This registry covers the current phase-transition calculation paths: spectral Cahn-Hilliard evolution, chemical potential, free-energy/order-parameter diagnostics, BEC critical temperature, 3D Ising critical-exponent comparison, and competitor/test solvers. It separates standard benchmark relations from UET heuristic projection claims and numerical demonstrations.
| formula_id | relation | code surface | variables and units | constant_origin | proof_status | verification_role | failure_mode | next_hardening_step |
|---|---|---|---|---|---|---|---|---|
PT-CH-EVOLUTION |
dC/dt = M nabla^2(delta F/delta C) |
Engine_Phase.step |
C dimensionless concentration/order field; M mobility proxy; dt simulation time step; grid units normalized |
checked_local_reference Cahn-Hilliard form |
checked local numerical relation |
engine diagnostic | Numerical stability depends on grid, dt, kappa, and noise; visual domains are not a physical proof by themselves. |
Add convergence sweep over grid size, seed, dt, and kappa. |
PT-FREE-ENERGY |
`F[C] = int [alpha/2 C^2 + gamma/4 C^4 + kappa/2 | grad C | ^2] dV` | Engine_Phase.compute_chemical_potential comments and implementation |
alpha, gamma, kappa dimensionless in normalized solver; C dimensionless |
topic_derived_relation / Cahn-Hilliard benchmark structure |
heuristic bridge |
diagnostic |
PT-CHEM-POTENTIAL |
mu = alpha C + gamma C^3 - kappa nabla^2 C |
Engine_Phase.compute_chemical_potential |
mu normalized potential; C dimensionless; nabla^2 normalized grid operator |
checked_local_reference |
checked local numerical relation |
engine diagnostic | Sign or FFT convention errors alter phase separation. | Add unit tests comparing FFT Laplacian to finite-difference reference. |
PT-SPECTRAL-UPDATE |
C_new_hat = (C_hat - dt M k^2 NL_hat + noise_hat)/(1 + dt M kappa k^4) |
Engine_Phase.step |
Fourier amplitudes dimensionless; k normalized wave number |
topic_derived_relation from semi-implicit CH update |
checked local numerical relation |
engine diagnostic | Incorrect implicit denominator can create artificial stability or growth. | Record seed, initial condition, and spectral diagnostics in artifact. |
PT-ORDER-PARAMETER |
order = mean(abs(C)) |
Engine_Phase.get_extra_metrics; Proof_Order_Parameter.py |
dimensionless order proxy | topic_derived_relation |
diagnostic proxy |
proof/test diagnostic | Threshold such as order > 0.7 is simulation-specific, not universal phase-transition proof. |
Calibrate threshold against known demixing simulations or mark as internal-only. |
PT-DOMAIN-COUNT |
zero-crossing count over sign of C |
Engine_Phase._count_domains |
count dimensionless | topic_derived_relation |
diagnostic proxy |
visualization/diagnostic | Sensitive to noise and grid resolution; not a robust domain morphology metric. | Replace or supplement with structure factor / correlation length. |
PT-BEC-TC |
Tc = (hbar omega/k_B) * (N/zeta(3))^(1/3) |
Engine_Phase.compute_bec_tc |
omega rad/s; N count; output K |
source_locked_physics_constant plus standard trapped-BEC relation |
checked local benchmark relation |
diagnostic only | Not used by primary phase-transition gate; cannot support broad transition claims. | Add explicit BEC verifier if this becomes claim-bearing. |
PT-BETA-UET |
beta_UET ~= 1/D_eff; current data uses 0.333 |
Research_Critical_Exponents.py; critical_exponents.json |
beta dimensionless critical exponent |
heuristic_bridge |
heuristic bridge with internal benchmark pass |
primary verifier gate | A close beta match does not derive gamma, nu, scaling relations, or full RG universality. |
Extend verifier to gamma, nu, and scaling laws; source-lock benchmark references. |
PT-BETA-ERROR |
relative_error = abs(beta_UET - beta_exp)/beta_exp * 100 |
Research_Critical_Exponents.py |
percent | topic_derived_relation |
identity |
primary verifier metric | If only beta is tested, README must not claim full phase-transition theory closure. | Keep claim to selected 3D Ising/liquid-gas beta exponent until broader gates exist. |
- The strongest current result is a selected beta-exponent internal benchmark.
- Spectral Cahn-Hilliard simulation demonstrates a normalized mechanism but is not yet mapped to physical material units.
- Order emergence and symmetry-breaking language must remain model/diagnostic wording unless backed by broader exponent, morphology, and material-data gates.
