B47: Does B34's criterion discriminate, or return each edge's own m_e?

[NGL321]

Part of #532. Opened by B42 (#605)'s resolution, which found B40 (#603)'s arm-4 falsifier had fired and been scored on a statistic that could not see it.

Question

Does B34's criterion discriminate, or does it return each edge's own m_e dressed as a reading?

Why this is a ticket

B40 carried the flat bundle as arm 4, a falsifier, stated as: "if holonomy cannot fail then the count reads full width everywhere and carves nothing." It reported the falsifier did not fire, on the grounds that the counts still spread — std 1.2–1.5, 6–7 distinct values, two seeds.

Full width is m_e, and m_e is not a constant. Wide edges on this surface run 10–16. So a criterion that simply returns each edge's own width reproduces exactly the spread the widths already have, and any statistic taken over the counts alone scores it as discriminating. B42 re-ran the falsifier on a bundle that is genuinely flat (identification 0.0000 through the mask and ADR-0032's band, where B40's arm 4 was 0.0386) and compared the count to m_e edge for edge (b42_mirror.py, reserve_p12 seed 42, threshold 0.9):

surface	count == m_e	mean shortfall below full width
trained control	0 / 104 (0%)	−13.8
B40 arm 4	68 / 104 (65%)	−1.1
B42 reserved frame	69 / 104 (66%)	−1.0

The trained surface genuinely selects — it discards ~14 of ~14 directions. On the flat bundle the criterion keeps ~93% of full width and discards about one. That is the falsifier's own antecedent, met.

What this must settle

1. Whether B34's decision survives. B34 decided holonomy-count is a usable carve criterion. It decided that against a falsifier the record says did not fire. B34 is not reopened by this ticket — this indicts the evidence, and the map's shape is that a resolved ticket advises rather than rescopes. What is decided here is whether the criterion needs replacing, repairing, or nothing.
2. What the right null is. The spread statistic cannot separate carving pressure from the width distribution echoing back. Any replacement must be scored against a surface where the answer is known — count − m_e is one candidate and was enough to expose this, but it is not obviously the right one, and normalising by how many cycles an edge reads was already on B41's list.
3. What this does to the clauses B34 already had. Only the floor acts, and it leaks at √1.25 because pruning concentrates the band's norm; 90 of 194 wide edges are true bridges with no cycle to read at all. If the count is a mirror on cycle-bearing edges too, the criterion acts nowhere.

Why it blocks B46

B46 (#613) designs a gate around this criterion. Designing a gate for a mirror is work that could be wasted, and B42's own resolution enlarged B46's subject to the node stalk mask as well.

Notes

Instruments on worktree-b42-flat-bundle-605 (7e02410): b42_mirror.py is the edge-for-edge comparison, b42_falsifier.py re-runs B40's scoring beside it, b42_reserve.py builds the genuinely flat surface. Threshold 0.9; B40 reported at 0.8/0.9/0.95 and nothing here rests on the value.

Plan, don't do.

[NGL321]

Advisory from B48 (#615)'s resolution, plus a queue audit the user asked for. Not a rescoping — the body stands and every ask is still valid, unchanged. The reason for commenting is mainly to stop a misreading.

B48 suspended holonomy, and it does not reach this ticket

B48 ruled that holonomy is suspended, not struck — the user's own amendment — and a careless reading would take B34 and this ticket out with it. It does not.

What is suspended is B33's local holonomy term in the objective — a thing that would be trained toward, whose optimum B42 showed is collapsed lanes at audience differentiation 0.0000. B34's criterion is holonomy as a read-only prune criterion: nothing descends on it and it has no optimum to collapse into. Different use, different failure mode, untouched. This ticket's question — does the criterion discriminate, or return each edge's own m_e — is entirely unaffected, and its answer is needed whether or not holonomy is ever revived as a term. The re-entry for the objective-term question is B54 (#624) and is a separate matter.

Worth stating because the suspension rests on premises that would not transfer here anyway: B32's flatness attains the maximum of dim H⁰ is about what an objective optimises toward, and B42's collapse is about exact path-independence. Neither is an argument against counting holonomy per edge.

One input that may bear on ask 2

Ask 2 asks what the right null is, noting count − m_e was enough to expose the mirror but is not obviously right, and that normalising by how many cycles an edge reads was on B41's list.

B48's joint scoring rule is now a standing constraint on this map: any agreement statistic is reported alongside audience differentiation at a cell and the exposure it cost, and a candidate must show agreement rising while differentiation stays nonzero. A holonomy count is not an agreement statistic in B48's sense — it is a per-edge cycle reading, not a count of shared invariants — so the rule does not straightforwardly bind. But B42's own constraint already does, and it is the closer relative: any objective carrying a local holonomy term reports audience differentiation at a cell alongside the holonomy it achieves. Since the mirror was exposed precisely by a surface at differentiation 0.0000, reporting audience differentiation beside any candidate null looks cheap and diagnostic here — the flat bundle keeps ~93% of full width and discards about one direction, and that is what a differentiation of zero looks like read through this criterion.

Also worth knowing

• B48 found the trained architecture's earned H⁰ is zero and retired earned as a candidate bar — reportable as a diagnostic only. If any replacement null for this criterion reaches for H⁰, read B48 first.
• This ticket still blocks B46 (#613), whose motivation survived B42 (the per-edge counterfactual is real, so gating's advantage is intact). So the designing a gate for a mirror risk this ticket names is still live and still the reason for the edge.