# Reviewer Overview: Active-Route Collatz Proof Package

This archive contains a review package for a proposed active-route constructive
proof of the Collatz conjecture. The package reduces the proof obligation to
five explicit bridge targets: global entry / Lemma 1a, finite launch menu,
finite splice menu, bounded-tail splice, and (R, lambda) determinism /
finiteness / stock splice. No infinite mechanism remains outside this finite
structure. The purpose of this overview is not to replace the
proof files, but to give reviewers a short map of what to check.

## Core Idea

All theorem-relevant trajectories are forced into a finite audited structure.
On the cheap-side, Lemma 1a gives global entry: every live branch reaches a
canonical continuation object Sigma(q_*), or enters admitted downstream stock.
On the core-side, terminal, continuation, and feeder contributions are absorbed
by a finite stock/splice system through Appendices C, D, and E. On the standard
side, the final bridge uses negation conjugacy, low-valued re-entry, finite
launch/splice stock, and strict descent to close the ordinary Collatz dynamics.

One central active-route splice is:

13-bank -> 125 (mod 512) -> 486w + 121 -> 13122t + 1333 -> finite closure.

Thus every trajectory is either terminated, absorbed into finite stock, or
reduced to a strictly smaller odd integer, and no trajectory can avoid this
classification.

## Term Translation

The review files use some short internal terms. For checking purposes:

- `stock` means a previously proved terminal, descent, or capture class.
- `splice` means a transition into such a previously proved class.
- `terminal lift-menu closeout` means a finite directed-graph check on terminal
  continuation states: edges are the allowed type-`D` terminal transitions, and
  the proof checks that no reachable directed cycle remains in that graph.
- `no autonomous infinite mechanism` means that no reachable directed cycle or
  unclassified continuation type remains outside the proved classes.

## Proof Architecture

Reachability -> Identification -> Input A -> Input B -> Lemma 1a ->
core-side global closure -> standard-side strict descent -> Collatz theorem.

The review package is organized so that each arrow is tied to a named carrier
file or finite verification artifact. The main proof-stock file is:

ACTIVE/foundation/active_route_proof_stack.md

The readable concept guide is:

Proof_Concept.md / Proof_Concept.pdf

The main review entry point is:

ACTIVE/review/README_FOR_REVIEW.md

## Key Features

- Finite-state projection K = (C, t mod 2, p) for active live branches.
- Explicit finite directed-graph check eliminating infinite type-D terminal
  continuations.
- Exhaustive residual menu classification for terminal splice branches.
- Exact feeder splice route with finite reducer verification.
- Separation between theorem-facing proof carriers and audit certificates.
- A dependency matrix that asks reviewers to attack five bridge targets rather
  than reading the archive as one undifferentiated file tree.

## Finite Verification Boundary

Finite scripts and JSON artifacts are included as reproducible verification
boundaries for bounded ledgers and certificates. They do not replace the
theorem-facing proof carriers. In particular, terminal K coverage is recorded
as verified under the manuscript terminal continuation finite-graph interface,
not as a claim that the script alone proves full branch exhaustiveness.
Independent audit of the computer-assisted components is a separate validation
step.

## Recommended Reading Order

1. ACTIVE/review/README_FOR_REVIEW.md
2. Proof_Concept.md / Proof_Concept.pdf
3. ACTIVE/review/dependency_matrix.md
4. ACTIVE/review/final_review_manuscript.md
5. ACTIVE/foundation/active_route_proof_stack.md
6. ACTIVE/review/modules/lemma1a_active_line.md
7. ACTIVE/review/modules/core_side_global_closure.md
8. ACTIVE/review/modules/appendix_C_feeder_splice.md
9. ACTIVE/review/modules/appendix_D_suffix_pullback.md
10. ACTIVE/review/modules/appendix_E_3939_package.md
11. Named imports, proved_lemmas, scripts, and certificates as cited.

## Reviewer Challenge

Please try to break one of the five bridge targets:

1. global entry / Lemma 1a
2. finite launch menu
3. finite splice menu
4. bounded-tail splice
5. (R, lambda) determinism / finiteness / stock splice

The proof is complete if and only if all five bridge targets are correct.

If all five bridge targets withstand review, the package's assembled route
gives the Collatz theorem through the standard minimal-counterexample descent
argument.