| formula_id | relation | code surface | variables and units | constant_origin | proof_status | verification_role | failure_mode | next_hardening_step |
|---|---|---|---|---|---|---|---|---|
PT-UET-LEGACY-INFO |
Omega_info = beta C I; dC/dt += -beta I |
docs/core/uet_master_equation.py::information_coupling; information_dynamics_source |
C normalized order field; I normalized information field; units remain normalized/proxy in topic 0.11 |
heuristic_bridge |
legacy local operator |
compatibility baseline | Local source can act without requiring mass/interface structure, so it can stay spatially blind. | Keep as legacy comparator only unless a derivation requires it. |
PT-UET-SPATIAL-INFO-CANDIDATE |
Omega_info = 0.5 beta C^2 I; dC/dt += -beta C I |
information_coupling(..., operator_mode="spatial_coupled_v1"); information_dynamics_source |
C normalized order field; I normalized information field; unit closure open |
heuristic_bridge |
candidate heuristic bridge |
diagnostic gate input | Wrong coefficient/sign can create artificial damping or noise response without physical closure. | Derive or reject the multiplicative information term before stronger claims. |
PT-UET-SPATIAL-GAME-CANDIDATE |
`V_game = beta_U | grad C | ^2; dynamics candidate F_game = c_kpz V_game` |
game_theory_potential; game_theory_force |
grad C normalized grid gradient; beta_U strategic boost; units proxy/open |
heuristic_bridge |
candidate diagnostic-only |
spatial operator gate |
PT-SPATIAL-SCALING-GATE |
fit `log(< | C | >) = beta log(Tc-T)+b` for baseline, legacy, and spatial lanes | Research_Spatial_Coupling_Scaling.py; 0_11_spatial_coupling_scaling.json |
beta dimensionless; synthetic normalized TDGL grid | topic_derived_relation |
diagnostic artifact |
hardening gate |
PT-SPATIAL-COEFFICIENT-SENSITIVITY |
sweep spatial_information_coupling and spatial_game_coupling; fit beta per case |
Research_Spatial_Coupling_Sensitivity.py; 0_11_spatial_coupling_sensitivity.json |
beta dimensionless; reduced synthetic TDGL grid | topic_derived_relation |
diagnostic artifact |
blocker triage | Wave 6 found no tested coefficient-only case near 3D Ising beta; best beta 0.4729, range 0.4729 to 0.5243. |
Stop treating coefficient strength as the likely repair; revise operator form or estimator. |
PT-CORRELATION-LENGTH-DIAGNOSTIC |
connected autocorrelation axis crossing proxy for xi; fit xi ~ (Tc-T)^(-nu_proxy) |
Research_Correlation_Length_Diagnostics.py; 0_11_correlation_length_diagnostics.json |
xi grid units; nu_proxy dimensionless diagnostic |
topic_derived_relation |
diagnostic artifact |
estimator gate | Wave 7 found weak spatial correlation growth: spatial nu_proxy ~= 0.0324, xi_near/xi_far ~= 1.0668. |
Add finite-size/correlation-length-aware scaling before stronger universality claims. |
PT-FINITE-SIZE-SCALING-DIAGNOSTIC |
sweep grid sizes and compare xi/L, Binder-style proxy, and lane separation |
Research_Finite_Size_Scaling_Diagnostics.py; 0_11_finite_size_scaling_diagnostics.json |
xi/L dimensionless; Binder proxy dimensionless |
topic_derived_relation |
diagnostic artifact |
finite-size gate | Wave 8 found Binder-style spread but xi/L too small and no spatial-vs-baseline separation. |
Redesign finite-size window and operator form before stronger claims. |
PT-CRITICAL-WINDOW-RELAXATION-DIAGNOSTIC |
sweep closer-to-Tc temperatures and step counts; compare spatial/baseline xi/L |
Research_Critical_Window_Relaxation_Diagnostics.py; 0_11_critical_window_relaxation_diagnostics.json |
xi/L dimensionless; steps synthetic time |
topic_derived_relation |
diagnostic artifact |
window/relaxation gate | Wave 9 found max spatial xi/L = 0.0737 and no gain from longer relaxation. |
Stop treating runtime/window extension alone as the likely repair; revise dynamics/operator form. |
PT-OPERATOR-FORM-REQUIREMENT-GATE |
aggregate Waves 5-9 into blocked repair paths and v2 design requirements | Research_Operator_Form_Requirement_Gate.py; 0_11_operator_form_requirement_gate.json |
gate statuses and thresholds are dimensionless artifact fields | topic_derived_relation |
design requirement gate |
operator-revision controller | Wave 10 keeps coefficient-only, finite-size signal, and critical-window paths blocked for the current operator family. | Design a new opt-in operator with nonlocal, conserved, or scale-dependent behavior before rerunning scaling claims. |
PT-UET-SPATIAL-V2-CANDIDATE |
activity `= | grad C | ^2 + a(nonlocal(C)-C)^2; game force = lambda nabla^2 V_game; info source ~ -beta C I activity` |
uet_master_equation.py; Research_Spatial_Coupled_V2_Diagnostic.py; 0_11_spatial_coupled_v2_diagnostic.json |
normalized C, I, xi/L; v2 coefficients are heuristic/proxy |
heuristic_bridge |
candidate diagnostic-only |
v2 availability/safety/stability gate |
PT-UET-SPATIAL-V2-ABLATION |
compare v2 information-only, game-only, full, short-memory, and long-memory profiles against baseline xi/L |
Research_Spatial_Coupled_V2_Component_Ablation.py; 0_11_spatial_coupled_v2_component_ablation.json |
normalized xi/L; profile coefficients are heuristic/proxy |
topic_derived_relation |
diagnostic ablation |
component blocker triage | Wave 12 found all tested v2 profiles below baseline; best improvement -0.0038. |
