AperioGenix Inc. | Core Architecture Repository | v1.0
- Golden Retriever Edition - completely self-contained, made-for-dummies version of the paper
- Full Paper - full technical paper
AxCore is an executable model of one idea:
If a system has finite energy and finite compute, it naturally contracts from flexible multi-path behavior into stable cached behavior.
This repo gives runnable probes for that idea. You can run them and reproduce the outputs in generated/.
Read the results with the same scope used in the paper: this repo contains one exact contraction theorem, several exact algebraic bridge checks, and a larger set of probe-level measurements under explicit controls and calibrations.
Strategically, this repo is arguing for AxCore as a stronger unification architecture than a stack of disconnected effect-specific models. The claim is not "physics is finished." The claim is that AxCore turns multiple effects into one executable benchmark layer.
- One metric, many effects. Route cost is reused as the shared ledger for decoherence, gravity-like attraction, time-slowing, and mass-equivalent energy.
- Forward executable scaling. The mass bridge does not just quote
0.511 MeV; it solves for the substrate capacity that yields electron parity from a measured route cost and then checks that scaling against a copied forward runtime run. - Endogenous decoherence. Classicalization is modeled as a budget problem, not an observer miracle.
- Compact law reuse. The same small law family is reused across the probes instead of introducing a separate formal system for each domain.
- Benchmarkability. The copied runtime artifacts can fail. If the kernel bridge or the 45.4M-dimension forward mass run missed badly, the repo would expose that directly.
| Feature | Standard sector-style framing | AxCore bridge framing |
|---|---|---|
| Mathematical unity | Different formalisms for different sectors | Shared runtime currency: route cost |
| Mass scale | Observed constants inserted into the theory | Substrate-capacity scaling applied to measured route costs |
| Decoherence | External/open-system postulate | Endogenous budget-driven contraction |
| Time | Coordinate plus separate dynamical law | Internal tick throughput under route burden |
| Testing style | Analytic fit plus specialized solvers | Shared-kernel probes plus copied runtime benchmarks |
- Twenty-one executable Python probes:
proofs/axcore_emergent_gravity_proof.pyproofs/axcore_n_path_lindblad_proof.pyproofs/axcore_landauer_erasure_proof.pyproofs/axcore_cga5_particle_catalog_proof.pyproofs/axcore_mass_resolution_scaling_proof.pyproofs/axcore_forward_mass_parity_proof.pyproofs/axcore_lag_ceiling_proof.pyproofs/axcore_strong_confinement_proof.pyproofs/axcore_weak_decay_proof.pyproofs/axcore_quantum_phase_transition_proof.pyproofs/axcore_double_slit_proof.pyproofs/axcore_vs_einstein_mond_proof.pyproofs/axcore_resolution_limit_proof.pyproofs/axcore_entanglement_aliasing_proof.pyproofs/axcore_area_law_proof.pyproofs/axcore_kleiber_biocore_proof.pyproofs/axcore_life_metabolic_loop_proof.pyproofs/axcore_time_dilation_proof.pyproofs/axcore_vsl_cavity_proof.pyproofs/axcore_boson_sampling_proof.pyproofs/axcore_biocore_steric_fold_proof.py- Shared theorem kernel used across probes:
proofs/axcore_theorem_kernel.py - Shared support-check module used across probes:
proofs/axcore_support_tests.py - Root runner for all probes:
run_all_proofs.py - Generated outputs (PNG/CSV/JSON):
generated/... - Artifact inputs and two-path traces:
artifacts/... - Theory document:
AxCore Informational Bridge Model.md
Note: this repository contains standalone mathematical and executable probe artifacts. It does not include proprietary AperioGenix engine source code.
