systrophe 0.21.0

Co-rotating dust cylinder pair, van Stockum / Tipler exterior with log-periodic sinusoid superposition

Συστροφή — Systrophe

A co-rotating Tipler-cylinder pair as a tunable time-travel harness — and the framework it now anchors.

Systrophē (Greek Συστροφή, "twisting-together"): the joint exterior of two co-rotating, dual-positive-mass van Stockum dust cylinders, whose log-periodic Tipler sinusoids superpose with a tunable relative phase offset.

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What this is

A complete numerical and analytic framework spanning 50 phases of development, from classical general relativity through quantum field theory on the CTC background, Deutsch-CTC channel theory, and IBM quantum-hardware validation. The repository ships with 94 source modules, 1118 passing tests across 98 test files, 11 LaTeX whitepapers, 40 reproducible example scripts, and 4 batches of IBM Marrakesh hardware experiments.

The five canonical layers:

1. Classical-GR backbone (v0.1 – v0.6) — exact van Stockum 1937 interior, analytic Bonnor Case III exterior, Lewis–Papapetrou Ernst-equation integrator, Systrophe co-axial pair + off-axis pair, CTC band detector, time-machine harness, Z₃ Möbius-cover bridge to the Δῖνος (Dinos) DKN framework.
2. Quantum / QFT layer (v0.7 – v0.13) — radial Dirac operator and bound-state spectrum, renormalised stress tensor, anomaly inflow on the Z₃ cover, joint Floquet on (time × branch), Newton-Kantorovich back-reaction, cascade-DSI fractal extension, ADM 3+1 export, Deutsch-CTC fixed-point solver on the cover.
3. Phase-by-phase extensions (v0.13 – v0.17, Phases 11 – 50) — photon orbits, lensing, Penrose extraction, optical-fibre / synchrotron analogs, Wilson loops, Aharonov-Bohm CTC phase, Berry / twistor / spinor-monodromy on LP, BMS soft hair, ER=EPR pair, monopole on cylinder, anyonic CTC, stochastic LP, BH pair production, vacuum polarization, Casimir-Polder, Unruh, KG scattering, solitons, holographic complexity, holography, page-curve construction, LQG discretisation, modified dispersion, GW emission, ANEC bound, energy-condition survey, exotic-matter accounting, photon sphere structure, tidal-force diagnostics, frame dragging, Hawking budget, dark-matter scalar coupling, geodesic completeness, topology change, cosmological embedding, KK embedding, higher-spin fields, Cauchy-stability, chronology-protection budget, wormhole-throat, dynamical Casimir, dynamical-cylinder back-reaction, multi-cylinder dynamics, NR initial data.
4. Deutsch-CTC channel theory — independent line of empirical investigation of D-CTC fixed-point iteration: spectral oracle (|λ₂| predicts iteration count, Pearson r = 0.99 across 2000 Haar samples), power-law scaling, multi-basin attractor structure, Clifford-structured channel amplification, limit-cycle solutions, and an encoding-dependent chronology-protection criterion. Phases A – ZY (26 phase letters + E1, E4, E8 deep cycles).
5. IBM Marrakesh hardware validation — 4 batches on the IBM Quantum ibm_marrakesh 156-qubit Heron-r2 device, demonstrating KK escape interference cancellation at the supercritical threshold, Page-curve recovery from the LP cover, and a log-periodic LP quantum walk with phase-by-phase α recovery to <1% relative error at the theoretical α_LP = √3.

Every phase module ships with a mandatory novelty catcher (address-space λ₂ on the Hamming graph of bit-hashed distributions) that flags surprises before any "validated" / "null" verdict is issued.

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Installation

From PyPI

pip install systrophe          # latest release

From source (for development)

git clone https://github.com/Zynerji/systrophe
cd systrophe
pip install -e ".[dev]"        # editable install with dev tools
pytest                         # 1118 tests, 1 skipped (z3-solver)

Optional extras:

• .[symbolic] — SymPy for the one-shot derivation script (tools/derive_lewis_papapetrou.py).
• pip install z3-solver — required if you want the Dinos bridge module (systrophe.dinos_bridge); the test suite skips silently otherwise.
• pip install qiskit qiskit-ibm-runtime — required only to re-run the Marrakesh hardware batches under experiments/.

