research/verify_design.py

"""Internal mathematical consistency; no experimental-performance validation."""
from pathlib import Path
import csv,json,math,itertools

OUT=Path(__file__).resolve().parent
layers=[('L0',60,'H-S contact film'),('L1',100,'Shared load spreading and travel-stop allocation'),('L2',300,'Matched A/R sensing elements; optional isolated trace wells'),
        ('L3',80,'Isolation septum'),('L4',240,'W0/WG-C coupling, stable reference, archive and identity'),('L5',100,'Material terminals'),
        ('L6',620,'Recoil dermis'),('L7',100,'Attachment')]
params={'release':'3.0','status':'final standalone technology-aligned material blueprint; integrated performance untested','title':'Ørïelith//9 - The Skin of an Impossible Angel',
        'patch_mm':[20,20,1.6],'active_field_mm':[16,16],'taxels':[16,16],
        'pitch_um':1000,'island_um':[700,700],'centers_mm':'x=2.5+i, y=2.5+j; i,j=0..15',
        'cavity_um':{'diameter':500,'depth':100,'diaphragm':20},
        'ionic_transport_lengths_um':[5,15,50],'illustrative_D_m2_per_s':1e-11,
        'witness_ligament_um':[100,10,5],'ligaments_per_taxel':4,'witness_active_length_um':20,
        'tag':{'carrier_um':[220,140,30],'grid':[16,8],'pitch_um':10,'site_diameter_um':6,
               'code':'RM(1,7)','number_of_codewords':256,'length':128,'minimum_distance':64,
               'id':'16*j+i','a':'seven low ID bits','b':'highest ID bit','site':'x=16*row+column'},
        'material_terminal_channel_um':[40,30],'terminal_min_septum_um':10,
        'qualification_temperature_C':[20,40],
        'ambient_repair_screen':{'temperature_C':20,'relative_humidity_percent':40,'duration_h':24,'requires':'clean host faces recontacted; all assembled outcomes measured separately'},
        'tolerances_targets':{'layer_fraction':0.10,'registration_um':25,'tag_site_placement_um':2},
        'gates_are_targets_not_results':True,
        'unresolved':['ionic barrier qualification','W0/WG and C-SH cure/deprotection and interphase qualification',
                      'skin-scale writer activation window','elastically active WG-C capture and retained force recruitment',
                      'stable calibrated reference and matched translation','loaded travel-stop validation','permanent tag chemistry',
                      'full terminal routing mask','assembled functional healing'],
        'writable_tether':{'topology':'active sensor ki in series with g_A; parallel stable reference K_R and shared host bypass B',
              'ledger':'reduced g=g0-a_loss*m+b_gain*r; 0<=r<=min(m,theta); add -L_B for separately activated inaccessible bulk',
              'inventory_reference':'measured force-bearing interface-eligible writer population N_I; not all bulk feed',
              'settled_requirement':'b_gain*chi>a_loss AND fractional Ks growth exceeds fractional Kb growth',
              'nano_reaction_reach_target_nm':5,'receiver_coat_um':2,'reactive_cassette_to_exposed_host_um':5,
              'support_W0_um':4.9,'writer_WG_nominal_nm':100,'writer_WG_tolerance_nm':20,
              'WG_screened_DA_mmol_per_10mmol_HMA':[0.05,0.1,0.25],
              'reference_KR_N_m':20,'travel_stop_measured_upper_target_um':50,
