Foundry F1 — Pure-J Core API Surface
Mapping of the C++ mathematical surface to J Core verbs/nouns.
No implementation. Names, ranks, and domains only.
Preferred license for derivative pure-J work: AGPL-3.0.
Convention: J ranks — 0 atom, 1 list/vector, 2 table/matrix, 3 rank-3. Domains name the mathematical carrier.
Nouns (data carriers)
| Noun |
Rank |
Domain |
Maps from |
Fp |
0 |
atom u64 with (0 \le v < p) |
Goldilocks::Elem |
FpVec |
1 |
list of Fp |
batch Elem arrays |
Signature |
1 |
length-2 integer list (delta_source; delta_target) |
pmc::Signature |
PMatEntry |
1 |
boxed/record: sign (±1), Signature, row, col |
pmc::PMatEntry |
PMat |
1–2 |
sparse list of PMatEntry plus shape (rows; cols) |
pmc::PMat |
Jacobian |
2 |
real matrix ( n\times n ) |
vector<vector<double>> spectral input |
State |
1 |
real vector ( x_t ) |
recurrence state |
Weights |
1 |
length-2 (or dim) real list for Ξ / Λ schedule row |
xi_schedule_[t], lambda_schedule_[t] |
StepInfo |
0–1 |
record: step, q, epsilon, n_xi, n_lam, projected, residual |
pmc::StepInfo |
SpectralResult |
0–1 |
record: spectral_radius, contractive, gershgorin_bound, power_iter_bound, used_power_iteration |
SpectralGovernor::Result |
AceCert |
0–1 |
record: lipschitz_upper, safety_margin, tail_bound, certified |
pmc::AceCertificate |
Tier |
0 |
enum atom T1..T4 |
pmc::Tier |
GatePolicy |
0 |
enum: PassThrough / Suppress / Hold / Attenuate |
pmc::GatePolicy |
P64 |
1 |
length-64 list of first primes |
pmc::P_64 |
PrimeMask |
0 |
u64 bitmask over P64 indices |
pmc::PrimeMask |
ResonanceWord |
0 |
u64 packed class∥payload |
pmc::ResonanceWord |
Named constant nouns (must match PROPERTIES.md)
| Noun |
Rank |
Value source |
GOLDILOCKS_PRIME / p |
0 |
0xFFFFFFFF00000001 = 18446744069414584321 |
EPSILON_FOLD |
0 |
0xFFFFFFFF = (2^{32}-1) (fold; README name EPSILON) |
K_MAX |
0 |
133144 |
MAX_DRIFT |
0 |
300000000000000000 |
PIRTM_MAGIC |
0 |
0x7F504952 |
PHI |
0 |
1.618033988749895 |
tier_epsilon |
0←0 |
T1:0.10 T2:0.05 T3:0.02 T4:0.01 |
Verbs — Goldilocks field
| Verb |
Rank |
Domain → range |
Meaning |
fp_reduce |
0→0 |
u64 → Fp |
conditional ( x-p ) if ( x\ge p ) |
fp_add |
0 0→0 |
Fp×Fp → Fp |
( (a+b)\bmod p ) |
fp_sub |
0 0→0 |
Fp×Fp → Fp |
( (a-b)\bmod p ) |
fp_mul |
0 0→0 |
Fp×Fp → Fp |
mulmod via reduction identity |
fp_mulmod |
0 0→0 |
u64×u64 → u64 |
128-bit product + fold ( \mathrm{lo}+\mathrm{hi_lo}\cdot\varepsilon-\mathrm{hi_hi} ) |
fp_pow |
0 0→0 |
Fp×u64 → Fp |
square-and-multiply |
fp_inv |
0→0 |
Fp → Fp |
( a^{p-2} ) (Fermat) |
fp_add_batch |
1 1→1 |
FpVec×FpVec → FpVec |
elementwise add |
fp_mul_batch |
1 1→1 |
FpVec×FpVec → FpVec |
elementwise mul |
Verbs — PMAT
| Verb |
Rank |
Domain → range |
Meaning |
pmat_new |
0 0→1 |
(rows;cols) → empty PMat |
allocate shape |
pmat_insert |
1 0 0 0 1→1 |
PMat,row,col,sign,Signature → PMat|fail |
