Three new proof files over the CurveField extraction, composing the proven
group-law layer (no new axioms, no associativity assumed — computational
layering over the abstract `edAdd`):
- `Proofs/DsmTableSpec.lean` — `NafLookupTable5::from(&A)`: the 8 entries
are valid `ProjectiveNielsPoint` caches of valid on-curve points denoting
the odd multiples A, 3A, ..., 15A as the `edOdd` double-and-add recursion.
7 explicit loop peels over edwards_as_projective_niels_spec /
add_projniels_law / compl_as_extended_law, seeded by edwards_double_law.
`select`: both masserts (x odd, x < 16) DISCHARGED — panic-freedom is
proven, not assumed; post enumerates all 8 digit cases.
- `Proofs/DsmStepSpec.lean` — `proj_double_law` (the projective doubling
denotes `edAdd P P`; same Z^2-scaled linear_combination discipline as the
extended-coordinate law), `compl_as_projective_law` ((X:Z),(Y:T) to
(XT:YZ:ZT) preserves the point), `naf_select_entry` (digit-indexed lookup
returns THE entry: NafEntryOf r A ((x-1)/2)), and `dsm_step_p_law` /
`dsm_step_b_law`: the three-way NAF digit step denotes `edDigit` — add
the d-th odd multiple, add its negation, or pass through.
- `Proofs/DsmLoopSpec.lean` — the 256-iteration Straus loop by GENUINE
induction on the counter (one symbolic body walk, no unrolling):
`dsm_loop_spec` — from the identity, the loop returns a valid on-curve
point denoting `dsmFold ... edId 256`, the abstract double-and-add fold
of both digit arrays over the table points. Digit and table hypotheses
are exactly what the NAF spec and naf_table_spec provide (layering).
check.sh wired: PROOFS + AUDIT_IMPORTS + 7 new CERTS (naf_table_spec,
naf_select_spec, proj_double_law, compl_as_projective_law, dsm_step_p_law,
dsm_step_b_law, dsm_loop_spec), each `#print axioms`-audited to exactly
[propext, Classical.choice, Quot.sound]. Full check.sh green.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