All probes use the same theorem-kernel primitives from proofs/axcore_theorem_kernel.py:
- shared state map from probability:
$H_t, S_t, \Omega_t, I_t, D_t$ where$S_t$ is a routing-balance term, not conventional sparsity - semantic/geometric route cost
- finite energy update $E_{t+1} = \text{clip}(E_t - \mathcal{L}t + \text{recharge}, 0, E{\max})$
- contraction map
$\kappa_t = (E_t / E_{\max})^\gamma$ - thermodynamic calibration bridge (Landauer anchored, with Joule, MeV, and inverse-capacity helpers):
$\text{joules_per_full_budget} = N_{\text{bit-eq}} \cdot k_B T \ln 2$ $E_{J,t} = (E_t/E_{\max}) \cdot \text{joules_per_full_budget}$ $\Delta Q_t = ((E_t - E_{t+1})/E_{\max}) \cdot \text{joules_per_full_budget}$ - $m_{\text{MeV}} = (\mathcal{L}t / E{\max}) \cdot \text{joules_per_full_budget} / (1 \text{ MeV in Joules})$
Each probe now uses either a direct overlay-equivalence check or an explicit null/adversarial control, so the README claims should be read as either exact kernel identities or probe-level results under the stated conditions.
from proofs.axcore_theorem_kernel import (
joules_per_full_budget,
energy_to_joules,
delta_q_joules,
normalized_dissipation_to_mev_landauer,
)
j_full = joules_per_full_budget(n_bit_eq=1_000_000, temperature_k=300.0)
e_j = energy_to_joules(e_t=0.5, e_max=1.0, j_per_full_budget=j_full)
q_j = delta_q_joules(e_before=0.72, e_after=0.181, e_max=1.0, j_per_full_budget=j_full)
m_mev = normalized_dissipation_to_mev_landauer(burn_t=0.25, e_max=1.0, n_bit_eq=1_000_000, temperature_k=300.0)At 300 K and N_bit-eq = 1,000,000, this gives:
j_full = 2.870978885078724e-15 Je_j (50% budget) = 1.435489442539362e-15 Jq_j (0.72 -> 0.181) = 1.547457619057432e-15 Jm_mev (25% dissipative burn) = 0.004479810190951025 MeV
- Python 3.10+ (3.11 recommended)
numpymatplotlib
pip install numpy matplotlib
# Run everything (default, no arguments)
python run_all_proofs.py
# Or run any single probe
python proofs/axcore_emergent_gravity_proof.pyAll values below come from the current JSON outputs in generated/.../*_current.json. Some are exact bridge checks; others are calibrated or probe-level measurements and should be read that way.
- Script:
python proofs/axcore_emergent_gravity_proof.py - Cost-proxy slope (
inverse_r):-1.882302468992497 - Trajectory-derived slope (
inverse_r):-1.8494362391682408 - Cost-proxy null slope:
0.007209077040617918 - Trajectory null slope:
0.294016253901303 - Adversarial monotone surrogate set:
inverse_r: cost-1.882302468992497, trajectory-1.8494362391682408inverse_r2_pivot: cost-2.3003885552684937, trajectory-1.8828373958354612exp_pivot: cost-2.1271547464637868, trajectory-1.8724222453754826lorentz_pivot: cost-2.0029606760492182, trajectory-1.8648960217335133adversarial_stair_pivot: cost-1.877007652760369, trajectory-1.849173131566794adversarial_warp_pivot: cost-1.9369331483240906, trajectory-1.8682055082535465- Harness flags:
supports_surrogate_robustness_cost_proxy = truesupports_surrogate_robustness_trajectory = truesupports_measurement_agreement = truesupports_strict_harness = true
There is also a --run-window-sweep argument to this probe which shows a scale-dependent change in the measured slope. By adjusting the integration macro-scale window from stochastic (
- Script:
python proofs/axcore_n_path_lindblad_proof.py - RMSE (off-diagonal overlay):
6.905985859359126e-20 - Max absolute overlay error:
1.3010426069826053e-18 - Support flag:
supports_lindblad_overlay = true
- Script:
python proofs/axcore_quantum_phase_transition_proof.py - Max RMSE across ticks:
1.9626155733547188e-18 - Final energy:
0.0 - Final kappa:
0.0 - Support flag:
supports_machine_precision_overlay = true
- Script:
python proofs/axcore_double_slit_proof.py - Primary final coherence:
0.0 - Null final coherence (no budget depletion):
1.0 - Primary interference decay ratio:
0.0 - Null interference decay ratio:
1.0 - Support flag:
supports_thermodynamic_decoherence_vs_null = true
- Script:
python proofs/axcore_vs_einstein_mond_proof.py - Measured AxCore slope:
-1.86197838324592(derived from simulation, not hardcoded) - Error vs
-2:0.13802161675407998 - Shuffled-radius null slope:
0.1653049184843184 - Support flag:
supports_inverse_square_like_behavior = true
- Script:
python proofs/axcore_resolution_limit_proof.py - Primary sub-lattice slope:
-1.0634643326537123 - Null sub-lattice slope (coarse-cap control):
4.5447147494667146e-17 - Primary growth factor (min-scale vs unit-scale):
8809.113704039733 - Divergence gain vs null:
8809.113704039733 - Support flag:
supports_resolution_limit_divergence_vs_null = true
- Script:
python proofs/axcore_entanglement_aliasing_proof.py - Mean prior delta on A-updates (shared alias):
0.03897326806850622 - Mean prior delta on A-updates (isolated):
0.0 - Mean prior delta on A-updates (delayed-copy):
0.0 - Mean delayed-copy prior delta one tick later:
0.06632656901805263 - Support flag:
supports_pointer_aliasing_nonlocal_update_vs_controls = true
- Script:
python proofs/axcore_area_law_proof.py - Boundary-model slope vs area:
1.0 - Boundary-model slope vs volume:
0.6849159299700465 - Null-model slope vs volume:
1.0 - Large-scale throughput ratio (null over boundary):
7.977462437395659 - Support flag:
supports_area_law_boundary_bottleneck_vs_null = true
- Script:
python proofs/axcore_kleiber_biocore_proof.py - Main slope (
BvsM):0.7898246790884726 - Null slope (
BvsM, volume-wide writes):0.9999999999999994 - Slope separation:
0.2101753209115268 - Support flag:
supports_kleiber_scaling_vs_null = true
- Script:
python proofs/axcore_life_metabolic_loop_proof.py - Main births:
20 - Null births (no harvest):
0 - Alive AUC gain (main/null):
83.53333333333333 - Starvation rate (main):
0.013168395849960097 - Starvation rate (null):
0.39166666666666666 - Support flag:
supports_life_metabolic_loop_vs_null = true
- Script:
python proofs/axcore_time_dilation_proof.py - The probe measures fewer internal ticks near the core than in deep space over the same macro-budget.
- Deep Space Internal Ticks logged: ~
2,938 - Core-field Internal Ticks logged: ~
1,366 - The result is interpreted in-repo as processor-lag time slowing in the tested setup, not as a complete first-principles derivation of relativistic time dilation.
- Script:
python proofs/axcore_vsl_cavity_proof.py - Free-space entropy:
1.0 - Cavity-core entropy:
0.3003513160224718 - Free-space viscosity
$\Omega$ :0.5 - Cavity-core viscosity
$\Omega$ :0.7448770393921349 - Local speed ratio in cavity (
c_local/c0):1.4897540787842698 - Main speed gain:
48.97540787842698% - Null speed gain (no cavity mode exclusion):
0.0% - Support flag:
supports_vsl_cavity_mode_exclusion = true
- Script:
python proofs/axcore_boson_sampling_proof.py - Emulates the highly dispersive optical network used in Jiuzhang to test "Quantum Supremacy".
- Maps how maintaining coherent unitary interference cascades in high dispersion
$H_t + S_t$ drains computational energy$E_t$ . - Final Coherence Retention (
$\kappa$ ):0.0 - The system gracefully abandons calculating the exponentially complex "Ideal Quantum" solution and transitions cleanly into simple probabilistic Classical scattering mid-network.
- Script:
python proofs/axcore_biocore_steric_fold_proof.py - An amino acid chain starts unfolded (random walk), yielding high computational dispersion and generating immense route-cost (
$\Omega$ spikes). - As the energy drops and
$\kappa \to 0$ , the mathematical thermodynamic "pull" crushes dispersion to save compute, while steric hindrance (atomic volume constraints) enforce physical space. - The outcome geometrically bounces and packs into a stable 3D fold that tightly matches theoretical atomic volume limits without requiring an ML database of molecular behavior.