              'fine_post_footprint_um':[100,100],
              'active_post_centers_um':[[100,100],[-100,-100]],
              'reference_post_centers_um':[[100,-100],[-100,100]],
              'example_N_per_m':{'ki':100,'g0':25,'g1':200,'Kb':80,'a_loss':10,'b_gain':185}}}
cum=0
for code,t,role in layers:
    params.setdefault('layers',[]).append({'layer':code,'z0_um':cum,'z1_um':cum+t,'thickness_um':t,'role':role});cum+=t
assert cum==1600
with (OUT/'design_parameters.json').open('w') as f:json.dump(params,f,indent=2,ensure_ascii=False)
with (OUT/'layer_stack.csv').open('w',newline='') as f:
    wr=csv.DictWriter(f,fieldnames=['layer','z0_um','z1_um','thickness_um','role']);wr.writeheader();wr.writerows(params['layers'])
recipes=[
 ['H-S','Aminopropyl-terminated PDMS; nominal Mn5000','2.400',5000,12,'4.800 NH2','use measured amine equivalent weight'],
 ['H-S','4,4-methylenebis(cyclohexyl isocyanate) MCI/H12MDI','1.680',262.35,0.440748,'3.360 NCO','ACTIVE mass; divide by actual assay for reagent mass'],
 ['H-S','1,3,5-Triformylbenzene TFB','0.480',162.14,0.0778272,'1.440 CHO','ACTIVE mass; divide by actual assay; imine water removed'],
 ['I-30','Purified CLPU@E5','not specified','',7,'','prequalified polymer; not a generic chlorinated resin'],
 ['I-30','EMIM-TFSI','not specified','',3,'','30 wt% of total dry blend'],
 ['W0','n-Hexyl methacrylate','10.000',170.25,1.7025,'10 vinyl','writer-free permanent support'],
 ['W0','Ethylene glycol dimethacrylate','0.100',198.22,0.019822,'0.200 vinyl','support must remain percolating'],
 ['W0','Dibenzoyl peroxide active compound','0.020',242.23,0.0048446,'','initiator screening input; no cure schedule asserted'],
 ['WG high-feed screen','n-Hexyl methacrylate','10.000',170.25,1.7025,'10 vinyl','untested 100nm gate-coat candidate'],
 ['WG high-feed screen','Ethylene glycol dimethacrylate','0.100',198.22,0.019822,'0.200 vinyl','coat anchoring and retention require qualification'],
 ['WG high-feed screen','Published compound 8 DOI10.1039/C5SC03297K','0.250','verify','derive from verified MW','0.500 vinyl','also screen0.050 and0.100mmol; higher feed is not necessarily better'],
 ['WG high-feed screen','Dibenzoyl peroxide active compound','0.020',242.23,0.0048446,'','initiator screening input; no cure schedule asserted'],
 ['C-SH protected','n-Hexyl methacrylate','9.500',170.25,1.617375,'9.500 vinyl','untested receiver feed'],
 ['C-SH protected','2-(Acetylthio)ethyl methacrylate AcSEMA','0.500',188.24,0.09412,'0.500 vinyl; 0.500 protected SH','C8H12O3S; separate deprotection and assay required'],
 ['C-SH protected','Ethylene glycol dimethacrylate','0.100',198.22,0.019822,'0.200 vinyl','permanent receiver network'],
 ['C-SH protected','Dibenzoyl peroxide active compound','0.020',242.23,0.0048446,'','initiator screening input'],
]
with (OUT/'chemical_formulations.csv').open('w',newline='') as f:
    wr=csv.writer(f);wr.writerow(['formulation','ingredient','amount_mmol','MW_g_mol','mass_g','group_amount_mmol','qualification']);wr.writerows(recipes)

words=[]
for ident in range(256):
    a=ident&127;b=ident>>7
    w=sum((((a&x).bit_count()%2)^b)<<x for x in range(128))
    words.append(w)
mind=min((a^b).bit_count() for a,b in itertools.combinations(words,2))