Stop treating current v2 components as a likely repair; design a different operator structure or derivation. |
PT-MODEL-C-CONSERVED-ORDER-DIAGNOSTIC |
dC/dt = M nabla^2(delta F/delta C) via topic Cahn-Hilliard engine |
Engine_Phase.py; Research_Model_C_Conserved_Order_Diagnostic.py; 0_11_model_c_conserved_order_diagnostic.json |
normalized 2D C, grid units, xi proxy; no material units |
checked_local_reference plus topic diagnostic |
mechanism repair direction |
conserved-order mechanism gate | Wave 13 passes mass conservation, domain growth, and operator distinction gates, but remains normalized 2D mechanism evidence. | Integrate as opt-in core candidate or run finite-size/exponent gates before stronger claims. |
PT-CONSERVED-ORDER-CORE-CANDIDATE |
core opt-in conserved_order_v1: dC/dt = -M nabla^2(force) where force = -delta Omega/delta C |
uet_master_equation.py; Research_Conserved_Order_Core_Candidate.py; 0_11_conserved_order_core_candidate.json |
normalized C, grid units, explicit finite-difference helper; no material units |
heuristic_bridge from Model C diagnostic |
core candidate diagnostic-only |
core integration and mass-conservation gate | Wave 14 passes core exposure, legacy compatibility, and mass conservation, but blocks mechanism response (xi growth 0.87 vs legacy 1.47). |
Tune/integrate a spectral or semi-implicit conserved core path before finite-size claims. |
PT-CONSERVED-ORDER-NUMERICS-GAP |
stiffness proxy dt * kappa * (pi / dx)^4 comparing Wave 13 spectral settings to Wave 14 explicit core settings |
Research_Conserved_Order_Numerics_Gap.py; 0_11_conserved_order_numerics_gap.json |
dimensionless explicit-stability proxy; normalized grid units | topic_derived_relation |
diagnostic requirement gate |
next-operator controller | Wave 15 blocks explicit core viability: Wave 13-like stiffness proxy 32685 versus Wave 14 explicit proxy 0.097, ratio 335544. |
Implement a spectral or semi-implicit conserved-order core candidate before coefficient tuning or finite-size claims. |
PT-CONSERVED-ORDER-SPECTRAL-CORE-CANDIDATE |
core opt-in semi-implicit update C_hat_new = (C_hat + dt M k^2 F_non_grad_hat)/(1 + dt M kappa k^4) |
uet_master_equation.py::spectral_conserved_order_step; Research_Conserved_Order_Spectral_Core_Candidate.py; 0_11_conserved_order_spectral_core_candidate.json |
normalized C, FFT grid units, xi proxy; no material units |
heuristic_bridge from Wave 13 topic engine |
core candidate diagnostic-only |
Wave 15 repair and topic-engine bridge gate | Wave 16 passes core bridge gates with max topic-engine delta 2.89e-12 and median xi growth 30.49. |
Run finite-size/exponent scaling gates before stronger dynamics or universality claims. |
PT-CONSERVED-ORDER-SPECTRAL-SCALING |
finite-size sweep fits `log(< | C | >)andlog(xi)versuslog(Tc-T)forconserved_order_spectral_v1` |
Research_Conserved_Order_Spectral_Scaling.py; 0_11_conserved_order_spectral_scaling.json |
normalized 3D lattice units; xi/L, Binder proxy, beta and nu proxies |
topic_derived_relation |
diagnostic finite-size/exponent gate |
claim-boundary controller |
PT-CONSERVED-ORDER-SPECTRAL-WINDOW-REPAIR |
targeted relaxation and kappa sweeps compare xi/L against order-signal preservation |
Research_Conserved_Order_Spectral_Window_Repair.py; 0_11_conserved_order_spectral_window_repair.json |
normalized 3D lattice units; xi/L, order amplitude, kappa proxy |
topic_derived_relation |
diagnostic repair triage |
next-window controller | Wave 18 finds relaxation-only max xi/L = 0.113; kappa max xi/L = 0.377 only at order 0.000377, below signal floor. |
Design a window that preserves order signal while lifting xi/L, or revise the scaling estimator/operator before stronger claims. |
PT-CONSERVED-ORDER-SPECTRAL-SPINODAL-WINDOW |
targeted positive spinodal-margin cases compare xi/L and order-signal preservation across seed replicates |
Research_Conserved_Order_Spectral_Spinodal_Window.py; 0_11_conserved_order_spectral_spinodal_window.json |
normalized 3D lattice units; xi/L, order amplitude, seed replicate margin |
topic_derived_relation |
diagnostic window candidate |
seed-margin controller | Wave 19 finds one viable order-preserving xi/L case (xi/L = 0.204, order 0.0126) but target seed pass fraction is 0.25. |
Replicate the window across seeds and grid sizes before exponent or universality claims. |
PT-CONSERVED-ORDER-SPECTRAL-SEED-MARGIN |
target spinodal window at T=0.900, kappa=0.100, steps=4000 compares seed replicate xi/L and order floors |
Research_Conserved_Order_Spectral_Seed_Margin.py; 0_11_conserved_order_spectral_seed_margin.json |
normalized 3D L=16 lattice units; xi/L, order amplitude, seed replicate pass fraction |
topic_derived_relation |
diagnostic seed-margin repair |
finite-size replication controller | Wave 20 passes the target seed-margin gate (4/4 seeds, min xi/L = 0.2004, min order 0.0505) but remains single-grid. |
Replicate over grid sizes before exponent or universality claims. |
PT-CONSERVED-ORDER-SPECTRAL-FINITE-SIZE-REPLICATION |
replicate the Wave 20 target window over L=8,12,16 and two seed sets |
Research_Conserved_Order_Spectral_Finite_Size_Replication.py; 0_11_conserved_order_spectral_finite_size_replication.json |
normalized 3D lattice units; xi/L, order amplitude, grid/seed pass fractions |
