# Agent Report — Semi-Real Order Denominator Gate

timestamp: 2026-05-07 09:23 UTC
category: gate_falsification_semireal
verdict: scoped_operator
observables_registry: 1.0.0-2026-05-06
observables_used: [SR, SR2, L1, L2, triple_var]
tool: tools/exp_semireal_order_denominator_gate.py
data: tools/data/semireal_order_denominator_gate_20260507_0923.json
seed_check: tools/data/semireal_order_denominator_gate_20260507_0923_seedcheck.json

## Claim Under Test

Verificato dal campo vivo: il cycle 0901 ha nominato `ORDER_DENOMINATOR_GATE`
come supporto one-sided dell'ordine generato, ma lo ha fatto su perimetri
sintetici. Il mandato corrente chiede falsificazione su domini non-sintetici o
semi-reali.

Domanda: se l'endpoint coerente è una sequenza ordinata reale/semi-reale e
l'endpoint illusorio è una permutazione che preserva la marginale, il supporto
denominatore resta one-sided o compare un controesempio?

Perimetri:

- `prime_gaps_first`: primi 4096 gap fra primi.
- `zeta_zero_spacings_first`: primi 512 spacing fra zeri non banali di zeta,
  calcolati localmente con `mpmath.zetazero`.
- `logistic_return_intervals`: 4096 intervalli di ritorno a `x > 0.95` nella
  mappa logistica caotica `x -> 4x(1-x)`.

Gate: osservabile stabile se `abs(original - shuffle_mean) / shuffle_std >= 2`.

## Deposito Numerico

Run principale: `n_replicates=20`, `n_beta=11`, `n_baseline=32`,
`seed=202605070923`. Seed check: `n_replicates=12`, `n_baseline=24`,
`seed=202605070924`.

| perimeter | coherent one-sided observables | stable_count coherent | stable_count illusory | endpoint distance gated | beta ambiguous gated |
|---|---:|---:|---:|---:|---:|
| prime_gaps_first | SR, L1, triple_var | 3.000 | 0.650 | 3.270 | 0.30 |
| logistic_return_intervals | [] | 0.200 | 0.100 | 0.000 | [] |
| zeta_zero_spacings_first | SR, L2 | 2.150 | 0.250 | 2.666 | [] |

Seed check:

| perimeter | coherent one-sided observables | stable_count coherent | stable_count illusory | endpoint distance gated | beta ambiguous gated |
|---|---:|---:|---:|---:|---:|
| prime_gaps_first | SR, L1, triple_var | 3.000 | 0.250 | 3.288 | 0.30 |
| logistic_return_intervals | [] | 0.000 | 0.583 | 0.000 | [] |
| zeta_zero_spacings_first | SR, L2 | 2.417 | 0.333 | 2.700 | [] |

Endpoint-stable observables: `[]` in all three perimeters in both runs.

## Risultato

1. **The order gate transfers to arithmetic and zeta spacing order.**

   Prime gaps carry one-sided support on `SR`, `L1`, and `triple_var`.
   Zeta-zero spacings carry one-sided support on `SR` and `L2`. In both cases
   the illusory endpoint remains weak-denominator under the same marginal.

2. **The logistic return perimeter is the counter-scope.**

   The logistic return sequence is ordered and generated by a deterministic
   chaotic system, but this canonical observable suite does not read its order
   as denominator support. The coherent endpoint stable count is `0.200` in the
   main run and `0.000` in the seed check. The gate does not transfer to this
   return-time observable.

3. **The transferable object is narrower than "real order".**

   `ORDER_DENOMINATOR_GATE` names order that survives a marginal-preserving
   shuffle in the canonical gap observables. It does not name every generated
   sequence. The node regressivo is the observable contract, not the gate
   threshold: if the order lives in return-time tail structure or symbolic
   itinerary, `SR/SR2/L1/L2/triple_var` can be blank.

4. **The beta layer is not universal.**

   Prime gaps reproduce beta `0.30` as the ambiguous protocol layer. Zeta has
   no gated ambiguous beta in this run. Logistic has no gated classifier because
   the one-sided observable set is empty. This extends 0901: beta `0.30` was a
   protocol fold in the synthetic matrix, not a cross-domain coordinate.

## Consecutio

`ORDER_DENOMINATOR_GATE` survives as scoped operator:

> In semi-real arithmetic/spectral spacing perimeters, the denominator gate is
> one-sided support for order against a marginal-preserving shuffle. In
> logistic return intervals, the canonical gap observables do not carry that
> support; the gate output is blank rather than false-positive.

Next experiment: do not tune `z_min`. Change the observable perimetro for the
logistic counter-scope: symbolic itinerary block entropy, return-tail exponent,
or recurrence-plot diagonal statistics, each with the same original-vs-shuffle
denominator gate. That tests whether logistic order is absent for this gate or
only invisible to the current canonical gap suite.

## Self-Audit: 5 Lenti

L1 hard constraint vs bias: no universal claim is made. `endpoint_stable_observables: []`
is exact for the run perimeters; "weak" means below the declared `abs(z)>=2`
gate frequency, not numerical zero.

L2 quantity vs ratio: raw stable counts and z means are reported before endpoint
distances. No percentage drift claim is used.

L3 no silent patching: 0901 claimed transfer on synthetic generated-order
perimeters. This report narrows the scope after observing the logistic
counter-perimeter; it does not rescue the original wording.

L4 edge cases: logistic illusory stable_count is `0.583` in the seed check,
so the claim is not "illusory endpoint absent." It is "no coherent one-sided
support under the declared frequency rule."

L5 re-discovery vs discovery: prime gap and zeta spacing order-vs-shuffle tests
sit near known arithmetic/RMT order diagnostics; logistic return intervals sit
near known recurrence and return-time diagnostics for chaotic maps. No NEW
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_semireal_order_denominator_gate.py`
- Verificato: `tools/data/semireal_order_denominator_gate_20260507_0923.json`
- Verificato: `tools/data/semireal_order_denominator_gate_20260507_0923_seedcheck.json`
- Inferito: logistic return intervals are a counter-scope for the canonical
  gap-observable form of `ORDER_DENOMINATOR_GATE`.