Demonstration proofreading and corrections
Komorebi P. collection; 1 November 2026
Base revision: db5e0ae6e6c51d13d8a0d9b9147b172b971b4046

Scope: all ten Markdown pages in docs/demonstrations/. This is a conservative
proofreading pass over prose, notation, displayed calculations and local
references, with replay of existing checks. No independent proof audit,
literature verification or Lean execution is claimed.

Applied corrections:
1. FACTORIAL_LANES: distinguish the entire omitted step-10 lane,
   (10)_{n;10}=10^n(1)_n=10^n n!, from its Pochhammer factor (1)_n=n!.
2. ROOTS_UNITY_FALLING_FACTORIAL: remove the incorrect description of the
   polynomial-function space over F_3 as having three elements.
3. ROOTS_UNITY_FALLING_FACTORIAL: describe the geometric ratio as different
   from one. A root of unity is a unit in the stated coefficient field.
4. ROOTS_UNITY_FALLING_FACTORIAL: restrict the displayed lowering calculations
   to k>=1 and state separately that differences and derivatives of 1 vanish.
5. FACTORIAL_LANES: say that normalization factors out the leading monomial
   and its coefficient, rather than removing a term by subtraction.
6. STIRLING_BELL_FUBINI: identify the evaluation and moment columns by their
   formulas, rather than ambiguous numerical column positions.
7. STIRLING_BELL_FUBINI: call the mod-3 split a decomposition. It follows a
   parity split but does not refine that partition.
8. WAVELET_POLYPHASE: say that the three displayed squared norms agree.
9. EULER_PACKETS: identify the continuous Z_2 extension as the map whose
   image is the full 2-adic coset, with preimages in Z_2.
10. EULER_PACKETS: identify the zero-centered Appell expansion by its
    generating function instead of referring to an earlier display.
11. REFINEMENT: distinguish exact integer arithmetic from lossless
    reconstruction. The run includes a deliberately discarded packet.

Mathematical-token changes are confined to the scale identity in item 1,
the explicit ranges/constant case in item 4, and the already-constructed
extended domain in item 9. No displayed coefficient table, reciprocal
recurrence, projector, transfer matrix or executable example was changed.

Continuation coverage: PACKETS.md, REFINEMENT.md and RECOVERY.md were read in
full after the seven other pages. Item 11 was the only new objective issue
identified in those introductory pages. No source correction was needed in
PACKETS.md, RECOVERY.md, SEQUENCE_SHAPES.md or HAAR_LAB.md.

Validation:
- 56 existing arithmetic/publication tests passed across factorial lanes,
  wavelets, Stirling/Bell/Fubini, roots/Newton and Euler publication.
- Three Python sequence-preset and interactive-diagram tests passed using
  the pinned Komorebi Math source, without installing a package.
- Nine JavaScript interactive-diagram tests passed, including every Haar
  detail mask and the published introductory examples.
- tools/check_demonstrations.py reproduced all three documented outputs.
- tools/check_euler_case.py reproduced the retained finite Euler results,
  both printed-output blocks and the existing pinned-library comparisons.
  The fresh execution is recorded in euler-packets/cross-check-009/.
- The source pin was a3aa04ac18a523f30c50c7f5dba709f88e904eff; runtime Python
  3.12.14 and NumPy 2.3.5. No scientific confidence label was promoted.

The first local test run encountered Windows CRLF-converted wavelet fixtures
and the default Windows text decoder. Restoring exact Git fixture bytes and
using Python UTF-8 mode resolved those setup failures. The complete selected
suite then passed. No fixture content or executable code was changed.

Earlier execution manifests and reviews retain their original source
identities. The previous manuscript-bound cross-check-008 is historical;
cross-check-009 binds the corrected Euler manuscript to the replayed checks.
The review above does not establish correctness of the broader cited works.