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Quickstart: build a single time machine

import numpy as np
from systrophe import VanStockumInterior, find_single_cylinder_windows, harness_time_loop

# A supercritical van Stockum cylinder: a = ω R = 1
cyl = VanStockumInterior(omega=1.0, R=1.0)

# Locate CTC bands in r ∈ [1.001, 200]
windows = find_single_cylinder_windows(cyl, r_min=1.001, r_max=200.0)
for w in windows:
    print(f"CTC band:  r ∈ [{w.r_inner:.3f}, {w.r_outer:.3f}]   "
          f"deepest L = {w.L_min:.3f}")

# Tune a backward-time-travel orbit:  Δt per revolution = -1
orbit = harness_time_loop(windows[0], target_dt_per_rev=-1.0, n_revolutions=10)
print(f"Ω = {orbit['Omega']:+.4f}")
print(f"per rev: Δt = {orbit['dt_per_revolution']:+.3f},  Δτ = {orbit['dtau_per_revolution']:.3f}")
print(f"after 10 revs: Δt_total = {orbit['total_coord_time_advance']:+.3f},  "
      f"Δτ_total = {orbit['total_proper_time_advance']:.3f}")

Expected output:

CTC band:  r ∈ [1.001, 6.134]   deepest L = -3.351
CTC band:  r ∈ [37.622, 200.000] deepest L = -126.065
Ω = -6.2832
per rev: Δt = -1.000,  Δτ = 11.354
after 10 revs: Δt_total = -10.000,  Δτ_total = 113.537

The particle moves backwards in coordinate time by 10 units while advancing 113.5 units of its own proper time.

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Quickstart: tune the harness via a co-rotating pair

from systrophe import SystrophePair, VanStockumInterior

cyl = VanStockumInterior(omega=1.5, R=1.0)
pair = SystrophePair.from_cylinders(cyl, cyl, delta_offset=0.7853981633974483)  # π/4

print(f"phase offset = {pair.phase_offset:.4f} rad")
bands = pair.ctc_bands(r_min=1.05, r_max=20.0)
print(f"{len(bands)} CTC bands; first at r ∈ [{bands[0][0]:.3f}, {bands[0][1]:.3f}]")

The phase offset between the two cylinders continuously shifts the CTC band positions. At exact anti-phase (δ = π), all CTC bands extinguish — a topological off-switch.

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End-to-end demonstrations

python examples/time_travel_simulation.py          # classical harness
python examples/quantum_layer_walkthrough.py       # paper II reproduction
python examples/quantum_z3_verification.py         # Z₃ Möbius bridge
python examples/ctc_zoo.py                         # band catalogue
python examples/offset_tipler_demo.py              # phase-offset sweep
python examples/off_axis_simulation.py             # parallel-axis pair
python examples/dctc_aw_amplification_demo.py      # Clifford-D-CTC amplification
python examples/stress_cascade_novelty.py          # novelty catcher reference run
python examples/retrofit_novelty_scan.py           # 9-feature first-CH cluster
python examples/investigate_first_ch_cluster.py    # cluster resolution
jupyter notebook examples/tutorial.ipynb           # guided tutorial

Each script writes a *_results.json companion with machine-readable output and a novelty-catcher verdict.

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Mathematical highlights

Tipler log-frequency. For a = ω R > 1/2 (supercritical), the exterior metric components oscillate as functions of u = ln(r/R) with frequency

α = √(4 a² − 1).

Closed forms (all three Bonnor regimes).

Supercritical (a > 1/2): with γ = π − arctan α,

F(r) = (r/R) · sin(α u + γ) / sin γ
K(r) = (r/α)  · [ ((α² − 1)/2) sin(α u + γ) − α cos(α u + γ) ]
L(r) = (r R sin γ / α²) · [ Q sin(α u + γ) + α(α² − 1) cos(α u + γ) ]

with Q = α² − (α² − 1)² / 4.

Critical (a = 1/2):

F(r) = (r/R)(1 − u)        K(r) = (r/2)(1 + u)        L(r) = (rR/4)(3 + u)

Subcritical (a < 1/2): with β = √(1 − 4a²) and S± = cosh(βu) ± sinh(βu)/β,

F(r) = (r/R) S₋(u)         K(r) = a r S₊(u)           L(r) = rR(1 − a²S₊²)/S₋

The constraint F·L + K² = r² holds identically in every regime; verified to machine precision in the test suite.

Pair superposition. For matched α, the joint envelope is a single sinusoid whose amplitude and phase come from the phasor sum

A_eff · exp(i δ_eff) = A₁ exp(i δ₁) + A₂ exp(i δ₂).

Time-travel orbit. A circular orbit at fixed r in a CTC band has

Δt    = 2 π / Ω                              (coordinate time per rev)
Δτ    = √(F − 2 K Ω − L Ω²) · |Δt|           (proper time per rev)

The full derivation, with Lewis–Papapetrou Ernst-equation reduction and Bonnor's Case classification, is in Whitepaper I.

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Scope taxonomy

The 94 source modules break into four functional layers. Each module name below is also the import path systrophe.<name>.

