t81-foundation

H04-R02 unified research conclusion

The original H04-R02 inference is invalidated by accounting, comparator and validation defects. Corrected H04-R02 provides conditional symbolic cost results and a concrete reversible packing demonstration. H04 remains unresolved.

• Mathematically established: exact trit ranges, code capacity, finite byte lengths and crossover equations in MATHEMATICS.md.
• Modeled: optimized AT/AB winners depend on r, mode boundaries, metadata, transition and conversion assumptions. The legacy boundary trace retains an AT window; the 10-bit control narrows it to r<5/3, which includes 1.60. Equal metadata cannot erase a payload advantage. Constant-large adaptation loses to fixed precision at the default parameters. The historical 96% claim describes one ratio-1 trace and is not a workload-independent attribution.
• Implemented and tested: C++ prefix DP, Python suffix oracle, independent rational enumeration, block sharing, reoptimized crossover and reversible Base-243 / packed 10-bit codecs. See CORRECTED_RESULTS.md and VERIFICATION.md.
• Measured: actual encoded byte lengths. No new CPU performance, bandwidth, hardware area or energy benchmark supports an execution advantage or loss. Timing ratios from other experiments cannot be transplanted into this codec.
• Unresolved: physical ternary devices, alternative arithmetic, stronger binary codecs, causal adaptation, real conversion/selection costs, and independent cross-platform/laboratory reproduction. H04-R01’s source and tests are recovered here; reexecuting its own verifier is not independent validation of all of its mathematical assumptions.

Track R continues with falsifiable experiments; Track F maintains reliable runtime/evidence apparatus; Track M records corrections and provenance. This packet neither closes ternary software research nor establishes ternary-specific computational superiority. Canonical H01–H08 remain unchanged.

The discrepancy resolutions are in DISCREPANCY_LEDGER.md. Prior invalid claims and negative results remain exact, explicitly superseded snapshots under history/.

Next experiment: matched codec and access control

Test whether Base-243’s saving over fixed 10-bit fields survives an equally optimized binary block code for the same 729-state domain and a declared access contract. Predeclare block sizes 1,5,64,1024; equal count framing, adaptive tags if used, 1/8/64-byte alignment, and sequential versus random-index reads. Include packed 10-bit, Base-243 and integer block coding of base-729 digits; use the same input distribution and exact round trips for all arms. Report actual bytes separately from encode/decode latency distributions and bandwidth. Pin source/toolchain, seeds and timing procedure before measuring.

Falsifier for a radix-exclusive storage claim: a binary block code matches or beats Base-243 under the same contract (it can encode the same byte language). Falsifier for a practical codec win: the predefined byte-saving and end-to-end latency/bandwidth targets fail after framing, access and conversion. Do not reinterpret storage-only success as faster computation. No VM/ISA expansion is needed. A native-device cost experiment is a separate H01/H04 question.

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