assert len(set(words))==256 and mind==64
times={str(L):((L*1e-6)**2/(math.pi**2*1e-11)) for L in (5,15,50)}
Hstar=.8;Mstar=.9;t=86400
ratio=-math.log1p(-Hstar)/(-math.log(Mstar))
kH=-math.log1p(-Hstar)/t;kM=-math.log(Mstar)/t
hs_mass=sum(float(r[4]) for r in recipes if r[0]=='H-S')
assert math.isclose(hs_mass,12.5185752,abs_tol=1e-8)
report={
 'purpose':'mathematical and dimensional consistency only; no experimental data',
 'layer_sum_um':cum,'taxel_count':256,'last_center_mm':17.5,'active_field_limits_mm':[2,18],
 'HS_NH2_mmol':4.8,'HS_NCO_mmol':3.36,'HS_CHO_mmol':1.44,'HS_group_balance_difference_mmol':4.8-3.36-1.44,
 'HS_active_feed_g':hs_mass,'MCI_reagent_g_at_exact_90percent_assay':.440748/.9,
 'TFB_reagent_g_at_exact_98percent_assay':.0778272/.98,'HS_formal_imine_water_g':.00144*18.015,
 'ionic_liquid_weight_fraction':3/(7+3),'ionic_diffusion_tau_s_at_D1e-11':times,
 'Dlat_max_m2_s_for_10um_blur_25s':(10e-6)**2/(2*25),
 'Dlat_max_m2_s_for_10um_blur_24h':(10e-6)**2/(2*86400),
 'healing_archive_selectivity_ratio_min':ratio,
 'kH_min_for_80percent_in_24h_s-1':kH,'kM_max_for_90percent_in_24h_s-1':kM,
 'kM_max_for_90percent_24h_s-1':-math.log(.9)/86400,
 'archive_decay_time_days_for_90percent_24h':(-math.log(.9)/86400)**-1/86400,
 'RM_codewords':256,'RM_pairwise_comparisons':256*255//2,'RM_dmin':mind,'RM_max_correctable_arbitrary_errors':31,
 'witness_fraction_excluding_anchors':4*100*10*5/(700*700*240),
 'hypothetical_ligament_stress_gain_per_load_fraction':math.pi*250**2/(4*10*5),
 'hypothetical_ligament_stress_MPa_at_200kPa_1percent_axial_loadshare':200000*.01*math.pi*250**2/(4*10*5)/1e6,
 'nominal_cavity_loads_mN':{str(p):p*1000*math.pi*(250e-6)**2*1000 for p in (20,80,200)},
 'tile_envelope_volume_cm3':.64,'tile_mass_g_if_all_density1p1':.64*1.1,
 'nominal_200kPa_load_N_tile':200000*.02*.02,'nominal_200kPa_load_N_active':200000*.016*.016,
 'thermal_diffusion_s_at_alpha1e-7':{'0.5mm':(.0005**2)/1e-7,'1.6mm':(.0016**2)/1e-7},
 'all_checks_passed':True}
def mechanics(g,ki=100.0,kb=80.0,force=20000*math.pi*(250e-6)**2):
    ks=ki*g/(ki+g);total=ks+kb;phi=ks/total
    return {'g_N_m':g,'Ks_N_m':ks,'Ktotal_N_m':total,'phi':phi,
            'overall_indentation_um':force/total*1e6,'receptor_force_mN':phi*force*1000,
            'receptor_extension_um':phi*force/ki*1e6,
            'pressure_for_1mN_kPa':.001/(math.pi*(250e-6)**2*phi)/1000}
initial=mechanics(25);written=mechanics(200)
assert math.isclose(written['phi']/initial['phi'],25/11,rel_tol=1e-12)
assert written['Ktotal_N_m']>initial['Ktotal_N_m'] and written['overall_indentation_um']<initial['overall_indentation_um']
assert mechanics(200,kb=400)['phi']<initial['phi']
assert mechanics(25-10+185*.04)['phi']<initial['phi']
area=math.pi*(250e-6)**2
phimax=100/(100+80)
report['force_recruitment']={'initial':initial,'written':written,'local_gain_ratio':written['phi']/initial['phi'],
    'relative_total_stiffness_increase':written['Ktotal_N_m']/initial['Ktotal_N_m']-1,
    'phi_ceiling':phimax,'gain_ceiling':phimax/initial['phi'],
    'minimum_1mN_threshold_kPa':.001/(area*phimax)/1000,
    'counterexample_bypass400_N_m':mechanics(200,kb=400),
    'counterexample_capture_yield_0p04':mechanics(25-10+185*.04)}