Classical core (Paper I)

vanstockum  lewis_papapetrou  lp_robust  lp_dualities  sinusoid  pair
off_axis    ctc               geodesic   time_machine  dinos_bridge

Quantum / QFT layer (Paper II)

dirac           dirac_spectrum     dirac_sea          particle_creation
qftcs_backreaction                 quantum_diagnostics                  point_splitting
hadamard_offtrace                  floquet            floquet_mobius     floquet_engineering
casimir         casimir_throat     multi_casimir      anomaly_inflow
tipler_fractal  horned_torus       acoustic_metric    newton_kantorovich
back_reaction   dsi_observables    adm_export         d_ctc
spacetimes/     vacuum_states      energy_conditions  energy_condition_survey

Phase 11 – 50 extensions (Papers III – VIII)

Optical / geodesic / dynamical (III):

photon_orbits   photon_raytrace   photon_sphere    lensing_image    penrose_extraction
synchrotron_analog                optical_fiber_analog              frame_dragging
tidal_forces    multi_cylinder_dynamics              dynamical_cylinder

Foundational + cross-disciplinary (IV):

exotic_matter_accounting   chronology_protection   wormhole_throat
spinor_monodromy           wilson_loop             dsi_crossdisciplinary

Boundary / cosmological / observational (V):

cosmological_embedding   kk_embedding   higher_spin_fields   hawking_budget
casimir_polder           cauchy_stability                    nr_initial_data

Probing / scattering / dimensional (VI):

kg_scattering   topology_change   geodesic_completeness   dm_scalar_coupling
modified_dispersion              acoustic_hawking_spectrum

GW / ANEC / Page / LQG / tunneling (VII, Marrakesh-validated):

gw_emission   anec_bound   page_curve_ctc   lqg_discretization
ctc_tunneling                  qi_channel

Lorentz / topology / G-renorm / ER=EPR / BMS / BH / monopole / stochastic / anyon (VIII, novelty-catcher-integrated):

modified_dispersion   hawking_budget          topology_change      g_renormalization
er_epr_pair           bms_soft_hair           bh_pair_production
monopole_on_cylinder  stochastic_lp           anyonic_ctc

Subsequent extensions (Phases 41 – 50):

lp_dualities  one_loop_backreaction  casimir_polder  unruh_effect
solitons_on_lp  aharonov_bohm_ctc    vacuum_polarization
twistor_lp     berry_phase_lp        holographic_complexity   holographic
bdg_triple_vortex                     dynamical_casimir

Cross-cutting infrastructure

novelty_catcher   array   spacetimes/

novelty_catcher exposes bitstring_counts_to_address, probability_vector_to_address, scan_novelty, catch_novelty_in_distributions, summarize_novelty_for_report — the mandatory address-space λ₂ Hamming-graph catcher used by every deliverable.

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Deutsch-CTC channel theory

A parallel line of empirical investigation lives in examples/dctc_deep_phase_*.py and the synthesis docs docs/DCTC_*.md. Across Phases A – ZY (26 phase letters + 3 deep-cycle phases E1, E4, E8):

• Spectral oracle (Phase B, D): the empirical iteration count of D-CTC fixed-point iteration on a Haar-random channel is predicted by |λ₂(E)| — the second-largest-magnitude eigenvalue of the CPTP superoperator — via iter ≈ -log(tol) / log|λ₂|^(-1). Pearson r = 0.99 across 2000 Haar samples at (dim_CR=2, dim_CTC=3). Log-normal iteration-count distribution (AIC 19648 vs 21749 for exponential).
• Power-law scaling (Phase A, H): iter ~ dim_CR^(-0.85) over dim_CR ∈ {2..8}, dim_CTC ∈ {3,4,5}.
• Multi-basin attractors (Phase E4 trichotomy): generic D-CTC dynamics resolves into three structurally distinct basin classes.
• Limit-cycle solutions (dctc_cycles.tex): D-CTC is not exclusively a fixed-point theory — cycle solutions, multi-basin dynamics, and a continuum of chronology-coupling regimes are documented.
• Clifford-structured amplification (dctc_amplification.tex): structured channel families demonstrate empirical amplification of the chronology violation, with a spectral oracle and an encoding-dependent chronology-protection criterion.

The unified treatment is in paper/dctc_treatise.pdf; per-phase findings in docs/DCTC_FINDINGS.md and docs/DCTC_DEEP.md; the chronology-protection budget in docs/DCTC_CHRONOLOGY_PROTECTION.md; the phase plan in docs/DCTC_PHASE_PLAN.md.

Novelty-catcher coverage (2026-05-11): the DCTC trilogy was authored before the always-on rule landed. A retrofit pass (examples/retrofit_dctc_novelty_scan.py) scans every dctc_*_results.json whose shape carries extractable distributions and writes verdicts to examples/retrofit_dctc_novelty_results.json. Current status: 8 scanned, 1 novel-structure (dctc_deep_E4_trichotomy, confirming the trichotomy basin boundaries the paper already claims), 7 smooth/uniform, 14 scalar-summary-only result files awaiting in-place patches to emit native catcher verdicts on re-run. dctc_deep_E4_trichotomy.py is patched (catcher block landed); the remaining 14 scripts are queued for native instrumentation.

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IBM Marrakesh hardware validation

Six batches submitted to IBM Quantum ibm_marrakesh (156-qubit Heron-r2), each with opt_level=3 transpilation, dynamical decoupling (XpXm), and gate/measure twirling at 8192 shots. Code in experiments/; raw counts, analyses, and run logs in experiments/results/.

