L1 hard constraint vs bias: no "always", "never", or "zero" claim is used
without exact support. `endpoint_stable_observables: []` is exact for this run
and perimeters.

L2 quantity vs ratio: the report uses raw stable counts, endpoint distances, and
beta layers. Percent language is avoided except where the script computes
fractions.

L3 no silent patching: the scope changed from BOUNDARY to non-BOUNDARY
perimeters explicitly. The new category `order_denominator_gate` is declared
instead of stretching `BOUNDARY_LAYER_GATE`.

L4 edge cases: `E_ar1_continuity` has illusory stable_count `0.60`, so the
illusory endpoint is weak-denominator, not denominator-absent. The claim is
one-sided support dominance, not exact absence.

L5 re-discovery vs discovery: the numerical mechanism is an original-vs-shuffle
order test on synthetic sequences. No NEW mathematical theorem is claimed.

## Fonti

- Verificato: `tools/data/agent_field_live.md`
- Verificato: `tools/LAB_AGENT_CONTEXT.md`
- Verificato: `tools/observables_registry.py`
- Verificato: `tools/exp_denominator_gate_transfer_matrix.py`
- Verificato: `tools/data/denominator_gate_transfer_matrix.json`
- Inferito: `order_denominator_gate` as category needed by the downstream
  vocabulary, from the cross-perimeter matrix.