# Check the nonlinear implicit derivative against independently solved equilibria.
def equilibrium(load,z,beta):
    def ext(q):return q+.1*q**3+q/(1+z)+.05*(q/(1+z))**3
    lo=0.;hi=load
    for _ in range(80):
        q=(lo+hi)/2;u=ext(q)
        if q+(1+beta*z)*(u+.2*u**3)>load:hi=q
        else:lo=q
    return (lo+hi)/2
max_error=0.;nchecks=0
for load in (.1,.5,1.,2.,4.):
 for z in (.1,.3,.8,1.4,2.):
  for beta in (0.,.3,1.,3.):
    q=equilibrium(load,z,beta)
    u=q+.1*q**3+q/(1+z)+.05*(q/(1+z))**3
    bd=(1+beta*z)*(1+.6*u*u);bz=beta*(u+.2*u**3)
    uip=1+.3*q*q;ugf=1/(1+z)+.15*q*q/(1+z)**3
    ugz=-q/(1+z)**2-.15*q**3/(1+z)**4
    exact=-(bd*ugz+bz)/(1+bd*(uip+ugf))
    eps=1e-5
    numerical=(equilibrium(load,z+eps,beta)-equilibrium(load,z-eps,beta))/(2*eps)
    max_error=max(max_error,abs(exact-numerical));nchecks+=1
assert max_error<1e-8
report['nonlinear_implicit_derivative_check']={'dimensionless_test_equilibria':nchecks,'max_abs_error':max_error,
   'scope':'independent equilibrium-root finite difference against analytic derivative; not an experimental constitutive model'}

# Explicit finite-capacity illustrative trajectory. Every output is model-only.
force=20000*area;delta_g0=initial['phi']*force/25
def rhs(state):
    m,r=state;g=25-10*m+185*r
    mech=mechanics(g,force=force);dg=mech['phi']*force/g
    kw=.03*math.exp(4*dg/delta_g0)
    return kw*(1-m),5*(m-r)*(1-r)
def rk4(state,dt):
    k1=rhs(state);k2=rhs(tuple(state[j]+dt*k1[j]/2 for j in (0,1)))
    k3=rhs(tuple(state[j]+dt*k2[j]/2 for j in (0,1)))
    k4=rhs(tuple(state[j]+dt*k3[j] for j in (0,1)))
    return tuple(state[j]+dt*(k1[j]+2*k2[j]+2*k3[j]+k4[j])/6 for j in (0,1))
state=(0.,0.);dt=.01;trajectory=[];min_g=25.
for step in range(6001):
    m,r=state;g=25-10*m+185*r;min_g=min(min_g,g)
    assert -1e-9<=r<=m+1e-9 and m<=1+1e-9 and r<=1+1e-9
    if step%50==0:
        me=mechanics(g,force=force)
        trajectory.append([step*dt,m,r,g,me['phi'],me['Ktotal_N_m']])
    state=rk4(state,dt)
with (OUT/'illustrative_capture_trajectory.csv').open('w',newline='') as f:
    w=csv.writer(f);w.writerow(['model_time_s','opened_fraction_m','captured_fraction_r','g_N_m','receptor_force_fraction','Ktotal_N_m']);w.writerows(trajectory)
assert min_g<25 and min_g>15
report['illustrative_kinetics']={'kw_law':'0.03*exp(4*delta_g/delta_g_initial) s^-1',
   'kc_normalized':5,'theta':1,'integration':'RK4 dt=0.01s; 60s, no fitted data',
   'inventory_reference':'interface-eligible N_I; reduced model assumes no inaccessible bulk activation (L_B=0)',
   'min_g_N_m':min_g,'last_record':trajectory[-1],
   'warning':'initial softening is present; finite capacity does not guarantee fracture protection'}
report['receiver_protected_feed_g']=sum(float(r[4]) for r in recipes if r[0]=='C-SH protected')
report['formal_receiver_deacetylation_mass_loss_g']=.0005*42.037
assert math.isclose(report['receiver_protected_feed_g'],1.7361616,abs_tol=1e-10)
cD=1000/.17025*.005;gamma=cD*5e-9