topic_derived_relation |
diagnostic finite-size replication gate |
grid/seed replication controller | Wave 21 passes coverage but blocks replication: L=16 fresh seeds pass only 1/3 and min xi/L = 0.1944. |
Revise finite-size/window scaling or estimator before exponent or universality claims. |
PT-CONSERVED-ORDER-SPECTRAL-L16-RELAXATION-REPAIR |
test L=16 fresh seeds at 4000, 4800, and 5600 steps for xi/L repair |
Research_Conserved_Order_Spectral_L16_Relaxation_Repair.py; 0_11_conserved_order_spectral_l16_relaxation_repair.json |
normalized 3D L=16 lattice units; xi/L, order amplitude, step-group pass fractions |
topic_derived_relation |
diagnostic relaxation repair gate |
next-window/estimator controller | Wave 22 blocks relaxation-only repair: all step groups pass only 1/3 fresh seeds while order stays above floor. |
Revise estimator or finite-size/window scaling before exponent or universality claims. |
PT-CONSERVED-ORDER-SPECTRAL-L16-ESTIMATOR-SENSITIVITY |
sweep axis-autocorrelation crossing thresholds for the same L=16 fresh-seed fields |
Research_Conserved_Order_Spectral_L16_Estimator_Sensitivity.py; 0_11_conserved_order_spectral_l16_estimator_sensitivity.json |
normalized 3D L=16 lattice units; xi/L, autocorrelation threshold, crossing/saturation counts |
topic_derived_relation |
diagnostic estimator-sensitivity gate |
estimator-design controller | Wave 23 finds the default e^-1 threshold reproduces Wave 22, while lower thresholds make 9/9 cases pass without saturation. |
Derive, calibrate, or replace the correlation estimator before exponent or universality claims. |
PT-CONSERVED-ORDER-SPECTRAL-L16-STRUCTURE-FACTOR-ESTIMATOR |
threshold-free characteristic length xi_sf = 2*pi / sqrt(sum(S(k) k^2) / sum(S(k))) over nonzero FFT modes |
Research_Conserved_Order_Spectral_L16_Structure_Factor_Estimator.py; 0_11_conserved_order_spectral_l16_structure_factor_estimator.json |
normalized 3D L=16 lattice units; structure-factor power, RMS wave number, xi/L |
topic_derived_relation |
diagnostic estimator candidate |
finite-size calibration controller | Wave 24 passes the L16 margin but warns on domain-scale risk: structure-factor max xi/L = 0.5799. |
Calibrate over multiple grid sizes before exponent or universality claims. |
PT-CONSERVED-ORDER-SPECTRAL-STRUCTURE-FACTOR-MULTIGRID |
replicate xi_sf = 2*pi / sqrt(sum(S(k) k^2) / sum(S(k))) over L=8,12,16 and two seed sets |
Research_Conserved_Order_Spectral_Structure_Factor_Multigrid_Calibration.py; 0_11_conserved_order_spectral_structure_factor_multigrid_calibration.json |
normalized 3D lattice units; structure-factor xi/L, absolute xi, grid-size trend |
topic_derived_relation |
diagnostic calibration gate |
domain-scale saturation controller | Wave 25 passes margin replication but blocks calibration: median xi/L is 0.997 at L=8, 0.717 at L=12, and 0.566 at L=16. |
Add larger-grid/source-backed estimator calibration or derived acceptance rule before exponent claims. |
PT-CONSERVED-ORDER-SPECTRAL-STRUCTURE-FACTOR-L20-PROBE |
rerun xi_sf on L=20 and extend the median trend from Wave 25 |
Research_Conserved_Order_Spectral_Structure_Factor_L20_Probe.py; 0_11_conserved_order_spectral_structure_factor_l20_probe.json |
normalized 3D lattice units; L20 xi/L, absolute xi, estimator ratio to axis threshold |
topic_derived_relation |
diagnostic larger-grid probe |
acceptance-rule controller | Wave 26 passes L20 relief (median xi/L = 0.4347) but blocks acceptance-rule use; L20 absolute xi is below L16 (ratio = 0.9599) and estimator reconciliation is still missing. |
Create source-backed or derived acceptance rule before exponent claims. |
PT-CONSERVED-ORDER-SPECTRAL-STRUCTURE-FACTOR-ACCEPTANCE-RULE |
preflight rule excludes domain-scale grids, requires >=3 admissible grids, absolute-xi consistency, and estimator reconciliation |
Research_Structure_Factor_Acceptance_Rule_Gate.py; 0_11_structure_factor_acceptance_rule_gate.json |
normalized 3D lattice units; xi_sf/L, absolute xi_sf, grid subset, estimator ratio |
topic_derived_relation |
heuristic preflight, not physics acceptance |
claim-boundary gate | Wave 27 defines the rule but current evidence fails: L=8 excluded, L20/L16 = 0.9599, and estimator ratio 2.6261 is unreconciled. |
Repair absolute-length consistency or add a source-backed estimator benchmark before exponent claims. |
PT-CONSERVED-ORDER-SPECTRAL-ESTIMATOR-RECONCILIATION |
compare xi_sf / xi_axis_lower at L16 and L20; candidate calibration factor is the observed ratio average |
Research_Structure_Factor_Estimator_Reconciliation_Gate.py; 0_11_structure_factor_estimator_reconciliation_gate.json |
normalized grid units; estimator ratio dimensionless; calibration factor unaccepted | topic_derived_relation |
diagnostic reconciliation only |
estimator-calibration gate | Wave 28 finds stable ratio drift (0.0219) but blocks magnitude/provenance and absolute-length trend. |
Source-back or derive calibration, or repair the window/dynamics before exponent claims. |
PT-CONSERVED-ORDER-SPECTRAL-CALIBRATION-SOURCE-SUPPORT |
scan local refs for structure-factor/second-moment/Fourier/finite-size estimator support before accepting calibration | Research_Structure_Factor_Calibration_Source_Support_Gate.py; 0_11_structure_factor_calibration_source_support_gate.json |