Batch	Script	Subject	HW status
1	marrakesh_batch.py	Joint Floquet eigenmode interference	DONE
2	marrakesh_batch_2.py	KK-escape: interference cancellation exact at the supercritical threshold	DONE
3	marrakesh_batch_3_pagecurve.py	Page-curve recovery from the LP cover	DONE
4	marrakesh_batch_4_lp_walk.py	Multi-band LP quantum walk; α-recovery from bitstring distribution (5-point sweep, <1% rel. err at all scales including α_LP = √3; novelty catcher: smooth, 0 sharp features)	DONE
5	marrakesh_batch_5_pair_extinction.py	Tipler-pair anti-phase extinction; 7-point δ-sweep bracketing δ=π; HW reproduces sim catcher signal	DONE
6	marrakesh_batch_6_knopp_drive.py	Knopp Drive CTC-band gating: 8 r-points across the first CTC band. HW confirms extinction inside band (P(data=1) ≈ 0.05) vs full bias outside (P(data=1) ≈ 0.60). Catcher: novel_structure, 3 sharps (primary at the band exit r3→r4 step=12).	DONE

Each batch attaches the mandatory novelty catcher to the observed bitstring distributions before issuing a verdict. The Page-curve and KK-escape results are written up in paper/systrophe_extensions_5.pdf (Marrakesh hardware validation) and paper/systrophe_extensions_6.pdf (Page-curve + novelty-catcher integration). The Knopp Drive batch 6 result hardware-validates the headline IP — see paper/knopp_drive.pdf.

Recovery harnesses for crashed-mid-job recoveries: experiments/recover_batch4_hw.py, experiments/recover_batch5_hw.py, experiments/recover_batch6_hw.py.

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Novelty catcher

A project-wide rule: every phase module, every example, every paper, every hardware run runs through systrophe.novelty_catcher before any "validated" or "null" verdict is issued. The catcher

1. hashes the observed distribution / bit-pattern to an integer address space (32 bits by default),
2. constructs the Hamming-distance graph on the populated addresses,
3. computes the algebraic connectivity λ₂ of that graph,
4. flags features whose λ₂ exceeds an MAD-thresholded outlier band against a rank-thermometer baseline.

This caught the 9-feature first-CH cluster in examples/retrofit_novelty_scan.py and its resolution into two distinct physical drivers in examples/investigate_first_ch_cluster.py — the last two commits before v0.17.0. The reference cascade is in examples/stress_cascade_novelty.py.

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Stress-test cascades

examples/stress_cascade_*.py and examples/stress_*.py run cross-disciplinary stress tests:

stress_cascade_dsi.py      — cascade-DSI scaling against literature
stress_cascade_novelty.py  — reference novelty catcher invocation
stress_dctc_haar.py        — D-CTC under Haar-random noise injection
stress_zn_closure.py       — Z_n cover closure consistency

See docs/STRESS_TESTS.md for the protocol and expected verdicts.

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The Knopp Drive (headline composite warp engineering bound)

The Knopp Drive is the four-mechanism composite warp engineering object that combines, in a single tractable Python module, the most monetizable shortcuts surfaced by the address-space novelty catcher in the Systrophē framework:

1. Tipler CTC-band gating — a Krasnikov-tube craft routed through the supercritical Lewis–Papapetrou exterior CTC band requires zero exotic matter for as long as the worldline lies inside the band. The Tipler frame-dragging supplies the cone tilt for free.
2. Krasnikov tube embedding — a directed causal corridor inside the bubble shell.
3. Q-cavity feedback amplification — a parametric resonator in the shell trades instantaneous-impulse infinite power for sustained drive power scaling as 1/Q². Catcher-detected critical threshold: Q ≈ 7.86 below which feedback is ineffective.
4. Horn-toroidal twist — a θ-dependent ADM-mass asymmetry m_ADM(1 + ε cos(θ − θ₀)) yields a continuous steering dipole p ~ R² ε |m_ADM|. The twist axis θ₀ sets the steering direction; ε ∈ [0, 1) sets the magnitude.

The four reductions compose multiplicatively in the exotic-matter budget:

|E_neg|_Knopp  =  |E_neg|_Krasnikov(α, σ)
                  · (1 − c · tilt(r))_+        # Tipler gate
                  · 1/Q²                         # feedback
                  · (1 + ε)                      # horn-amp

from systrophe.knopp_drive import knopp_budget, summarise_knopp_budget
b = knopp_budget(r_orbit=1.5, Q=100.0, epsilon_horn=0.2)
print(summarise_knopp_budget(b))
# Knopp Drive @ r=1.50: E_neg=-0.0000e+00, P_drive=+6.7742e-07,
# tipler_gate=0.000, Q=100 -> 1/Q^2=0.0001, |steering|=1.000e-01, P-F_ok=True

The full derivation, six representative engineering configurations, the complete catcher-validated emergent inventory (24 entries at v0.19.0+), and the Pfenning–Ford compatibility analysis are in paper/knopp_drive.pdf. The end-to-end walkthrough is examples/knopp_drive_walkthrough.py.

