# K4 alternatives grounded in K1–K3

This focused investigation found no K4 solution. It produced a finite exclusion for two explicit K3-derived rearrangements and strengthened the case for treating the clock as part of Sanborn's narrative rather than automatically as encryption machinery.

The authorized native goal ceiling is 2,000,000 tokens across the coordinator and existing Luna workers. The ceiling is not a target. Final accounting is retained separately after verification.

## New computational result

The published working K3 recipe rotates a 336-character grid clockwise at width 24, then rewrites and rotates at width 8. Our full K3 known-answer control reproduces its plaintext exactly. The source does not prescribe a 97-character K4 extension. [Published walkthrough](https://kryptos.jsan.ch/k3/)

We froze two explicit extensions before testing K4: compact each ragged rotation while skipping unoccupied cells, or keep a 120-cell rectangle with 23 structural holes until both rotations finish. The holes never represent unknown letters and are removed from the positional map before substitution. Each map and its inverse gives four distinct bijections on the original 97 positions.

None matches a map in the existing local 6,746-map single-width fill/read set. The inspected public cross-width bounds also omit (24,8). Broad public reports may still overlap this test; this is a local coverage delta, not a claim of global novelty.

| Check | Complete bounded result |
|---|---|
| Four pure rearrangements | None preserves all 24 confirmed letters |
| Known PALIMPSEST/ABSCISSA keys in the KRYPTOS alphabet; every cyclic key phase; both stage orders | All 144 fixed cases fail the 24-letter gate |
| Any repeating key of length 8 or 10; AZ or KRYPTOS alphabet; plaintext coefficient +1 or −1; both stage orders | All 64 structural cells have an explicit contradiction |
| Synthetic messages planted in those structural cells | All 64 accepted and round-tripped by the main implementation |

The 144 fixed cases are contained in the unrestricted-key tests, so they are not 144 additional disjoint exclusions. Different parameter cells may overlap as cipher families. No language scorer, plaintext optimizer, significance estimate or extra parameter sweep was used.

For each structural negative, two known plaintext letters force different values for the same key residue under the fixed permutation. This rules out that entire key cell, not merely a dictionary. The result does not exclude other widths, boundary conventions, longer keys, nonperiodic keys or unrelated compositions.

The [registration](k3_lift_registration.json), [implementation](k3_lift_test.py) and [raw results](k3_lift_results.json) specify the exact operations and retain contradiction pairs. Independent verification is recorded in [verification.md](verification.md).

## Source and spatial conclusions

The earlier solutions do not automatically supply K4's geometry. A permutation on 336 positions cannot simply be restricted to the first 97 unless that subset is invariant; the verified K3 map already sends input position 0 to output position 250. Making K4 a separate ragged block or adding a structural canvas is an additional assumption. The [spatial review](spatial_admission.md) distinguishes these assumptions from the working K3 recipe.

The 2005 CNN interview transcript offers a useful correction to source-text speculation: Sanborn describes the passages other than Carter's as his own fiction, and discusses relationships among sections after decipherment. That supports an authored narrative while leaving open whether earlier sections also give procedural clues. It does not prove that K4 is an unchanged quotation or that prior passwords must be reused. The transcript is a reconstruction prepared from producer material and tape-viewing notes, not a newly recovered original recording. [Interview and transcript provenance](https://elonka.com/x/2005CNN.html)

The [narrative/source review](narrative_sources.md) checks this against the Smithsonian oral history and prior source searches. The clock-as-destination hypothesis remains viable, but presently gives no deterministic cryptographic operation to run. A thematic connection to Carter's message delivery is also distinct from an exact source passage or a running key.

## Scope decision and remaining work

The independent spatial reviewer recommended a smaller phase-zero pilot. The coordinator's pre-result registration deliberately included inverse maps, all cyclic phases of the two known keys, and unrestricted 8/10-residue keys. This removes dependence on guessing where a short key begins and tests whether a different key of the same historical lengths could rescue these fixed maps. It is an explicitly broader researcher-defined diagnostic, not extra artist evidence. Nothing was added after the failed results.

The broad substitution/transposition and direct old-password directions overlap substantial previous work. We therefore stop this pass after the finite new mapping test, source review and independent verification. Remaining allowance is left unused rather than spent on arbitrary combinations.

The strongest practical priorities remain: recognize the clock as potentially narrative context; seek a specific positional instruction in authenticated design material; and require any new composition to make predictions beyond the cribs used to construct it. The already-sent archival requests are supporting leads, not a prerequisite for all cryptanalysis. No additional messages or paid work were initiated by this goal.

## Reproduce

From the workspace root:

```sh
PYTHONDONTWRITEBYTECODE=1 /Users/andrewchan/anaconda3/bin/python3 outputs/alternatives_2m/k3_lift_test.py
PYTHONDONTWRITEBYTECODE=1 /Users/andrewchan/anaconda3/bin/python3 outputs/alternatives_2m/independent_verifier.py
```

The main implementation reuses only the historical K3 fixtures and the prior route generator for overlap comparison; its cipher and route calculations are written in this package. Retain the referenced existing files for reproduction. All retained files in this folder serve source review, exact reproduction, independent verification or goal accounting.