Preprint: Dynamic Integration of Level-3 Ordinal Synergy into the RECD

Working title: Integrating Φ₃ (excess³) into RECD Dynamics: From Parallel Metric to Structural Clock Contribution

Author: Johel Padilla-Villanueva
Status: Draft v0.5 — methods + synthetic S0–S2 + dual-domain real-data smoke, unified contrast narrative (July 2026)
Folder: Investigaciones/Preprint_Phi3_RECD_Dynamic_Integration/
Python package: phi3-recd v0.5.0 (optional coupling layer; NumPy only)

Purpose

Close a structural gap in the Systemic Tau / RECD programme: excess³ (Level Φ₃) is a strong continuous proxy for irreducible ordinal surplus, but in most operational pipelines it remains a parallel early-warning readout. This preprint proposes falsifiable, implementable ways to let Φ₃ modify the discrete clock update itself — linking the 2026 nested hierarchy to legacy surveillance pipelines.

Package (phi3-recd)

This is a clock-map library, not a new ordinal-metric suite. It does not recompute (\tau_s) or excess³; those come from prior work (e.g. nested-recd or Systemic Tau pipelines). What it ships:

Install (editable / local)

cd Investigaciones/Preprint_Phi3_RECD_Dynamic_Integration
python3 -m pip install -e ".[dev]"
python3 -m phi3_recd          # synthetic demo
pytest -q                     # contract tests

Optional extras: pip install -e ".[ordinal]" pulls nested-recd for excess³ upstream; .[full] adds plotting/pandas for the preprint smokes.

Minimal API

import numpy as np
from phi3_recd import ActivationConfig, P1Config, recd_base, recd_p1

# tau_s, excess3: precomputed series; baseline: bool mask for normalization
tau = np.asarray(...)
e3 = np.asarray(...)
baseline = np.zeros(len(tau), dtype=bool)
baseline[:50] = True

base = recd_base(tau)
p1 = recd_p1(tau, e3, baseline, n_vars=4, cfg=P1Config(beta=0.5),
             act_cfg=ActivationConfig())
# audit: P1Config(beta=0.0) recovers base["t"] exactly

Publish to PyPI (when you want)

python3 -m build
python3 -m twine upload dist/*

Not uploaded from this session — package is installable and versioned only.

Contents

Quick run

# package demo (after pip install -e .)
python3 -m phi3_recd

# preprint validation scripts
cd src
python3 validate_synthetic.py  # S0–S2 tables + PNG figures
python3 smoke_real_sddb.py     # needs ../Cardiac_CCTP_Pilot/data/
python3 smoke_dengai.py        # uses ../data/dengai/

v0.5 highlights (vs v0.4)

• Narrative: Holter + DengAI smokes merged into one §6.4 strategic contrast (protocol table + joint comparison + four defensible conclusions)
• Density: removed duplicated “honest reading” lists; single message across domains
• Consistency: soft_offset (s_0=3.25) + soft_floor aligned with phi3_recd.py; Appendix A → v0.5
• No new empirical runs — numbers same as v0.3–v0.4

v0.4 highlights (kept)

• DengAI smoke: SJ + IQ; IQ-2004 ΔT legacy +1.24; A₃ sens 3/6; control FAR ~1.6/52w
• Chaos-band still high (~98%) with 4-var proxy; dt_base active ~7% vs ~0.1% Holter

v0.3 highlights (kept)

• Holter smoke: SDDB 30/31/35 + NSRDB; Feigenbaum freeze; A₃ sparse under hyperpersist
• P2 experimental; Holter-path diagnostic clock reported alongside legacy T

v0.2 highlights (kept)

• Hardened A₃; synthetic S0–S2 gates; corr(Γ−1, f₃) ≈ 0.99 on S1

Scope

Is: mathematical coupling of Φ₃ into Δt_k; two graded designs (P1 recommended, P2 experimental); activation; synthetic results; dual-domain real-data smokes with limitations
Is not: strong ontology; full PID; operational EWS claim (smokes do not support FAR superiority)

Recommended citation (placeholder)

Padilla-Villanueva, J. (2026). Integrating Φ₃ (excess³) into RECD Dynamics: From Parallel Metric to Structural Clock Contribution (Preprint draft v0.5).