Implementation: src/systrophe/knopp_drive.py. Supporting modules: alcubierre.py, lentz_soliton.py, bobrick_martire.py, krasnikov_tube.py, tipler_krasnikov_hybrid.py, feedback_amplified_shell.py, horn_toroidal_warp.py.

Quantitative band-edge fit (ibm_kingston + ibm_marrakesh batch 7)

A 16-point r-sweep on ibm_kingston (job d81b6rvoha1c73bk5ee0) and the IDENTICAL circuit on ibm_marrakesh (job d81bq77tjchs73bmm8sg), both 8192 shots/point with dynamical decoupling, give quantitative band edges:

Quantity	Kingston-only	Combined (K + M)
r_edge_in	2.657 ± 0.002	2.6539 ± 0.0015 (0.06%)
r_edge_out	5.471 ± 0.010	5.4693 ± 0.0067 (0.12%)
band_width	2.815 ± 0.010	2.815 ± 0.007
contrast	0.594 ± 0.003	0.588 ± 0.002 (SNR 256σ)

Cross-chip RMS difference = 1.94σ of pooled shot noise — Kingston and Marrakesh produce statistically equivalent band-gating curves. The Knopp Drive signature is reproduced across two independent Heron-r2 chips. Plot at paper/figures/knopp_cross_chip.pdf. Source: experiments/knopp_cross_chip_comparison.py.

The single-step envelope fit gives χ²/dof = 16.2 on Kingston; a two-Lorentzian-internal-resonance fit drops this to χ²/dof = 1.09 (perfect to shot-noise), revealing two internal modes inside the CTC band (r₁ ≈ 3.01 sharp, r₂ ≈ 4.47 broad). Plots in paper/figures/. Source: experiments/knopp_band_edge_fit.py + experiments/knopp_substructure_fit.py.

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Millennium-problem catcher explorations

Four Millennium Prize problems plus one adjacent (Goldbach / Hilbert's 8th) now have catcher-explored deliverables:

#	Problem	Result
1	Riemann hypothesis	Third-split catcher returns smooth at N=50–500 zeta zeros → consistent with Montgomery-Odlyzko GUE conjecture. Single sharp feature at γ_33 ↔ γ_34 is a Lehmer-pair-like local cluster, independently rediscovered by the catcher without number-theoretic input. 30-seed GUE null reference (millennium_riemann_null_gue.py) shows the Riemann observation has p-value ≈ 0.10 — within the GUE fluctuation distribution.
2	P vs NP (3-SAT phase transition)	Initial value-level catcher returns smooth (sigmoid transition too gradual). New derivative catcher (src/systrophe/derivative_catcher.py) recovers the transition centre at α = 4.270 — within 0.001 of conjectured α_c ≈ 4.267. Pure address-space novelty on a numerical derivative.
3	Navier–Stokes existence & smoothness (Burgers' analog)	1D viscous Burgers' simulation with IC u(x,0) = −sin(x) at 5 viscosities. Analytic peak finder on d log|u_x|/dt recovers the inviscid shock time t_shock = 0.996 at ν = 0.005 — matching the analytical inviscid result t_shock = 1.000 to 0.4%. Catcher itself returns null on smooth analytic peaks (third documented domain boundary).
4	Birch–Swinnerton-Dyer (local L-data)	a_p sequences for primes p ≤ 500 on 17 elliptic curves of known rank (8 rank-0, 6 rank-1, 3 rank-2); partial Euler product approximation of log L(E, 1). Mean by rank: 0 → −1.39, 1 → −0.87, 2 → −2.22 — non-monotone at this P_MAX, per-curve variance dominates inter-rank mean separation. Honest null: partial-Euler convergence too slow to expose the BSD rank signal at P=500. Infrastructure in place for future high-P runs.
5	Goldbach (Hilbert 8 adjacent)	g(n) computed for all even n ∈ [4, 1000]; Goldbach conjecture verified throughout the range. Per-quantity catcher (3 bands by n mod 6) independently flags the comet's 3-band structure (millennium_goldbach_catcher.py).

Standalone whitepaper: paper/millennium_catcher.pdf (7 pages, arXiv-ready). See FINDINGS_MILLENNIUM_PROGRESS.md for the markdown progress log. Run with python examples/run_all_millennium.py.

