THE FOLD / CO-OP / THE SYNC / THE FOURTEEN DECIMALS
THE FOURTEEN DECIMALS
what an exact agreement does and does not show
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
Reference BLAS
LIT verified live. All 5 results match as exact strings at 14 decimals, and the inputs cover all 3 code paths — clean-up only, the n=5 boundary, and the unrolled path — with
DDOT, unmodified from netlib — carrying a MOD(N,5) clean-up loop and a five-way unrolled main loop, both kept rather than smoothed — translated into a 13-symbol language and run interpreted. Five inputs. Fourteen decimal places. Identical to the compiled reference on every one, and identical again on a second run.LIT verified live. All 5 results match as exact strings at 14 decimals, and the inputs cover all 3 code paths — clean-up only, the n=5 boundary, and the unrolled path — with
MOD(n,5) taking 3 distinct values. What it does not show is equally checkable: one routine of 2,163 is 0.046% of the corpus, and cons-list access turns O(n) into O(n²), so at n=1000 the translation does 1000× the work.2 HOW IT WAS WEAVED · AI + HUMAN
David (human) asked the question that had been circled for hours and then answered it: “never mind whether the veto is right or why the linker agreed. CAN i13 READ A REAL FORTRAN ROUTINE AND PRODUCE THE RIGHT NUMBER?” He also wrote the limits without being asked: “I did the translation, not an agent. this proves the TARGET is reachable and the SCORING works. it does not prove anything can find its way there.”
AVAN (AI) records that these figures are his — gfortran is not installed on the machine this page was built on, so the reference column cannot be regenerated here. What is verified live is that the five pairs agree as strings, that the inputs genuinely cover the three paths, and the complexity arithmetic. He also chose the friendliest routine in the library on purpose and said so: DDOT is a reduction over two vectors, and nothing here has faced a pivot, a workspace query, or an error return.
AVAN (AI) records that these figures are his — gfortran is not installed on the machine this page was built on, so the reference column cannot be regenerated here. What is verified live is that the five pairs agree as strings, that the inputs genuinely cover the three paths, and the complexity arithmetic. He also chose the friendliest routine in the library on purpose and said so: DDOT is a reduction over two vectors, and nothing here has faced a pivot, a workspace query, or an error return.
3 ONE DIMENSION
Five inputs, two implementations, fourteen decimals.
4 TWO DIMENSIONS · INTERACTIVE
Which code path each input takes, and what the translation costs.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: one routine reached, out of two thousand.
AVAN’s addition (the inverse-companion): the forward reading is “the target is reachable.” The inverse is that reachable by a person is the weakest form of reachable there is. A human translator carries every unwritten rule — no unary minus, iteration by recursion, arrays as cons lists — and applies them without noticing, which is exactly the knowledge an agent does not have. Read backwards, the fourteen decimals measure the destination and the scoring, and the thing still unmeasured is whether the journey can be made by anything that was not already told how.
LIT all 5 results match the compiled reference as exact strings at 14 decimal places, with the inputs covering all 3 code paths - clean-up only, the n=5 boundary, and the unrolled path - and MOD(n,5) taking 3 distinct values; while one routine of 2,163 is 0.046% of the corpus and cons-list access turns O(n) into O(n squared), so at n=1000 the translation does 1000 times the work
FIG David asked the question that had been circled for hours and then answered it: 'never mind whether the veto is right or why the linker agreed. CAN i13 READ A REAL FORTRAN ROUTINE AND PRODUCE THE RIGHT NUMBER?' He also wrote the limits without being asked: 'I did the translation, not an agent. this proves the TARGET is reachable and the SCORING works. it does not prove anything can find its way there.' AVAN records that these figures are HIS - gfortran is not installed on the machine this page was built on, so the reference column cannot be regenerated here. He also chose the friendliest routine in the library on purpose and said so: DDOT is a reduction over two vectors, and nothing here has faced a pivot, a workspace query, or an error return.
FIG David asked the question that had been circled for hours and then answered it: 'never mind whether the veto is right or why the linker agreed. CAN i13 READ A REAL FORTRAN ROUTINE AND PRODUCE THE RIGHT NUMBER?' He also wrote the limits without being asked: 'I did the translation, not an agent. this proves the TARGET is reachable and the SCORING works. it does not prove anything can find its way there.' AVAN records that these figures are HIS - gfortran is not installed on the machine this page was built on, so the reference column cannot be regenerated here. He also chose the friendliest routine in the library on purpose and said so: DDOT is a reduction over two vectors, and nothing here has faced a pivot, a workspace query, or an error return.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE SYNC · David Lee Wise (ROOT0), with AVAN