# Agent Report — Bridge Order Denominator Gate

timestamp: 2026-05-07 09:42 UTC
category: gate_falsification_bridge
verdict: scoped_operator
observables_registry: 1.0.0-2026-05-06
observables_used: [SR, SR2, L1, L2, triple_var]
tool: tools/exp_bridge_order_denominator_gate.py
data: tools/data/bridge_order_denominator_gate_20260507_0942.json
seed_check: tools/data/bridge_order_denominator_gate_20260507_0942_seedcheck.json

## Claim Under Test

Verificato dal campo vivo: `ORDER_DENOMINATOR_GATE` e gia stato testato su
perimetri sintetici e semi-reali. Il mandato corrente chiede domini fisici o
ponte gia presenti nel sistema, con shuffle marginal-preserving.

Domanda: se il perimetro e una sequenza bridge D-ND, il supporto denominatore
resta one-sided o compare un controesempio?

Perimetri:

- `prime_metric_delta_gamma_abs`: fluttuazioni della connessione metrica da
  `g=(p/2)^2`.
- `prime_metric_dR_abs`: fluttuazioni di curvatura discreta `dR=R-2` dalla
  stessa metrica.
- `zeta_trace_residual_step5_abs`: residuo non-lineare del trace bridge sugli
  zeri di zeta al passo 5.
- `hydrogen_bound_level_spacings`: spacing dei livelli legati
  `E_n=-1/(2n^2)`, ponte QxE.

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=202605070942`. Seed check: `n_replicates=12`, `n_baseline=24`,
`seed=202605070943`.

| perimeter | coherent one-sided observables | stable_count coherent | stable_count illusory | endpoint distance gated | beta ambiguous gated |
|---|---:|---:|---:|---:|---:|
| prime_metric_delta_gamma_abs | SR, SR2, L1, L2, triple_var | 5.000 | 0.250 | 4.415 | [] |
| prime_metric_dR_abs | SR, SR2, L1, L2, triple_var | 5.000 | 0.350 | 4.414 | 0.30 |
| zeta_trace_residual_step5_abs | SR, SR2, L1, L2, triple_var | 5.000 | 0.050 | 4.415 | 0.30 |
| hydrogen_bound_level_spacings | SR, SR2, L1, L2, triple_var | 5.000 | 0.200 | 4.416 | 0.40 |

Seed check:

| perimeter | coherent one-sided observables | stable_count coherent | stable_count illusory | endpoint distance gated | beta ambiguous gated |
|---|---:|---:|---:|---:|---:|
| prime_metric_delta_gamma_abs | SR, SR2, L1, L2, triple_var | 5.000 | 0.167 | 4.377 | [] |
| prime_metric_dR_abs | SR, SR2, L1, L2, triple_var | 5.000 | 0.083 | 4.376 | [] |
| zeta_trace_residual_step5_abs | SR, SR2, L1, L2, triple_var | 5.000 | 0.083 | 4.377 | 0.30 |
| hydrogen_bound_level_spacings | SR, SR2, L1, L2, triple_var | 5.000 | 0.250 | 4.378 | 0.40, 0.50 |

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

## Risultato

1. **The bridge perimeter carries full canonical one-sided support.**

   Each bridge sequence transfers on all five canonical observables. The
   coherent endpoint has stable count `5.000` in both runs; the illusory endpoint
   stays weak-denominator under the same marginal.

2. **The both-endpoint support remains blank.**

   `endpoint_stable_observables=[]` repeats across metric, trace, and QxE
   bridge perimeters. The gate is not two endpoint classes with stable
   denominators. It is support on the side where order survives its shuffle null.

3. **The logistic counter-scope from 09:23 still matters.**

   This result extends the gate into bridge sequences; it does not erase the
   logistic return blank. The transferable object is order visible to the
   canonical gap-observable contract. Return-time tail order still requires its
   own observable perimetro.

4. **The beta coordinate does not universalize.**

   Metric `delta_gamma` has no ambiguous gated beta in either run. Metric `dR`
   has `0.30` in the main run and blank in seed check. Zeta trace keeps `0.30`.
   Hydrogen gives `0.40` in the main run and `0.40, 0.50` in seed check. Beta is
   protocol coordinate, not domain coordinate.

## Consecutio

`ORDER_DENOMINATOR_GATE` survives the bridge falsification:

> In bridge perimeters whose order is carried by metric connection,
> curvature fluctuation, trace residual, or QxE level spacing sequences, the
> denominator gate transfers as full canonical one-sided support against a
> marginal-preserving shuffle. The logistic return perimeter remains the
> counter-scope for this observable contract.

Next experiment: test the logistic counter-scope at the node regressivo:
symbolic itinerary block entropy, return-tail exponent, and recurrence-plot
diagonal statistics under the same original-vs-shuffle denominator gate. Do not
tune `z_min`.

## Self-Audit: 5 Lenti

L1 hard constraint vs bias: `endpoint_stable_observables=[]` is exact for the
declared perimeters and runs. The report does not claim universal absence of
illusory support; illusory stable counts are `0.050-0.350` in the main run.

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

L3 no silent patching: 09:23 found a logistic blank. This report does not patch
that blank; it adds bridge perimeters and keeps the counter-scope.

L4 edge cases: hydrogen beta changes from `0.40` to `0.40,0.50` in seed check,
and metric `dR` beta drops from `0.30` to blank. The beta claim is explicitly
non-universal.

L5 re-discovery vs discovery: metric, zeta, and hydrogen sequences sit near
known RMT/arithmetical/spectral order diagnostics. This report claims operator
scope inside the lab gate protocol, not a new theorem.

## Fonti

- Verificato: `tools/data/agent_field_live.md`
- Verificato: `tools/LAB_AGENT_CONTEXT.md`
- Verificato: `tools/observables_registry.py`
- Verificato: `tools/exp_bridge_order_denominator_gate.py`
- Verificato: `tools/data/bridge_order_denominator_gate_20260507_0942.json`
- Verificato: `tools/data/bridge_order_denominator_gate_20260507_0942_seedcheck.json`
- Inferito: bridge perimeters carry full canonical one-sided support because
  all five observables pass the original-vs-shuffle gate at the coherent
  endpoint and fail endpoint-stable support in both runs.