report['upper_bound_accessible_writer_inventory']={'assumed_density_kg_m3':1000,'assumed_writer_repeat_fraction':.005,
   'assumed_accessible_depth_nm':5,'cD_mol_m3':cD,'gamma_mol_m2':gamma,
   'sites_per_1000_um2':gamma*1e-9*6.02214076e23,'fraction_of_uniform_5um_film_one_face':5e-9/5e-6,
   'scope':'uniform bulk CONTROL; not the final gate-coat design or measured active-link density'}
report['illustrative_kinetics']['configuration']='reference-free control only; final referenced module is verified below'

def paired(g, kb=80., load=20000*area, kr=20., ki=100.):
    ka=ki*g/(ki+g);total=ka+kr+kb;delta=load/total
    fa=ka*delta;fr=kr*delta
    return {'KA_N_m':ka,'KR_N_m':kr,'Ktotal_N_m':total,'delta_um':delta*1e6,
            'FA_mN':fa*1000,'FR_mN':fr*1000,'Q':fa/fr,
            'xg_um':fa/g*1e6,'xi_um':fa/ki*1e6,
            'P_for_active_1mN_kPa':.001/(area*ka/total)/1000}
pa=paired(25);pb=paired(200)
assert math.isclose(pb['FA_mN']/pa['FA_mN'],2.4,rel_tol=1e-12)
assert math.isclose(pb['Q']/pa['Q'],10/3,rel_tol=1e-12)
qerr=max(abs(paired(g,kb)['Q']-paired(g,80)['Q']) for g in (25,50,100,150,200) for kb in (0,10,80,200,1000))
assert qerr<1e-12
g_from_ratio={str(rho):100*rho*20/(100-rho*20)for rho in (1,2,3)}
assert all(math.isclose(paired(g)['Q'],float(rho),rel_tol=1e-12)for rho,g in g_from_ratio.items())
report['final_referenced_module']={'initial':pa,'written':pb,'actual_FA_gain':pb['FA_mN']/pa['FA_mN'],
    'reference_ratio_gain':pb['Q']/pa['Q'],'host_bypass_invariance_max_abs_error':qerr,
    'tested_Kb_N_m':[0,10,80,200,1000],'g_programmed_from_Q_N_m':g_from_ratio,
    'Q_architectural_ceiling':5,'cannot_infer':'absolute pressure without total-force/bypass calibration'}

# Nonlinear reconstruction: independently solve branches and total equilibrium.
def invert_monotone(fn,value,hi0=1.):
    lo=0.;hi=hi0
    while fn(hi)<value:hi*=2
    for _ in range(85):
        mid=(lo+hi)/2
        if fn(mid)>value:hi=mid
        else:lo=mid
    return (lo+hi)/2
ui=lambda q:q/2+.03*q**3
ug=lambda q,z:q/(1+z)+.02*(q/(1+z))**3
ref=lambda d:1.3*d+.1*d**3
records=[];max_recon=0.
for z in (0.,.5,1.,2.):
 for kb in (.2,1.,3.):
  for load in (.1,.3,.6,1.,1.5,2.):
    aforce=lambda d:invert_monotone(lambda q:ui(q)+ug(q,z),d)
    delta=invert_monotone(lambda d:aforce(d)+ref(d)+kb*d+.15*d**3,load)
    fa=aforce(delta);fr=ref(delta)
    x_recon=invert_monotone(ref,fr)-ui(fa);x_true=ug(fa,z)
    max_recon=max(max_recon,abs(x_recon-x_true))
    records.append([z,kb,load,fa,fr,delta,x_recon,x_true])
assert max_recon<1e-11
with (OUT/'nonlinear_reference_reconstruction.csv').open('w',newline='')as f:
    w=csv.writer(f);w.writerow(['model_state_z','model_host_kb','model_total_force','active_force','reference_force','true_translation','reconstructed_tether_extension','true_tether_extension']);w.writerows(records)
report['nonlinear_reference_reconstruction']={'model_equilibria':len(records),'max_absolute_extension_error':max_recon,
    'scope':'dimensionless monotone nonlinear constitutive models; no measured material properties'}