- Script:
python proofs/axcore_landauer_erasure_proof.py - Simulates a forced high-entropy to classical overwrite trajectory and computes route-cost dissipation using the shared theorem kernel.
- Converts normalized dissipation to Joules with the kernel Landauer bridge:
joules_per_full_budget = N_bit_eq * k_B * T * ln(2). - Total normalized route cost:
2.295240612312979 - Total Joules dissipated:
6.589587334125724e-15 - Theoretical Landauer minimum (
N=1e6,T=300K):2.8709788850787237e-15 - Thermodynamic overhead ratio:
2.295240612312979 - Support flag:
supports_physical_thermodynamics = true
- Script:
python proofs/axcore_strong_confinement_proof.py - Measures pull-apart work versus separation for a locked pair under theorem-kernel route cost.
- Uses a matched deconfined null channel to ensure growth is not just baseline route-cost drift.
- Peak step cost (main):
8.613046409726428 - Peak step cost (null):
0.7904329884454572 - Cumulative work (main):
73.11042500759241 - Cumulative work (null):
16.43881392999976 - Tail step ratio (main/null):
11.707460976510372 - Work growth exponent (main):
1.9791318475383535 - Work growth exponent (null):
1.6151899834752341 - Support flag:
supports_strong_confinement = true
- Script:
python proofs/axcore_weak_decay_proof.py - Runs metastable-to-stable transition trials under finite energy and local noise.
- Compares against a stable-geometry null with the same theorem kernel dynamics.
- Main decay fraction:
1.0 - Null decay fraction:
0.0 - Main mean decay tick:
6.365 - Main median decay tick:
6.0 - Null median decay tick:
1000.0 - Mean released Joules (main):
1.9277745813736125e-15 - Mean released Joules (null):
0.0 - Release ratio (main/null):
1927.7745813736124 - Support flag:
supports_weak_decay_transition = true
- Script:
python proofs/axcore_cga5_particle_catalog_proof.py - Source artifact:
artifacts/axcore_cga5_particle_catalog_current.json - Uses an exact copied runtime JSON from the external AxCore CPP CGA5 sweep and recomputes its thermodynamic mass equivalents through the shared theorem kernel.
- Max bridge absolute error:
0.0 MeV - Kernel bridge RMSE:
0.0 MeV - Constraint-count null RMSE:
1.5463972889867672e-06 MeV - Measured mass order (lightest to heaviest):
Circle -> Motor -> Sphere -> Point-Pair -> Point - Support flags:
supports_kernel_mass_bridge = truesupports_topology_specific_splitting = truesupports_particle_catalog_bridge = true
- Script:
python proofs/axcore_mass_resolution_scaling_proof.py - Source artifact:
artifacts/axcore_cga5_particle_catalog_current.json - Uses the measured Point-Pair route cost from the copied CGA5 runtime artifact and inverts the shared theorem-kernel Landauer bridge to solve for the substrate capacity required to hit target mass-equivalents.
- Baseline Point-Pair mass at
1024dims:1.1523001371740657e-05 MeV - Electron parity (
0.511 MeV) requires1453132518.1531758bit-eq, or45410391.192286745HDC dimensions. - Up-quark parity (
2.2 MeV) requires6256147827.665338bit-eq, or195504619.6145418HDC dimensions. - Max round-trip absolute error:
4.440892098500626e-16 MeV - Required-capacity ratio (
up/electron):4.305283757338553 - Support flag:
supports_mass_resolution_scaling = true
- Script:
python proofs/axcore_forward_mass_parity_proof.py - Source artifacts:
artifacts/axcore_cga5d_forward_fixed_dim_45410391.json,artifacts/axcore_cga5_particle_catalog_current.json - Uses the copied forward 45.4M-dimension runtime artifact to validate that the shared theorem kernel reproduces the runtime masses exactly and that the Point-Pair topology lands near electron parity in a raw forward run.
