MoneyRoot v0.2 — Lean Elaboration Receipt (human-readable)
============================================================

MANIFEST CHECK (sha256sum -c HANDOFF_MANIFEST.sha256):
  MoneyRoot_v0_2.lean:          OK
  lean-toolchain:                OK
  LEAN_RECEIPT_SUMMARY_v0_1.txt: OK
  CLAUDE_V0_2_HANDOFF.md:        OK

SOURCE FILE:         MoneyRoot_v0_2.lean
SOURCE SHA-256:       97795336a5156fe7301609649967a0d2f35fa18f6eb906f4aba8bbe095284f47   (matches manifest)

TOOLCHAIN FILE:       lean-toolchain
TOOLCHAIN SHA-256:     302cd63c54178885b89e669f33b38f12f4dd7ae7e5cac537b3203e3768d8fb2b   (identical to v0.1 — no re-download needed)
TOOLCHAIN SELECTOR:   leanprover/lean4:v4.33.0

LEAN VERSION (exact):
  Lean (version 4.33.0, x86_64-unknown-linux-gnu,
  commit d8b18978322de05a8f3dba51ef03cf5461676c17, Release)

COMMAND RUN:          lean MoneyRoot_v0_2.lean
EXIT CODE:            0

STDOUT:               <empty — 0 bytes — sha256 e3b0c442...b855, the hash of the empty string>
STDERR:               <empty — 0 bytes — sha256 e3b0c442...b855, the hash of the empty string>
  (Empty output on exit 0 is the correct signature of a fully clean
   elaboration with zero errors, warnings, or 'sorry' notices.)

POST-RUN INTEGRITY CHECK:
  MoneyRoot_v0_2.lean re-hashed after the run: 97795336a5156fe7301609649967a0d2f35fa18f6eb906f4aba8bbe095284f47
  -> identical to the pre-run hash above. Source was not modified.

GREP FOR sorry / admit / axiom IN SOURCE:
  0 matches.

AXIOM DEPENDENCY CHECK (empirical, via `#print axioms`, run on a separate
scratch copy — the certified MoneyRoot_v0_2.lean above was never edited):
  T1_injective_iff_read_equality_reflects_state ............ no axioms
  T2_factorization_iff_fiber_refinement ..................... Quot.sound only
  T2_eqkernel_inclusion_iff_fiber_refinement ................ no axioms
  T4_left_inverse_implies_injective ......................... no axioms
  T6_supplement_sufficient_iff_joint_equalities ............. no axioms
  T6_sufficient_supplement_separates_residual_pair .......... no axioms
  T6_decision_read_is_sufficient_supplement ................. no axioms
  T6_trivial_supplement_iff_base_sufficient ................. no axioms
  T6_info_trans .............................................. no axioms
  PriceSchema.collision ...................................... no axioms

  Quot.sound is one of Lean's three built-in kernel primitives for
  quotient types (the others being propext and Classical.choice) — it is
  not an optional or "smuggled" axiom, and every theorem that goes through
  ReadQuot/Quot.lift needs it. No theorem anywhere in the file — T1-T6 or
  the schema witnesses — depends on propext or Classical.choice. All of
  T6 specifically is axiom-free: SupplementSufficient is defined directly
  via FiberRefines/JointRead, without routing through the Quot apparatus
  at all.

STATUS:               LEAN_ELABORATION = CERTIFIED  (v0.2, T6 included)
SCOPE:                 Certifies only elaboration of the supplied pure
                       theorem kernel under the pinned toolchain. Does not
                       certify any empirical economic or legal adapter, and
                       does not certify existence of a canonical minimum
                       supplement (that remains an open, separately-typed
                       question — see semantic review below).


SEMANTIC REVIEW OF T6 (as requested)
============================================================

1. Direction of SupplementSufficient's fiber refinement — CORRECT.
   SupplementSufficient R S D := FiberRefines (JointRead R S) D means:
   whenever R x = R y AND S x = S y, then D x = D y. That's exactly
   "the joint read is fine enough to determine D," which is what
   "S is a sufficient supplement to R for D" should mean. The unpacked
   form (T6_supplement_sufficient_iff_joint_equalities) confirms this via
   Prod.ext / congrArg Prod.fst / congrArg Prod.snd in both directions —
   checked, both directions are valid.

2. Orientation of ReadNoMoreInformative S T — CORRECT, and the stated
   equivalence in the doc comment is accurate. The definition
   (∀ x y, T x = T y → S x = S y) does mean "every equality T preserves,
   S also preserves" — and by contraposition, "every distinction S makes,
   T also makes," i.e. T is at least as informative as S. Reflexivity and
   transitivity are both proved and both actually preserve that direction
   under inspection (T6_info_trans correctly chains h23 then h12, not the
   reverse) — this is a genuine, correctly-oriented preorder.

3. Classical choice / decidable equality / stronger structure — NONE
   found in T1-T6. Confirmed by direct axiom inspection (table above), not
   just by reading: only Quot.sound appears, only in the one theorem that
   needs it, and it's a Lean kernel primitive, not Mathlib or classical
   logic. `DecidableEq`/`decide` appear only inside the four schema
   witness namespaces, confined to concrete finite illustrations, never
   inside T1-T6 themselves.

4. "Decision is its own sufficient supplement" — CORRECTLY labeled as an
   existence upper bound. T6_decision_read_is_sufficient_supplement shows
   SupplementSufficient R D D holds trivially (D trivially determines D),
   and the doc comment explicitly disclaims that this says nothing about
   D being an appropriate observable or policy input. That's accurate: the
   result is real but circular in the practical sense, and the source
   doesn't oversell it as anything more.

5. No-canonical-minimum stop line — MATHEMATICALLY WARRANTED, not just a
   cautious hedge. ReadNoMoreInformative is proved reflexive and
   transitive, i.e. a genuine preorder — but a preorder alone does not
   generally have a least element among "sufficient supplements" without
   more structure: you'd need a specific candidate class (e.g. a fixed
   type of allowed supplements) and a proof that class has meets/infima
   under this order. Two sufficient supplements can be incomparable, and
   nothing in T6 constructs a canonical "meet" of two reads. Stopping
   here rather than asserting a minimizer is the correct call, not an
   understatement.

Net read: v0.2 does what the handoff says it does. T1-T5 unchanged and
still standard function/fiber facts, not novel to money. T6 is a real,
correctly-typed, axiom-light (mostly axiom-free) formalization of "what
must a supplement preserve to fix an insufficiency," and it stops exactly
where a canonical-minimum claim would have required unjustified extra
structure. No naming, direction, or strength issues found.