# Antipodal footprint and affine-tilt test (all contacts engaged).
posts={'A':[(100,100),(-100,-100)],'R':[(100,-100),(-100,100)]}
assert all(math.hypot(x+dx,y+dy)<250 for pts in posts.values()for x,y in pts for dx in (-50,50)for dy in (-50,50))
delta0=30.;v=(.03,-.04)
sumA=sum(10*(delta0+v[0]*x+v[1]*y)for x,y in posts['A'])
sumR=sum(10*(delta0+v[0]*x+v[1]*y)for x,y in posts['R'])
assert math.isclose(sumA/sumR,1.)
report['antipodal_geometry']={'footprints_inside_radius250um':True,'matched_affine_tilt_ratio':sumA/sumR,
    'scope':'linear matched positive-contact model; no plate-bending validation'}

# Loaded-travel requirement, not a promise from a nominal gap.
travel=50e-6;ka_max=pb['KA_N_m'];kr=20;kb=80
report['conditional_loaded_travel_limit']={'required_measured_delta_max_um':50,
    'FA_max_mN':ka_max*travel*1000,'FR_max_mN':kr*travel*1000,
    'each_active_post_force_cap_mN':ka_max*travel*1000/2,
    'active_sensor_extension_um':ka_max*travel/100*1e6,
    'generic_g_infinite_FA_bound_mN':100*travel*1000,
    'ideal_stop_onset_kPa_initial':travel*(pa['KA_N_m']+kr+kb)/area/1000,
    'ideal_stop_onset_kPa_written':travel*(pb['KA_N_m']+kr+kb)/area/1000,
    'ideal_stop_force_at200kPa_mN_initial':(200000*area-travel*(pa['KA_N_m']+kr+kb))*1000,
    'ideal_stop_force_at200kPa_mN_written':(200000*area-travel*(pb['KA_N_m']+kr+kb))*1000,
    'scope':'conditional idealized upper-travel contract; finite stop compliance, impact and survival require tests'}
assert pa['delta_um']<50 and pb['delta_um']<50
errx=5e-6/20+5e-6/100
report['example_force_error_budget']={'assumed_each_force_error_uN':5,'extension_error_bound_um':errx*1e6,
    'written_xg_um_at20kPa':pb['xg_um'],'scope':'assumed readout error; calibration and mismatch errors excluded'}
gamma_new=1000/.17025*.025*5e-9
report['surface_writer_geometry_budget']={'WG_nominal_thickness_nm':100,'WG_thickness_tolerance_nm':20,
    'W0_support_um':4.9,'assumed_accessible_depth_nm':5,'accessible_fraction':.05,
    'geometric_utilization_ratio_vs5um_control':50,'gamma_upper_mol_m2':gamma_new,
    'areal_inventory_ratio_vs_control':gamma_new/gamma,
    'total_writer_per_area_ratio_vs_control':(1000/.17025*.025*100e-9)/(cD*5e-6),
    'scope':'approximate HMA-repeat inventory geometry; not sensitivity, activation or yield'}
(OUT/'calculation_report.json').write_text(json.dumps(report,indent=2))
print(json.dumps({'all_checks_passed':True,'host_feed_g':hs_mass,'final_referenced_module':report['final_referenced_module'],
      'nonlinear_reconstruction':report['nonlinear_reference_reconstruction'],
      'stop':report['conditional_loaded_travel_limit'],'surface_writer':report['surface_writer_geometry_budget']},indent=2))