oxedyne/ore — oracle/PREDICTIONS_cycle

oxedyne/ore/oracle/PREDICTIONS_cycle_rule.md

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1	# Cross-file cycle rule: predictions, written before the engine was changed
2
3	Recorded 12026-07-28, before a line of `CycleRule` was written and before any of
4	these cases was run. Traced by hand through the split points, the claim register
5	and the in-order traversal. Anything below that the oracle contradicts is a
6	finding, not a typo, and is to be reported as a disagreement rather than quietly
7	corrected.
8
9	Rules, as they will be spelled in `repo.rs`:
10
11	- `Demote` -- D, the status quo of `sequence_with_move.md` §5.4.
12	- `ConfineVictim` -- A as the brief phrases it: the demotion victim, and only
13	it, is confined to its source position when demoting would land its content in
14	another file.
15	- `ConfineCycle` -- A read as a property of the cycle rather than of the
16	demotion: every cross-file member of the cycle is confined to its source.
17	In-file members of the cycle are left alone.
18	- `LowestEdge` -- B. The cross-file member lowest in op order is voided; every
19	other member proceeds.
20	- `WholeCycle` -- C. The member highest in op order wins wholly; every other
21	member of the cycle is voided.
22
23	A member is exempt from voiding under every rule if another member of the same
24	cycle is in its causal past: an author who saw the other move and moved anyway
25	is informed, not racing. (The `Flag::Torn` correction of `file_identity.md` §4.4
26	made the same distinction.)
27
28	## C1. Two-file cycle (the shipped case)
29
30	`a="abc\n"`, `b="xyz\n"`; `M1=(5,1)` moves the whole of a into b after `b[0]`;
31	`M2=(5,2)` moves the whole of b into a after `a[0]`.
32
33	\| Rule \| a \| b \|
34	\|---\|---\|---\|
35	\| D \| `""` \| `"axyz\nbc\n"` \|
36	\| ConfineVictim \| `"axyz\nbc\n"` \| `""` \|
37	\| ConfineCycle \| `"abc\n"` \| `"xyz\n"` \|
38	\| LowestEdge \| `"axyz\nbc\n"` \| `""` \|
39	\| WholeCycle \| `"axyz\nbc\n"` \| `""` \|
40
41	The prediction that matters: `ConfineVictim` does not stop a file
42	emptying. It confines M1, whereupon M2's anchor content is home in a, so M2
43	completes into a and carries b's whole block with it. The collapse is mirrored,
44	not prevented. If that holds, a rule phrased as a change to what demotion does
45	cannot deliver what candidate A was posed to deliver, and confinement has to be
46	a property of the cycle. Three of the five rules agree on this case; only
47	`ConfineCycle` gives each file its own block back.
48
49	## C2. Three-file cycle
50
51	`a="abc\n"`, `b="xyz\n"`, `c="123\n"`; `M1=(7,1)` a into b after `b[0]`,
52	`M2=(7,2)` b into c after `c[0]`, `M3=(7,3)` c into a after `a[0]`.
53
54	\| Rule \| a \| b \| c \|
55	\|---\|---\|---\|---\|
56	\| D \| `""` \| `"a1xyz\n23\nbc\n"` \| `""` \|
57	\| ConfineVictim \| `"a1xyz\n23\nbc\n"` \| `""` \| `""` \|
58	\| ConfineCycle \| `"abc\n"` \| `"xyz\n"` \| `"123\n"` \|
59	\| LowestEdge \| `"a1xyz\n23\nbc\n"` \| `""` \| `""` \|
60	\| WholeCycle \| `"a123\nbc\n"` \| `"xyz\n"` \| `""` \|
61
62	B and C come apart here, as the brief says they must. B breaks one edge, the
63	chain that remains is acyclic, and the two survivors cascade into one file: B is
64	barely better than D at length three. C empties one file, and that file was
65	emptied by the winning author's own move.
66
67	## C3. Four-file cycle
68
69	`a="abc\n"`, `b="xyz\n"`, `c="123\n"`, `d="pqr\n"`; `M1=(9,1)` a into b after
70	`b[0]`, `M2=(9,2)` b into c after `c[0]`, `M3=(9,3)` c into d after `d[0]`,
71	`M4=(9,4)` d into a after `a[0]`.
