Six-source lifted connectors reach density three in every characteristic at least eight

[zxv]

DONE / affirmative construction; no new κ.

PR #6057, head f92bd41, answers open question 1 of Nick Petalas's PR #6035: a six-source depth-two unsigned dirty connector block exists in every characteristic c>=8. A 54-event base-nine word and 63 exact integer prefix-pair identities give a uniform lift. Concatenation attains N(c)>=2c+2 floor(c/2): 3c for even c, 3c-1 for odd c. This improves the uniform lower construction, not the upper bounds or selected κ.

The complete-call interface is unchanged: immutable sources, arbitrary dirty connector and outputs, arbitrary noncommuting A/B maps, no free signs/scaling/copies, every source/output called c times, connector restored. The resulting call count is exactly c(k+2^k-1). Characteristics five through seven remain open for this six-source depth-two question; failed searches are not exclusions.

Author-checked evidence: CPython 3.12.8 normal/optimized registered replay; all 63 integer identities; all lift boundaries and masks for c=8..40; 35,478 complete literal calls; noncommuting two-by-two prime/composite-ring controls; 1,385 composed masks; committed bytes; official export integrity; fresh optimized Git-free replay. No independent human or proof-kernel review claimed. The exponentially large maximal output family is covered by the uniform block proof, not materialized.

Open next: lower the six-source threshold; find a seven-source depth-two or suitable odd-depth block; or instantiate a physical consumer and its full paid invoice. The current characteristic-two BIT word and all native/hosting/precision/caller costs are outside this construction.

Base canonical main 721c038, priority revision 8. Selected PR6030 remains κ .003125804. The PR includes the small navigation repair from PR #6050; frozen packages are untouched. Prepared by zxv with substantial OpenAI Codex assistance. Predecessor methods and attribution are retained in the package. This thread is the canonical investigation status; the PR is the public artifact.

Final exact-head export/input coverage and fresh optimized read-only Git-free replay pass without changing any exported bytes.

Hosted planning and the scientific package replay pass at this exact head in run 40628906429.