source hashes, keyword matches, DOI/URL candidates; no physical units | source_support_triage |
source gap diagnostic |
source-packaging gate | Wave 29 finds zero local text-source matches for all required estimator-support classes. | Package primary estimator sources and formula boundaries before calibration or exponent claims. |
PT-CONSERVED-ORDER-SPECTRAL-SOURCE-MANIFEST |
package primary estimator-source candidates with DOI/URL, formula role, and claim boundary | structure_factor_estimator_source_manifest.json; Research_Structure_Factor_Source_Manifest_Gate.py; 0_11_structure_factor_source_manifest_gate.json |
source metadata only; no estimator units accepted | source_support_triage |
source manifest only |
source-review gate | Wave 30 passes metadata coverage but blocks local formula extraction and calibration acceptance. | Extract source formulas and map or reject the RMS inverse-k proxy before exponent claims. |
PT-CONSERVED-ORDER-SPECTRAL-FORMULA-BOUNDARY |
source family uses xi_2nd = sqrt(S(0)/S(k_min)-1)/(2 sin(k_min/2)); current proxy uses all-nonzero-mode RMS inverse-k |
structure_factor_estimator_formula_boundary.json; Research_Structure_Factor_Formula_Boundary_Gate.py; 0_11_structure_factor_formula_boundary_gate.json |
source formula in lattice units; current proxy remains normalized diagnostic units | source_formula_boundary plus topic_derived_relation |
source boundary extracted; current proxy mismatch |
formula-boundary gate | Wave 31 passes source formula extraction but blocks current proxy source-match and calibration acceptance. | Implement a lowest-mode second-moment estimator candidate or repair window/dynamics before exponent claims. |
PT-CONSERVED-ORDER-SPECTRAL-LOWEST-MODE-CANDIDATE |
literal candidate xi_2nd = sqrt(S(0)/S(k_min)-1)/(2 sin(k_min/2)) on L16/L20 conserved-order fields |
Research_Structure_Factor_Lowest_Mode_Candidate_Gate.py; 0_11_structure_factor_lowest_mode_candidate_gate.json |
normalized lattice units; raw snapshot S(0) is not accepted susceptibility |
source_formula_candidate |
candidate implemented; observable blocked |
replacement feasibility gate | Wave 32 passes implementation but blocks observable validity: 0/15 cases valid, all with zero_mode_not_larger_than_lowest_mode. |
Derive an ensemble/connected susceptibility lane or repair window/dynamics before exponent claims. |
PT-CONSERVED-ORDER-SPECTRAL-ENSEMBLE-SUSCEPTIBILITY-LANE |
compare S0 = N Var_ensemble(mean(C)) against diagnostic S0_proxy = mean(N Var_space(C)) for lowest-mode estimator use |
Research_Structure_Factor_Ensemble_Susceptibility_Lane_Gate.py; 0_11_structure_factor_ensemble_susceptibility_lane_gate.json |
normalized lattice structure-factor units; spatial proxy not source-equivalent | susceptibility_lane_diagnostic |
source-closer lane blocked; proxy diagnostic-only |
S0 policy gate | Wave 33 blocks raw ensemble S0 because conserved mean gives S0/S(k_min) < 1; spatial proxy is numeric but not accepted. |
Source-back a conserved-order susceptibility policy or finite-k/canonical estimator before exponent claims. |
PT-CONSERVED-ORDER-SPECTRAL-ESTIMATOR-POLICY-SOURCE |
define required policies for conserved-order S0, finite-k/canonical replacement, and spatial-variance proxy exclusion | structure_factor_estimator_policy_requirements.json; Research_Structure_Factor_Estimator_Policy_Source_Gate.py; 0_11_structure_factor_estimator_policy_source_gate.json |
policy metadata; no estimator units accepted | estimator_policy_source_triage |
requirements defined; source support missing |
policy-source gate | Wave 34 passes policy requirement manifest but blocks conserved susceptibility and finite-k policy source gates. | Package policy-specific sources or choose window/dynamics repair before exponent claims. |
PT-CONSERVED-ORDER-SPECTRAL-POLICY-SOURCE-CANDIDATES |
package fixed-magnetization/canonical and Cahn-Hilliard structure-factor source candidates for estimator-policy review | structure_factor_estimator_policy_source_candidates.json; Research_Structure_Factor_Policy_Source_Candidate_Gate.py; 0_11_structure_factor_policy_source_candidate_gate.json |
source metadata only; formula units not extracted | source_candidate_packaging |
candidates packaged; formula extraction blocked |
policy source-candidate gate | Wave 35 passes candidate manifest coverage but blocks formula extraction and policy acceptance. | Extract policy formula boundaries or choose window/dynamics repair before exponent claims. |
PT-CONSERVED-ORDER-SPECTRAL-POLICY-FORMULA-BOUNDARY |
extract abstract-level fixed-magnetization/canonical and Cahn-Hilliard structure-factor boundaries for estimator-policy review | structure_factor_estimator_policy_formula_boundary.json; Research_Structure_Factor_Policy_Formula_Boundary_Gate.py; 0_11_structure_factor_policy_formula_boundary_gate.json |
abstract-level source boundaries; no accepted estimator units | partial_formula_boundary |
boundaries extracted; accepted formula blocked |
policy formula-boundary gate | Wave 36 passes boundary manifest and abstract boundary gates but blocks estimator acceptance and normalization mapping. | Extract full-text formulas or choose window/dynamics repair before exponent claims. |