72
73	\| Rule \| a \| b \| c \| d \|
74	\|---\|---\|---\|---\|---\|
75	\| D \| `""` \| `"ap1xyz\n23\nqr\nbc\n"` \| `""` \| `""` \|
76	\| ConfineVictim \| `"ap1xyz\n23\nqr\nbc\n"` \| `""` \| `""` \| `""` \|
77	\| ConfineCycle \| `"abc\n"` \| `"xyz\n"` \| `"123\n"` \| `"pqr\n"` \|
78	\| LowestEdge \| `"ap1xyz\n23\nqr\nbc\n"` \| `""` \| `""` \| `""` \|
79	\| WholeCycle \| `"apqr\nbc\n"` \| `"xyz\n"` \| `"123\n"` \| `""` \|
80
81	Three files emptied under D, B and A-as-phrased; one under C; none under
82	ConfineCycle.
83
84	## C4. Mixed cycle: one in-file member, two cross-file
85
86	`a="abc\n"`, `b="wxyz"`. `M1=(5,1)` moves a into b after `b[0]='w'`, crossing.
87	`M2=(5,2)` moves `"wx"` within b to after `'y'`, in-file. `M3=(5,3)` moves
88	`"yz"` out of b into a after `a[0]`, crossing.
89
90	\| Rule \| a \| b \|
91	\|---\|---\|---\|
92	\| D \| `""` \| everything, 8 bytes \|
93	\| ConfineVictim \| `"aywxzbc\n"` \| `""` \|
94	\| ConfineCycle \| `"abc\n"` \| `"ywxz"` \|
95	\| LowestEdge \| `"aywxzbc\n"` \| `""` \|
96	\| WholeCycle \| `"ayzbc\n"` \| `"wx"` \|
97
98	This is where C is dearest: it voids M2, an in-file move that never touched the
99	boundary, because it happened to be in the cycle. ConfineCycle lets M2 complete
100	and is the only rule that does.
101
102	## C5. Cycle with an edit inside a cycling block
103
104	C1 plus `E=(5,3)`, a third replica inserting `"!"` between `b` and `c` of a's
105	block, concurrently with both moves.
106
107	\| Rule \| a \| b \|
108	\|---\|---\|---\|
109	\| D \| `""` \| `"axyz\nb!c\n"` \|
110	\| ConfineVictim \| `"axyz\nb!c\n"` \| `""` \|
111	\| ConfineCycle \| `"ab!c\n"` \| `"xyz\n"` \|
112	\| LowestEdge \| `"axyz\nb!c\n"` \| `""` \|
113	\| WholeCycle \| `"axyz\nb!c\n"` \| `""` \|
114
115	The edit survives under every rule and stays with its block under every rule.
116	Only the file the block is in differs, so the edit costs nothing to any
117	candidate.
118
119	## C6. Supersession cycle
120
121	C1's M1 and M2, and then `M3=(6,1)`: replica 1, having received M2, moves its
122	own block again, anchoring after the last byte of b's original content. M3
123	supersedes M1 (it claims the same content and is later), so M1 owns nothing and
124	leaves the graph; the cycle is `{M2, M3}` and M2 is in M3's causal past.
125
126	\| Rule \| a \| b \|
127	\|---\|---\|---\|
128	\| D \| `"xyz\nabc\n"` \| `""` \|
129	\| ConfineVictim \| `""` \| `"xyz\nabc\n"` \|
130	\| ConfineCycle \| `""` \| `"xyz\nabc\n"` \|
131	\| LowestEdge \| `""` \| `"xyz\nabc\n"` \|
132	\| WholeCycle \| `""` \| `"xyz\nabc\n"` \|
133
134	Every candidate agrees, and every candidate honours the informed re-move; the
135	causal guard is what makes ConfineCycle agree rather than voiding M3 along with
136	M2. The status quo is the outlier: it demotes M2, M3 then follows M2's block,
137	and a block whose author twice said "into b" renders in a.
138
139	## C7. In-file cycles must not move
140
141	`reg_nested_destinations` (`ALPHA`, two moves with mutually nested
142	destinations) renders `5678901ABCDE234FGHIJ` under every rule, with the same
143	demotion flags, and the self-anchoring move (a cycle of length one) is likewise
144	untouched: no candidate may reach an in-file cycle at all.
145
146	## Sweep
147
148	Over the same generator as `mstage`, three files, three replicas:
149
150	- `ConfineCycle` will void the most moves and empty the fewest files.
151	- `LowestEdge` and `ConfineVictim` will be indistinguishable on two-file
152	cycles, which will be the great majority, and will separate only where a
153	cycle is longer than two.
154	- Moves rendering in a file their author did not name will be highest under D,
155	about the same under B and A-as-phrased, lowest under ConfineCycle, with C
156	between.
157	- No rule will lose a byte or render one twice, and every rule will be
158	order-independent, because none of them reads anything but the operation set.