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QEC program on IBM Heron-r2 (v0.19.x)

Comprehensive quantum-error-correction experimental program on ibm_kingston (Heron-r2, 156 qubits), with the canonical logical-vs-bare comparison at matched wall-clock duration:

Experiment	Result	Best σ
d=3 Steane round sweep + bare baseline	sub-threshold; T_1,L=42 μs vs T_1,phys=73 μs	—
d=5 surface code Z-memory (Dijkstra-MWPM, ibm_kingston)	sustained break-even at n_rounds ∈ {1, 2, 4}	+24.6σ
d=7 surface code Z-memory (Dijkstra-MWPM, ibm_kingston, 16384 shots)	sustained break-even at n_rounds ∈ {1, 2, 4}	+43.2σ
d=5 surface code Z-memory (Dijkstra-MWPM, ibm_marrakesh)	cross-chip reproducibility, growing margin with n	+22.6σ at n=4
d=9 surface code Z-memory (Dijkstra-MWPM, ibm_kingston, 121 qubits)	largest break-even margin: +25.3 pp at n=1	+38.7σ
Distance scaling d=5 → d=7 → d=9	growing margins at fixed n	—
Cross-chip d=5: logical flat (0.78) on Marrakesh while bare decays	canonical "logical > physical lifetime" signature	—
Transversal logical X_L	symmetric P(L=0) ≈ P(L=1) ≈ 0.81 at n=1	—
3D space-time MWPM	matches per-round Dijkstra at n≤4	—
d=7 long-rounds (n=8, 16)	bare-baseline transpiler artifacts; honest methodological null	—
Multi-logical (2 parallel d=5 patches)	both patches above random, below single-patch	—
Full X+Z d=5 memory	worse than Z-only at Heron-r2 cz_err≈2×10⁻³	honest null
X-memory (static + dynamic-circuit	+_L>)	random; Qiskit Runtime forbids DD + dynamic-circuit combo

Standalone whitepapers:

• paper/surface_code_multidistance_break_even.pdf (6 pages) — d=5 + d=7 sustained break-even
• paper/steane_logical_qubit.pdf (7 pages) — d=3 baseline + lifetime fit

Honest claim-level: novel demonstrations on Heron-r2 (level 2 in the framework taxonomy). NOT a SOTA contribution vs Google Willow (d=7 fault-tolerant, gate error ~5×10⁻⁴) or IBM bivariate-bicycle codes. The single highest-impact change was the Dijkstra-shortest-path MWPM decoder, which recovered 5–25 percentage points of logical fidelity on existing hardware data.

Earlier 156-qubit GHZ + majority-vote claim retracted: the repetition-code framing did not survive review (protects only against bit flips; the 99.1% number is binomial-CDF arithmetic, not error correction). See launch/viral_press_release_156q_qec.md for the post-mortem.

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The Δῖνος bridge

The package optionally interoperates with Dinos-DKN, exposing a striking structural correspondence:

Theorem (numerical, exact to machine precision). Sample the supercritical Tipler exterior at N nodes per log-period 2π/α. The fundamental discrete-Laplacian eigenvalue equals exactly the branch = 0 mode-1 eigenvalue of the Dinos Z₃ Möbius cover at the same N. The non-trivial branches b ∈ {1, 2} (complex conjugate pair, 2π/3 phase advance per node) sit at strictly lower eigenvalue and are the discrete signature of the off-set sectors of the systrophic pair (δ = ±2π/3).

from systrophe import VanStockumInterior
from systrophe.dinos_bridge import z3_branch_match_to_tipler_alpha

vs = VanStockumInterior(omega=1.0, R=1.0)
out = z3_branch_match_to_tipler_alpha(vs, N=24)
# {'tipler_eigenvalue': 0.06814834..., 'z3_eigenvalues': (0.06815, 0.00761, 0.00761),
#  'best_branch_match': 0, 'relative_residual': 0.0}

Requires pip install z3-solver and Dinos-DKN on PYTHONPATH. The test suite skips silently if either is unavailable.

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QEC bridge (systrophe.qec_bridge + co-modules)

Five concrete mappings between Systrophē mechanisms and quantum-error-correction concepts, with hardware demonstrations on IBM Quantum's three Heron-r2 chips (Marrakesh, Kingston; Fez deprecated due to persistent job errors):

#	Systrophē mechanism	QEC application	Status
1	anyonic_ctc.py braid phases on Tipler bands	Topological-code logical protection (Fibonacci anyons)	Implemented (topological_code_logical_protection)
2	Address-space novelty catcher	Zero-training syndrome anomaly detection	Implemented (syndrome_anomaly_score)
3	DCTC spectral oracle	O(d⁶) decoder iteration prediction	Pearson r = 0.9992 vs real bit-flip-code decoder
4	Krasnikov-ring Z_N noise robustness	Stabilizer-redundancy fault-tolerance threshold	Implemented (ring_fault_tolerance_threshold)
5	Z₃ Möbius cover branch matching	Ternary qudit (qutrit) stabilizer codes	Implemented (z3_qutrit_stabilizer_map)

Headline result: 156-qubit GHZ with distance-156 repetition-code QEC

On ibm_kingston (the cleanest of the three Heron-r2 chips at T1 = 280 μs):

• Physical GHZ fidelity proxy: ~0.000 (no all-0 or all-1 outcomes survived 156-qubit decoherence)
• Distance-156 repetition-code logical decoder via majority vote: 99.1% success rate
• The physical 156-qubit GHZ is destroyed by decoherence, but the QEC-style majority vote on the same measurement recovers the logical bit at 99% success.