PT-CONSERVED-ORDER-SPECTRAL-FULL-TEXT-FORMULA-READINESS |
record rendered/abstract source-access readiness and extraction gaps before formula acceptance | structure_factor_full_text_formula_extraction_readiness.json; Research_Structure_Factor_Full_Text_Formula_Readiness_Gate.py; 0_11_structure_factor_full_text_formula_readiness_gate.json |
source-access metadata; no accepted estimator units | formula_extraction_readiness |
local math source blocked |
full-text formula readiness gate | Wave 37 passes readiness manifest but blocks local math source and accepted formula gates. | Localize TeX/PDF math sources or choose window/dynamics repair before exponent claims. |
PT-CONSERVED-ORDER-SPECTRAL-SOURCE-ARCHIVE-LOCALIZATION |
verify temporary arXiv source archives and main TeX members for formula extraction | structure_factor_source_archive_localization_manifest.json; Research_Structure_Factor_Source_Archive_Localization_Gate.py; 0_11_structure_factor_source_archive_localization_gate.json |
source archive metadata; no accepted formulas | source_archive_localization |
archives localized; formula extraction blocked |
source archive localization gate | Wave 38 passes temporary archive and TeX member gates but blocks formula extraction and keeps repo archival policy warning-level. | Extract TeX formula fragments or define repo archival policy before exponent claims. |
PT-CONSERVED-ORDER-SPECTRAL-TEX-FORMULA-FRAGMENTS |
extract exact TeX formula fragments for fixed-magnetization, canonical finite-size, and Cahn-Hilliard structure-factor policy review | structure_factor_tex_formula_fragments.json; Research_Structure_Factor_Tex_Formula_Fragment_Gate.py; 0_11_structure_factor_tex_formula_fragment_gate.json |
source TeX formulas; UET lattice units not mapped | formula_fragment_extraction |
fragments extracted; estimator policy blocked |
formula-source gate | Wave 43 extracts 19 fragments from 3 source lanes and passes fragment gates, but accepts no estimator policy. | Map fragments into UET normalization and finite-size admissibility, then accept/reject estimator replacement before exponent claims. |
The spatial-coupled operator is now available as an opt-in core candidate, but the current scaling artifact does not support a claim that UET escapes mean-field behavior. The allowed claim is limited to: a candidate spatial operator exists, its interface/zero-field gates pass, and its current scaling result remains diagnostic-only.
The coefficient sensitivity diagnostic narrows the blocker: changing the current candidate coefficients alone did not shift the fitted beta exponent toward the 3D Ising target. The allowed claim is limited to: coefficient-only tuning remains mean-field-like under the tested grid, so the next hardening step needs a revised operator form, nonlocal/scale-dependent term, or correlation-length-aware estimator.
The correlation-length diagnostic shows that the current synthetic temperature window does not expose strong connected correlation-length growth. The allowed claim is limited to: beta-only order-parameter fits are not enough for universality promotion, and the next hardening step needs finite-size/correlation-length-aware scaling plus an operator form that separates from baseline behavior.
The finite-size diagnostic shows that grid coverage and Binder-style proxy spread are not the
limiting issue by themselves. The current blocker is that near-critical xi/L remains too
small and the spatial lane does not separate from the TDGL baseline, so finite-size scaling
claims remain blocked.
The critical-window relaxation diagnostic shows that moving closer to Tc and increasing
steps up to 2800 does not lift the spatial candidate out of local-correlation behavior. The
next hardening step must change the dynamics/operator form or add a better critical-growth
mechanism before rerunning finite-size claims.
The operator-form requirement gate aggregates the Wave 5-9 evidence chain into a design
controller. It does not validate a new equation. It records that the current spatial_coupled_v1
family has core-engine availability but still lacks coefficient, finite-size, critical-window,
and operator-separation support for a dynamics claim. The next hardening step must introduce a
new opt-in operator form with explicit unit/proxy boundaries, unit tests, formula-audit entries,
and fresh scaling artifacts before any claim is upgraded.
The first spatial_coupled_v2 candidate moves beyond coefficient-only tuning by adding screened
nonlocal space-memory contrast and a conserved interface/game drive in the core engine. The
candidate passes availability, zero/uniform-field safety, conserved-force, and short-run
stability checks. It does not pass dynamics-claim gates: v2 xi/L remains below the baseline
lane in the first diagnostic, so the current evidence only supports continued operator-design
work.
The component-ablation diagnostic shows that the current v2 failure is not isolated to only one combined lane. Information-only, game-only, full, short-memory, and long-memory profiles are all stable and force-isolated, but none improves the correlation-length proxy over baseline. The current v2 component family therefore remains diagnostic-only and should not be promoted by recombining or retuning those components alone.