domain checks ±1 and bounds |
pmat_validate_grading |
1→0 |
PMat → boolean |
global grading (stated identity) |
pmat_conservation |
1→1 |
PMat → Signature |
Σ monomials |
pmat_compose |
1 1→1 |
PMat×PMat → PMat |
sign multiply + monomial accumulate |
pmat_frobenius |
1→0 |
PMat → real |
( \sqrt{#entries} ) |
Verbs — Spectral governor
| Verb |
Rank |
Domain → range |
Meaning |
gershgorin_bound |
2→0 |
Jacobian → real |
max disk ( |
gershgorin_check |
2 0→1 |
Jacobian,ε → SpectralResult |
contractive iff bound ( <1-\varepsilon ) |
power_iteration |
2 0 0→0 |
Jacobian,max_iters,tol → real |
dominant |eigenvalue| |
power_iteration_check |
2 0 0→1 |
Jacobian,ε,max_iters → SpectralResult |
same contractive predicate |
spectral_analyze |
2 0→1 |
Jacobian,ε → SpectralResult |
Gershgorin then optional power iter |
Verbs — Banach recurrence
| Verb |
Rank |
Domain → range |
Meaning |
tier_eps |
0→0 |
Tier → real |
margin ε |
synth_weights |
0 0 1→2 |
max_steps,Tier,profile,[primes] → (Ξ schedule; Λ schedule) |
Uniform/Harmonic/LogDecay; 0.7/0.3 of ( q^\star ) |
soft_project |
1 1 0 0→1 1 |
Ξ,Λ,q,ε → scaled Ξ,Λ |
scale by ( (1-\varepsilon)/q ) if ( q>1-\varepsilon ) |
rec_step |
1 1 1 1→1 1 |
x, Ξ, Λ, g ; T ; p_op → (x_next; StepInfo) |
( x'=\Xi x+\Lambda T(x)+g ) then project |
rec_run |
1 0→2 |
x0, config, T, p_op → StepInfo history |
until residual < tol or max_steps |
residual_l2 |
1 1→0 |
x_next, x_t → real |
( |x'-x|_2 ) |
q_estimate |
1 1 1 1→0 |
Ξ,Λ,x,Tx → real |
( |\Xi|_\infty+|\Lambda|_\infty\cdot|T| ) (coded max-abs form) |
Transform T and projector p_op are rank-1→1 function nouns (hooks), not fixed verbs.
Verbs — Emission / CSL / certify (math-adjacent)
| Verb |
Rank |
Domain → range |
Meaning |
emit_apply |
1 1 0 0→1 |
out,prev,q,policy×ε → out' |
PassThrough/Suppress/Hold/Attenuate |
csl_neutrality |
1 1 0→0 |
x,Tx,ε → verdict |
pairwise Lip-style bound |
csl_beneficence |
1 1 0 0→0 |
x,Tx,residual,ε → verdict |
norm & residual growth |
csl_commutation |
1 0→0 |
x; T; filter; ε → verdict |
filter∘T ≈ T∘filter |
ace_safety_margin |
0 0→0 |
max_q,ε → real |
( (1-\varepsilon)-\max_q ) |
ace_tail_bound |
0 0→0 |
tail_norm,max_q → real |
( \mathrm{tail}/(1-\max_q) ) or ∞ |
ace_certify |
1 0→1 |
StepInfo list, delta → AceCert |
margin ≥ delta |
Coverage map (C++ → J)
| C++ module |
J surface |
goldilocks.h/cpp |
fp_* verbs + Fp / FpVec |
pmat.h/cpp |
pmat_* + Signature / PMat |
spectral.h/cpp |
gershgorin_* / power_* / spectral_analyze |
recurrence.h/cpp |
rec_* / synth_weights / soft_project / q_estimate |
types.h constants |
constant nouns + tier_eps |
gate.h/cpp (math) |
emit_apply / csl_* |
certify.h/cpp |
ace_* |
Non-math orchestration (SHA-256 WORM bytes, linker PIRTM, audit JSON) is out of this pure-J math Core inventory except where PROPERTIES.md cites seal-chain / consensus narrative for completeness.
