falsifier PROPAGATION is the cheap direction; Auslöschung is a reading, not a stored sum

[AdaWorldAPI]

Measures the claim that HHTL + a signed 24×i4 field makes falsification cheap, and that the hierarchy's cost is "more connective tissue than leaf nodes." PROBE-HHTL-FALSIFICATION-ASYMMETRY-1, 7/7 — with two costs measured rather than conceded.

Recut after review (commit 67405bc): the complexity claim is now scoped to propagation.

Why a signed field is categorically different

A signed field admits destructive interference — Auslöschung. +n and −n at one address cancel. A purely positive confidence scalar structurally cannot do this: it can be diluted, never extinguished. That is the whole distance between "my confidence went down" and "this was refuted."

The asymmetry — and exactly what is O(1)

propagate a KNOWN refutation   1 region, independent of subtree size
verify a universal claim at P  exhaust FAN_OUT (16) at this depth
                               …and every level BELOW stays open

The precise claim (corrected from a broader "falsification is O(1)"): once a valid counterexample region is known, applying it to a universal claim over an addressed subtree is O(1) in subtree population size via prefix containment. Discovering the counterexample is NOT proven cheap — that may involve probing, search, causal inference, I/O, or pair-field work, none of which this probe measures.

What the hierarchy makes cheap is the propagation of a falsifier, never its discovery. The distinction matters the moment this is compared against GPU or causal-representation-learning approaches, where discovery is the expensive half — claiming O(1) falsification without the qualifier would be comparing a propagation step against a search.

Propagation reaches a whole subtree with no enumeration (F2 — one depth-1 focus covers all 16 depth-2 and all 16 depth-3 probes by prefix test alone; the subtree is never materialized), and doesn't over-kill (F5 — silent on sibling subtrees, on other parents, and on its own ancestor, since a child's refutation is not the parent's).

Known-unknowns are addressable-without-a-value (F4)

state	address	value
known-known	a covered address	present
known-unknown	a real region to drill into	absent
unknown-unknown	no region at all	absent

Only the middle case admits a targeted counterfactual probe. It pairs with the shipped CausalTopology::IndirectUnknownIntermediates: the topology register says an intermediate exists, the address space says where it would live, the pothole says we don't have it yet.

F7 — inheritance is directional: downstream is covers, upstream is common_prefix. P.covers(C) but not C.covers(P).

⚠ COST 1 (F1) — Auslöschung must be a READING, never a stored sum

Measured: net(+3, −3) == net(unset) == 0. A summed slot cannot distinguish "support and refutation met and annihilated" from "nothing was ever asserted here." Those license opposite actions — a licence to LEARN vs a licence to LOOK. Two slots keep the three-way state and the registers differ bitwise even at net zero. Same shape as the standing rule that a contradiction is committed and preserved, not resolved away.

⚠ COST 2 (F6) — "all but one" is the worst case, and difference cannot help

• Collapse is free — all 16 children explicitly = 16 antichain entries, absorbing to 1.
• "All but one" costs 15 entries, and RowFocusMask::difference cannot reduce it: subtracting the hole from the parent yields 1 entry that STILL COVERS THE HOLE.

Sharper than "conservative": difference is not usable as an exclusion primitive, and reading its output as "everything except the hole" is unsound. This is the mechanical root of the standing P* rule.

Consequence: an exclusion needs its own channel — a signed negative at the excluded address — never a subtracted prefix. Which is Auslöschung again: you mark the hole, you don't carve it out.

Scope

Toy hierarchy, shipped operators. The signed field is the probe-local reading from PROBE-TARSKI-SIGNED-WITNESS-1, not the A9 Locus API. No claim that beliefs currently have such addresses; #1006 says they do not.

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