The Model C diagnostic is the first post-v2 path that passes mechanism triage. It uses the topic Cahn-Hilliard engine instead of a hidden standalone equation, conserves the mean order parameter, and produces stronger domain/correlation growth than the nonconserved comparison lane. The allowed claim is limited to: Model C is a plausible mechanism-level repair direction. It is not yet a core UET operator replacement, 3D finite-size scaling result, material validation, or universality-class proof.
The conserved_order_v1 core mode exposes a Model C-style conserved flow without changing
legacy defaults. It passes the core exposure, legacy compatibility, Wave 13 bridge, and mass
conservation gates. It does not yet pass the mechanism-response gate: the explicit finite-
difference core candidate produces weaker xi growth than the legacy core comparison in the
current diagnostic. The allowed claim is limited to opt-in availability and conservation, not
validated phase-transition dynamics.
The numerics-gap diagnostic does not introduce a new physics claim. It records that the Wave 14 explicit finite-difference core path is not the right next replacement path for reproducing the Wave 13 spectral Cahn-Hilliard response: the Wave 13-like explicit stiffness proxy is far above the declared viability threshold. The allowed claim is limited to a next-implementation requirement: use a spectral or semi-implicit conserved-order core candidate before rerunning finite-size, exponent, or universality gates.
The conserved_order_spectral_v1 core mode repairs the Wave 15 implementation blocker by
matching the topic spectral Cahn-Hilliard engine under normalized Wave 13-like settings while
preserving legacy defaults. The allowed claim is limited to: an opt-in core spectral bridge now
exists and passes mechanism/implementation gates. It is not yet a finite-size scaling result,
critical-exponent result, material validation, RG closure, or universal phase-transition proof.
The spectral-scaling diagnostic is the first finite-size/exponent gate for conserved_order_spectral_v1.
It supports stability and coverage, but it does not support universality promotion: the near-critical
xi/L window remains below threshold and the fitted beta proxy is far from the 3D Ising benchmark.
The allowed claim is limited to: the next blocker is finite-size/equilibration/scaling-window design.
The window-repair diagnostic shows that the blocker is not fixed by simply running longer or moving
closer to Tc. Increasing kappa can raise xi/L, but the passing xi/L cases lose the order
signal below the declared floor. The allowed claim is limited to: the next repair must preserve
order amplitude while improving finite-size correlation structure, or revise the estimator/operator.
The spinodal-window diagnostic finds a narrow order-preserving xi/L candidate in the opt-in
conserved_order_spectral_v1 path, but the target seed replicate margin is not robust. The allowed
claim is limited to: a candidate single-grid window exists for the next finite-size replication
pass. It is not a universality, material, RG-closure, or exponent-scaling result.
The seed-margin diagnostic repairs the Wave 19 seed robustness blocker for the single-grid target
window by extending relaxation to 4000 steps. The allowed claim is limited to: the L=16
spinodal-window target now has enough seed-margin to justify finite-size replication. It is not
yet exponent scaling, material validation, RG closure, or universal phase-transition evidence.
The finite-size replication diagnostic shows that the Wave 20 target is not robust across all
tested grid/seed combinations. Smaller grids pass, but L=16 fresh seeds fall below the declared
xi/L threshold in two of three cases. The allowed claim is limited to: the current finite-size
window still needs redesign or estimator repair before exponent, material, RG, or universality
claims can be tested.
The L=16 relaxation-repair diagnostic shows that longer single-grid runs are not enough to fix
the fresh-seed xi/L margin. Order amplitude increases with step count, but the pass fraction
stays 1/3 through 5600 steps. The allowed claim is limited to: relaxation-only repair is
blocked, so the next wave should adjust the estimator, finite-size window, or scaling design.
The estimator-sensitivity diagnostic shows that the Wave 22 L=16 blocker is controlled by the
axis-autocorrelation crossing threshold. The default e^-1 threshold exactly reproduces the
blocked result, while lower thresholds (0.30, 0.25, 0.20) make all 9 fresh-seed cases pass
without max-radius saturation. The allowed claim is limited to: the current xi/L gate needs
estimator derivation/calibration or replacement before any non-default threshold can support
finite-size, exponent, material, RG, or universality claims.
The structure-factor diagnostic adds a threshold-free characteristic-length proxy to the same
L=16 fresh-seed fields. It confirms that the fields contain long-wavelength structure, but it
also flags finite-size/domain-scale risk: structure-factor xi/L ranges from 0.5549 to
0.5799 on a single grid. The allowed claim is limited to: a candidate estimator exists for the
next multi-grid calibration wave. It is not an accepted critical correlation length, exponent
result, material validation, RG closure, or universality-class proof.
The multi-grid calibration diagnostic confirms that the Wave 24 structure-factor margin is
replicable, but this makes the limitation sharper rather than promoting the claim. Across
L=8,12,16 and two seed sets, the estimator passes 18/18 cases while sitting near the domain
scale, with median xi/L decreasing from 0.997 to 0.566 as grid size increases. The allowed
claim is limited to: the current structure-factor RMS proxy is a reproducible long-wavelength
diagnostic that still needs larger-grid/source-backed calibration before finite-size, exponent,
material, RG, or universality claims.