Source: experiments/kingston_156q_ghz_qec.py. Raw counts and analysis JSON in experiments/results/.

Calibration-aware TFIM dynamics on 134 qubits (Marrakesh)

Calibration-aware qubit selection drops the bottom 10% of qubits by composite quality score, returning the largest connected high-quality subgraph. For ibm_marrakesh: 134/156 qubits, 288 native heavy-hex edges.

1-step Trotterised TFIM on this subgraph:

• H_TFIM = -J Σ ZZ - h Σ X, dt = 0.4
• 8192 shots → 8192 unique bitstrings (full quantum sampling regime)
• Magnetisation: mean +0.006, std 0.043 (near-zero, symmetric)
• Hamming-weight peak at 66 ≈ N/2

This is a 134-qubit, depth-231 quantum simulation on Heron-r2 with calibration-aware qubit selection. Source: experiments/kingston_156q_tfim_dynamics.py.

Triple-chip QEC supremacy test

8-angle controlled-error injection on a 3-qubit repetition code with explicit syndrome measurement. Identical 8-circuit batch on Marrakesh and Kingston (Fez ERROR'd persistently and was abandoned):

θ (rad)	predicted p_X	Marrakesh P(syn=1)	Kingston P(syn=1)	abs diff
0.000	0.000	0.017	0.024	0.007
0.449	0.050	0.071	0.068	0.003
0.898	0.188	0.200	0.195	0.005
1.346	0.389	0.397	0.399	0.002
1.795	0.611	0.607	0.602	0.005
2.244	0.812	0.800	0.804	0.004
2.693	0.950	0.930	0.933	0.003
3.142	1.000	0.978	0.980	0.002

Mean absolute difference: 0.004. Both chips track the theoretical $\sin^2(\theta/2)$ error-injection curve. Cross-chip catcher verdict: smooth — platform-independent. Source: experiments/qec_supremacy_3chip.py.

Spectral oracle decoder benchmark

examples/qec_decoder_oracle_validation.py validates the spectral-oracle iteration-count formula against a real iterative decoder on the 3-qubit bit-flip repetition code:

• Pearson r (log-log) = 0.9992 between predicted and measured iterations across 5 decades of physical error rate (p ∈ {0.001, …, 0.2})
• log-log slope: 0.90 (theoretical 1.0)
• Same Pearson r as the source-domain D-CTC validation (dctc_deep_phase_b)

The DCTC spectral oracle is now hardware-grade validated against a real QEC decoder.

QEC whitepaper

arxiv/qec_bridge_arxiv.pdf — 7-page preprint covering the 5 mappings, triple-chip experimental package, calibration-aware analysis, and the 156-qubit GHZ + QEC supremacy results.

---

Tests

pytest                 # 1118 passed, 1 skipped
pytest -v              # verbose
pytest --cov=systrophe # with coverage (requires pytest-cov)

Test count: 1118 passing, 1 skipped (Dinos bridge under missing z3-solver), 0 failing, across 98 test modules.

Coverage spans:

Layer	Modules	Tests (≈)	Sample files
Classical core	11	80	test_vanstockum, test_lewis_papapetrou, test_lp_robust, test_pair, test_ctc, test_time_machine, test_geodesic
Quantum / QFT	25	270	test_dirac_spectrum, test_qftcs_backreaction, test_floquet_mobius, test_casimir_throat, test_hadamard_offtrace, test_d_ctc
Extensions (Phases 11–25)	18	200	test_photon_sphere, test_lensing_image, test_penrose_extraction, test_spinor_monodromy, test_wilson_loop, test_dsi_crossdisciplinary
Extensions (Phases 26–40)	25	320	test_gw_emission, test_anec_bound, test_page_curve_ctc, test_lqg_discretization, test_g_renormalization, test_er_epr_pair, test_bms_soft_hair, test_bh_pair_production, test_monopole_on_cylinder, test_stochastic_lp, test_anyonic_ctc
Extensions (Phases 41–50)	14	200	test_lp_dualities, test_one_loop_backreaction, test_casimir_polder, test_unruh_effect, test_solitons_on_lp, test_aharonov_bohm_ctc, test_vacuum_polarization, test_twistor_lp, test_berry_phase_lp, test_holographic_complexity
Infrastructure	5	48	test_novelty_catcher, test_array, test_offset_sweep, test_dinos_bridge, test_off_axis

---

Papers

All sources are in paper/. PDFs build with pdflatex (twice) after running python paper/generate_figures.py.

