secondAttackBlock_length
plain-language theorem explainer
The second attack block in the Gap-2 gauge-counting necessary-reasons census is a concrete list of exactly three reason entries. Census auditors and anyone checking table-length invariants against the reason table cite this. The proof is a one-line decidability check on a finite closed list.
Claim. The second attack block (the finite list of Gap-2 gauge-counting necessary-reason entries grouped under that pass) has length exactly $3$.
background
The module runs a necessary-reasons census for Gap 2 in the gravity stack: assume richer RecognitionLedger / posting-layer structure forces the Gauge Counting Principle for physical class mass (equivalently $\nu = 1/|\mathrm{Aut}|$). Every candidate fact that would make that unavoidable is scored THEOREM, OPEN, MODEL, or REFUTED.
Attack blocks partition those candidate reasons into finite lists for successive passes. The second block is one such closed list; its length is a structural invariant of the census table, parallel to sibling length facts such as the full reason-table length.
Upstream cost and forcing machinery (J-cost on recognition events, multiplicative recognizer cost, rung-coarsen cost) sits in the broader Recognition stack that the Gap-2 measure target depends on, but this declaration only measures list cardinality, not those costs.
proof idea
One-line wrapper: decide on the concrete finite value of secondAttackBlock.length. Lean reduces the list literal and checks equality to $3$ by decidable computation; no lemmas are invoked.
why it matters
Bookkeeping for the honesty layer of the Gap-2 gauge-counting census. The module doc records which reasons are theorems, which are refuted, and which residual (action-first prior / U15-style equilibrium identification) remains open. Length facts pin the census shape so later passes cannot silently drop or add entries.
The following third-block commentary notes that the child census resolved this second block: one unit-fugacity selector path refuted (scoped), another promoted to theorem via ledger-counted global balance forcing detailed balance and the inverse-factorial gluing law. No downstream theorem currently depends on this length fact; it is local structural hygiene for the reason table.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.