F419 sealed source contract

Schema:
  symcc-loop-memoryphi-byte-lane-induction-v9

Capability:
  bounded-nested-loop-memoryphi-affine-symbolic-value-summary

Dependencies:
  bounded-symbolic-alias
  bounded-loop-memoryphi-byte-lane-induction
  bounded-strided-loop-memoryphi-byte-lane-induction when required
  bounded-nested-loop-memoryphi-summary-composition
  bounded-nested-loop-memoryphi-last-write-value-summary
  bounded-nested-loop-memoryphi-two-dimensional-affine-summary

Address form:
  the exact F418 two-dimensional affine address domain

Value form:
  V(o,i,x) = constant + outer_scale*o + inner_scale*i + input_scale*x
             modulo 2^bits

Sealed limits:
  exact two-level F418 topology and finite instance domain
  byte-complete integer store width 8..64 bits
  same-width ConstantInt, outer IV, inner IV, or at most one entry argument
  add or multiplication by a direct positive constant
  expression depth <= 4 and definition in the inner body before the store
  non-negative constant/coefficient values <= INT64_MAX
  at least one nonzero symbolic coefficient
  source nuw/nsw, sub, multiple inputs, cross-block and deep formulas rejected

Input binding:
  exact argument SSA variable
  contiguous unique input bytes
  little-endian identity/zext, shl, or assembly
  recorded offset and byte count

Last-write order:
  descending outer induction
  descending inner induction
  descending writer ordinal

Activation:
  outer_bound >= outer_induction_value + 1 AND
  inner_bound >= inner_induction_value + 1

Value witness:
  IV terms specialized modulo 2^bits for each writer instance
  input term remains symbolic
  byte low_bit derived from target endianness
  constant writers use constant-byte overlays

Fallback:
  uninitialized when no case is active, never implicit zero
  unsupported producer shapes do not receive a partial v9 certificate

Runtime boundary:
  no loop skipping, memory prefill, or store replacement
  real loop execution and path-local byte-init bitmap remain authoritative