- Point-Pair forward mass:
0.5009360767138339 MeV - Point-Pair electron absolute error:
0.010063923286166121 MeV - Point-Pair electron relative error:
0.01969456611774192 - Max bridge absolute error:
0.0 MeV - Topology order preserved vs low-dimension catalog:
true - Route-drift vs parity-error mismatch:
4.151026560678117e-09 - Support flag:
supports_forward_mass_parity = true
- Script:
python proofs/axcore_lag_ceiling_proof.py - Source artifact:
generated/axcore_time_dilation_proof/axcore_time_dilation_proof_current.json - Combines the measured deep-space baseline from the time-dilation probe with an explicit bounded theorem-kernel action ceiling under benchmark weights.
- Deep-space rest cost:
0.10306250000000002 - Observed near-core cost:
0.18166666666666664 - Benchmark action ceiling:
3.285 - Observed core lag factor:
1.7626844552253886 - Max lag factor:
31.87386294724075 - Minimum internal tick floor:
0.031373668188736686 - SR beta-equivalent at ceiling:
0.9995077253050039 - For comparison, standard SR at
0.9995cgivesgamma ≈ 31.6, numerically close to the AxCore ceiling. - The classic CERN muon storage-ring time-dilation result was reported at
gamma ≈ 29.3, just below the AxCore benchmark ceiling. - Interpreted conservatively, the new proof places the AxCore lag ceiling in the same extreme-relativistic regime as familiar textbook and accelerator examples; it does not yet prove that physical SR literally saturates at the AxCore benchmark.
- Support flag:
supports_lag_ceiling = true
generated/axcore_emergent_gravity_proof/axcore_emergent_gravity_proof_current.{json,csv,png}generated/axcore_emergent_gravity_proof/axcore_emergent_gravity_proof_current_surrogates.csvgenerated/axcore_n_path_lindblad_proof/axcore_n_path_lindblad_proof_current.{json,csv,png}generated/axcore_landauer_erasure_proof/axcore_landauer_erasure_proof_current.{json,csv,png}generated/axcore_cga5_particle_catalog_proof/axcore_cga5_particle_catalog_proof_current.{json,csv,png}generated/axcore_mass_resolution_scaling_proof/axcore_mass_resolution_scaling_proof_current.{json,csv,png}generated/axcore_forward_mass_parity_proof/axcore_forward_mass_parity_proof_current.{json,csv,png}generated/axcore_lag_ceiling_proof/axcore_lag_ceiling_proof_current.{json,csv,png}generated/axcore_strong_confinement_proof/axcore_strong_confinement_proof_current.{json,csv,png}generated/axcore_weak_decay_proof/axcore_weak_decay_proof_current.{json,csv,png}generated/axcore_quantum_phase_transition_proof/axcore_quantum_phase_transition_proof_current.{json,csv,png}generated/axcore_double_slit_proof/axcore_double_slit_proof_current.{json,csv,png}generated/axcore_double_slit_proof/axcore_double_slit_proof_current_tick_metrics.csvgenerated/axcore_vs_einstein_mond_proof/axcore_vs_einstein_mond_proof_current.{json,csv,png}generated/axcore_vs_einstein_mond_proof/axcore_vs_einstein_mond_proof_current_binned.csvgenerated/axcore_resolution_limit_proof/axcore_resolution_limit_proof_current.{json,csv,png}generated/axcore_entanglement_aliasing_proof/axcore_entanglement_aliasing_proof_current.{json,csv,png}generated/axcore_area_law_proof/axcore_area_law_proof_current.{json,csv,png}generated/axcore_kleiber_biocore_proof/axcore_kleiber_biocore_proof_current.{json,csv,png}generated/axcore_life_metabolic_loop_proof/axcore_life_metabolic_loop_proof_current.{json,csv,png}generated/axcore_time_dilation_proof/axcore_time_dilation_proof_current.{json,png}generated/axcore_vsl_cavity_proof/axcore_vsl_cavity_proof_current.{json,csv,png}generated/axcore_boson_sampling_proof/axcore_boson_sampling_proof_current.{json,png}generated/axcore_biocore_steric_fold_proof/axcore_biocore_steric_fold_proof_current.{json,png}artifacts/axcore_cga5_particle_catalog_current.jsonartifacts/axcore_cga5d_forward_fixed_dim_45410391.json