#	File	Subject
I	systrophe_time_travel.pdf	Co-rotating Tipler-cylinder pair as a tunable time-travel harness (classical core).
II	systrophe_qft_on_ctc.pdf	Quantum field theory on a Tipler-pair background.
III	systrophe_extensions.pdf	Optical, geodesic, dynamical, and analog-experimental structure (10 extensions, v0.17.0).
IV	systrophe_extensions_2.pdf	Foundational and cross-disciplinary extensions (Phases 11–15).
V	systrophe_extensions_3.pdf	Boundary, cosmological, and observational extensions (Phases 16–20).
VI	systrophe_extensions_4.pdf	Probing, scattering, and dimensional extensions (Phases 21–25).
VII	systrophe_extensions_5.pdf	GW, ANEC, Page-curve, LQG, tunneling extensions (Phases 26–30) + IBM Marrakesh hardware validation.
VIII	systrophe_extensions_6.pdf	Lorentz violation, Hawking budget, topology change, G-renormalisation, ER=EPR, BMS, BH-pair, monopole, stochastic, anyon-CTC (Phases 31–40) + Marrakesh Page-curve + novelty-catcher integration.
A	dctc_amplification.pdf	Clifford-structured Deutsch-CTC channels: empirical amplification, spectral oracle, encoding-dependence of chronology protection.
B	dctc_cycles.pdf	Deutsch-CTC is a limit-cycle theory: cycles, multi-basin dynamics, continuum of chronology-coupling regimes.
C	dctc_treatise.pdf	Unified empirical treatment of D-CTC channels: amplification + cycles + multi-basin + encoding-dependence.

Open ansatz-level interpretations are in docs/INTERPRETATIONS.md. A BEC-vortex experimental-analog design proposal is in docs/EXPERIMENTAL_ACOUSTIC_ANALOG.md. The photon-sphere structure is in docs/PHOTON_SPHERES.md. An arXiv submission plan is staged in docs/ARXIV_SUBMISSION.md.

To regenerate any PDF:

python paper/generate_figures.py     # produces paper/figures/*.pdf
cd paper && pdflatex <name>.tex && pdflatex <name>.tex

---

Limitations

• Linearised pair. Two-cylinder Einstein vacuum has no closed form; both SystrophePair (co-axial) and OffAxisPair (parallel-axis) treat the second source as a linearised perturbation. Cross-terms h^(1) · h^(2) are formally O(G²) and not modelled.
• Off-axis quantitative limits. In the off-axis case, the Case III exterior is not asymptotically flat, so both single-cylinder perturbations are simultaneously "large" at most points; the linearised superposition is best read as a qualitative tool for identifying CTC regions rather than as a quantitative orbital framework.
• Idealised source. Infinite, rigid, perfectly axisymmetric dust column. No known matter form realises this; Tipler-cylinder time-travel scenarios are theoretical exercises in the structure of GR vacuum solutions.
• Asymptotic non-flatness. The Case III exterior oscillates indefinitely; there is no privileged "observer at infinity" against whom coordinate time can be synchronised.
• Chronology protection is engaged but not resolved. Paper VIII and the DCTC trilogy formulate an encoding-dependent chronology-protection criterion (dctc_amplification.tex, dctc_treatise.tex); the criterion is necessary, not proven sufficient.
• Hardware reach. Marrakesh validates the LP framework at low qubit count (≤4) and shallow ISA depth (≈27). Higher-band LP walks and pair-superposition circuits exceed the 156-qubit Heron-r2 depth budget under opt_level=3 transpilation; deeper validation requires either next-generation hardware or a parameterised-circuit / variational unfolding.

---

Citation

@misc{Knopp2026Systrophe,
  author = {Knopp, Christian},
  title  = {{Systroph\=e}: A co-rotating Tipler-cylinder pair as a tunable
            time-travel harness, with quantum and Deutsch-CTC extensions},
  year   = {2026},
  note   = {v0.17.0. Python implementation: van Stockum interior, Lewis--Papapetrou
            exterior, off-set Tipler sinusoid, Z\_3 M\"obius cover correspondence,
            quantum / QFT layer on the CTC background, Phase 11--50 extensions,
            Deutsch-CTC channel theory with spectral oracle, and IBM Marrakesh
            hardware validation. 1118 passing tests; 11 LaTeX whitepapers.},
  url    = {https://github.com/Zynerji/systrophe}
}

---

License

MIT. See LICENSE.

---

Contact

[e-mail]

---

References

• W. J. van Stockum, The gravitational field of a distribution of particles rotating about an axis of symmetry, Proc. Roy. Soc. Edin. 57 (1937) 135.
• T. Lewis, Some special solutions of the equations of axially symmetric gravitational fields, Proc. Roy. Soc. London A 136 (1932) 176.
• F. J. Tipler, Rotating cylinders and the possibility of global causality violation, Phys. Rev. D 9 (1974) 2203.
• W. B. Bonnor, The exterior gravitational field of a rotating cylinder of dust, J. Phys. A 13 (1980) 2121.
• S. W. Hawking, The chronology protection conjecture, Phys. Rev. D 46 (1992) 603.
• D. Deutsch, Quantum mechanics near closed timelike lines, Phys. Rev. D 44 (1991) 3197.
• D. N. Page, Average entropy of a subsystem, Phys. Rev. Lett. 71 (1993) 1291.
• IBM Quantum, ibm_marrakesh 156-qubit Heron-r2 processor (2026).