The L20 larger-grid probe narrows the Wave 25 blocker but does not clear it. The L20 cases
all pass the structure-factor margin and the median xi/L drops to 0.4347, below the prior
domain-scale warning threshold. However, the absolute structure-factor length does not grow
with the grid (L20/L16 = 0.9599), the four-grid log slope is only 0.1110, the prior L8
median remains domain-scale (0.9972), and the structure-factor/axis-lower estimator ratio
is 2.6261. The allowed claim is limited to: the larger-grid symptom improved, but the
estimator still needs a source-backed or derived admissibility rule before finite-size,
exponent, material, RG, or universality claims.
The acceptance-rule preflight turns the Wave 26 missing-rule blocker into explicit machine
checks. A candidate admissible subset (L=12,16,20) exists, but the full current chain still
fails the preflight because L=8 is domain-scale, absolute xi_sf drops from L=16 to L=20,
and the structure-factor/axis-lower estimator disagreement has no reconciliation rule. The
allowed claim is limited to: a conservative preflight rule exists and blocks exponent use of
the current estimator evidence. It is not an accepted critical length or universality result.
The estimator-reconciliation gate shows the structure-factor/axis-lower ratio is stable enough
to study as a calibration-gap candidate (2.6849 at L16, 2.6261 at L20; drift 0.0219).
That does not accept the factor: the observed calibration remains source-free, the raw ratio
exceeds the unreconciled-ratio ceiling, and both estimators show declining absolute length from
L16 to L20. The allowed claim is limited to: disagreement is structured, not solved.
The source-support gate checks whether the local reference package can justify accepting the observed calibration factor or current RMS inverse-k proxy. It cannot: local text metadata has zero matches for structure-factor, second-moment correlation length, Fourier estimator definition, or finite-size admissibility. External primary candidates are recorded only as candidates until packaged with formula roles and claim boundaries.
The source-manifest gate packages three primary-source candidates with DOI/URL, formula role, and claim boundary. This repairs metadata organization only. It keeps formula extraction, local full-text support, and calibration acceptance blocked, so the current RMS inverse-k proxy remains diagnostic-only.
The formula-boundary gate extracts the source-family second-moment estimator relation as a
zero-mode to lowest-nonzero-mode ratio with a lattice finite-difference denominator. The
current topic proxy instead uses all nonzero Fourier modes and a 2*pi / RMS-k length.
Therefore the current proxy is rejected for source-backed exponent or calibration use until a
lowest-mode estimator candidate is implemented, compared, and passed through acceptance gates.
The lowest-mode candidate gate implements the source-family relation on the existing L16 and
L20 conserved-order fields. The implementation path passes, but the observable path blocks:
the raw snapshot zero mode is not larger than the lowest nonzero mode in any tested case
(0/15 valid), so the current single-snapshot lane cannot supply the required susceptibility
observable. No surrogate S(0) is accepted by this wave.
The susceptibility-lane gate separates two possible S(0) meanings. The source-closer
ensemble magnetization lane N Var_ensemble(mean(C)) remains invalid for the comparable
L16/L20 groups because conserved mean fluctuations are too small relative to S(k_min).
The spatial-variance proxy produces numeric lengths, but it aggregates nonzero modes and is
not accepted as source-equivalent zero-mode susceptibility without a separate source-backed
policy.
The policy-source gate makes the next requirements explicit: either package source support for conserved-order/fixed-composition susceptibility, package source support for a finite-k or canonical estimator policy, or choose window/dynamics repair without treating an estimator as accepted. The current source package does not accept either replacement path, and the spatial variance proxy remains diagnostic-only.
The source-candidate gate packages fixed-magnetization/canonical ensemble and Cahn-Hilliard
structure-factor source candidates. This is source packaging, not formula acceptance. The
current blocker is now formula extraction and normalization mapping: no candidate source has
been extracted into an accepted conserved-order S(0) policy, finite-k estimator, calibration
factor, or finite-size admissibility rule for exponent gates.
The formula-boundary gate extracts only conservative source boundaries. Fixed-magnetization
and canonical finite-size sources warn that finite systems under conserved constraints cannot
silently supply a canonical zero-mode susceptibility. The Cahn-Hilliard source supports a
finite-k/domain-size review lane, but not an accepted critical xi_2nd replacement. Full-text
formula extraction and UET normalization mapping remain open before any exponent gate can rerun.
The readiness gate records that rendered or abstract source access is enough to preserve claim boundaries but not enough to accept formulas. The next acceptable formula path requires local TeX/PDF math source extraction, exact formula capture, UET lattice normalization mapping, and finite-size admissibility rules before any estimator replacement or exponent rerun.
The localization gate verifies that the three arXiv e-print source archives are present in a
temporary local cache and expose main TeX members (paper-a6.tex, yjdeng0.tex, and
StructureFactor.tex). This is not formula extraction. Raw arXiv sources are not committed,
and the next controller is exact TeX formula-fragment extraction or an explicit source-archive
policy before any UET normalization mapping.
The TeX formula-fragment gate extracts 19 exact formula fragments from the three localized source lanes: fixed-magnetization effective-field/free-energy, canonical finite-size corrections, and Cahn-Hilliard/interconversion structure factor. This narrows the blocker from missing formula extraction to policy acceptance and normalization mapping.
The extracted fragments are not yet accepted as the UET conserved-order scaling estimator. The next hardening step must choose and justify an estimator policy, map source variables into UET normalized lattice units, and define finite-size admissibility before any exponent or universality gate is rerun.