run_all_proofs.py: root runner for all proofs (no arguments needed)proofs/axcore_theorem_kernel.py: shared theorem primitives used by probes, including Landauer-based normalized-budget to Joules and MeV calibration helpers plus inverse capacity scaling helpersproofs/axcore_support_tests.py: shared statistical support checks for all probe support flagsproofs/axcore_emergent_gravity_proof.py: emergent gravity harness with adversarial monotone surrogates and trajectory-derived acceleration checksproofs/axcore_n_path_lindblad_proof.py: AxCore decoherence map vs Lindblad overlayproofs/axcore_landauer_erasure_proof.py: forced-memory erasure probe mapping AxCore normalized route cost to physical Joules via Landauer calibrationproofs/axcore_cga5_particle_catalog_proof.py: bridge probe that takes the external CPP CGA5 catalog as a measured artifact and verifies its route-cost-to-mass map against the shared theorem kernelproofs/axcore_mass_resolution_scaling_proof.py: fixed-route-cost scaling lemma that inverts the shared thermodynamic bridge to estimate the substrate capacity required for electron and up-quark mass parityproofs/axcore_forward_mass_parity_proof.py: forward-validation probe that checks the copied 45.4M-dimension runtime run against the shared kernel and tests Point-Pair electron proximity plus topology-order preservationproofs/axcore_lag_ceiling_proof.py: bounded-action lag-ceiling probe that combines the measured time-dilation baseline with a theorem-kernel action ceiling to derive a finite processor-lag redshift floorproofs/axcore_strong_confinement_proof.py: confinement-gradient probe comparing locked-pair pull-apart work against a deconfined nullproofs/axcore_weak_decay_proof.py: metastable decay transition probe with stable-geometry null and Landauer-mapped release accountingproofs/axcore_quantum_phase_transition_proof.py: snapshot-based phase transition with overlay metricsproofs/axcore_double_slit_proof.py: budget-driven double-slit decoherence with no-depletion nullproofs/axcore_vs_einstein_mond_proof.py: measured AxCore slope vs Newton/MOND references + nullproofs/axcore_resolution_limit_proof.py: sub-lattice divergence probe with coarse-cap nullproofs/axcore_entanglement_aliasing_proof.py: shared-pointer aliasing vs isolated and delayed-copy controlsproofs/axcore_area_law_proof.py: area-law throughput scaling vs volume-write nullproofs/axcore_kleiber_biocore_proof.py: Kleiber-like scaling vs volume-write nullproofs/axcore_life_metabolic_loop_proof.py: self-sustaining routing-agent ecology vs no-harvest nullproofs/axcore_time_dilation_proof.py: measures reduced internal tick throughput near the core and interprets it as processor-lag time slowing within the probe harness.proofs/axcore_vsl_cavity_proof.py: resonant-cavity mode-exclusion probe mapping local entropy depression to viscosity and local wave-speed ratio shift.proofs/axcore_boson_sampling_proof.py: models the collapse of computational complexity into classical probabilistic distributions during high-dispersion optical routing (Jiuzhang optical limits).proofs/axcore_biocore_steric_fold_proof.py: bridges mathematical scaling limits to a practical packing fold by mapping thermodynamic starvation pressure against simulated physical atomic volume thresholds.generated/: current run outputs and figuresartifacts/: two-path support artifacts plus copied external runtime bridge inputsAxCore Informational Bridge Model.md: whitepaper-style model description
- These are executable internal probes in the AxCore framework.
- They demonstrate internal numerical consistency for the mappings implemented here, plus controlled probe-level behavior under the stated harnesses.
- Some results are exact within the repo's equations and overlays; others are calibrated bridges or empirical fits from the probes.
- They are not a full first-principles derivation of all fundamental physics.





















