Dependency and Scope

0.1 — What this paper does

AP47 prices the strained hold: what a configuration pays, at second order, to keep a difference open against its ground state. Three things, each at its stated grade.

First. It derives the form and scope of the cost. A held distinction discounts the booking of the difference itself — a quotient, never a new term — and the cost is defined on flips: no flip, no cost, the ground excluded by definition.

Second. It names the cost as one process — the window's leak — with a located rate (the substrate's, α, from AP30's own lemma), a located depth (the held grain's α-worth, carried with its conditional), and a located geometry (the pair's eight dimensional expressions under AP30's own construction, giving 1/(8π)).

Third. It freezes one row against nature. Δ_real = Δ_bare/(1 + α²/8π) = 2.53098857035 at CODATA-2022 α, against the measured 2.530988574 ± 7.4×10⁻⁷ — a residual of −0.005σ where the bare row fired at 7.24σ — with the switches of section 10 armed on it.

It also rules the bound neutron (the distinction is held against the structural alternative; binding closes the exit, not the window) and declares, rather than dresses, that the ruling carries no mass-face observable.

0.2 — Dependencies

AP30 (The Resistance): the dimensional-expression construction and its leakage lemma — the static count through the four spacetime dimensions, the isotropic 1/(count·π) normalisation, the substrate's rate ("the substrate speaks at α_em"), and the principle quoted at its own hedge: "the leakage is normalised by the very structure it leaks through." AP46 (The Stretch, v0.2): the mechanism in its exact words — "holding is tension, and tension sheds" — the pairs-balance ruling, and the thread ruling that fixes the family's one base rate. AP45 (The Blink, draft v0.2.1 — the version of record by the author's word; a draft awaiting his lock, and every inheritance from it says so): the toll's two faces, the spent clause, the no-new-energy-term refusal, the grain's denomination. AP44 (The Snap, locked): the ε = α_em selection, argued in its section 5, booked as D-CCC.4. AP06 (The Leakage Constant, published corpus): the domain field the selection was made among, held open at its section 0.7. WP-ROAD.1 v1.2: the family instrument. One measured comparator, CODATA 2022, lines named in section 6. No other inputs exist.

0.3 — Claimed, and refused

Claimed: that a configuration holding a distinction — an orientation differing from its ground state under the same grip — pays a continuous second-order cost on the booking of the difference itself; that the cost is one process, the window's leak, with a located rate, depth, and geometry; that its order is α² (the grain's worth times the substrate's rate) at the structural register, riders stated; that its divisor is 8π, derived by AP30's own construction at support two; that the realised difference is the expression Δ_bare/(1 + α²/8π) at CODATA-2022 α; that the bound neutron pays; and that the binding ruling carries no mass-face observable, under either answer, declared rather than dressed as an edge.

Refused, in advance: any new term in any energy budget at any size; any identification of Δ_bare's terms with the standard electromagnetic/strong decomposition; any repair of the fired row KS-NPP.1; any third-order term; any claim on the bound neutron's mass face; any probability deviation; and any contact between the construction and standing measured numbers beyond those disclosed in this paper — the eliminations of section 5 and the proton check of section 7, where data killed candidates and generated none, and the single frozen comparison of section 6 — all made after the structure was described, in the order the record shows.

0.4 — The honesty box

The bare row fired at 7.24σ and is shown in full in section 7; this paper prices the structure the fired row was missing and never touches the corpse. The paper's central structural claim — AP30's maintenance mechanics read at a strained hold instead of a ground's upkeep — is STATED, located, and switch-guarded, not derived from anything deeper; every grade in this paper rides it in the open. The order carries three riders (T-b, a registered conjecture; D-CCC.1, the formalisation; the ε = α_em closure, DERIVED-CONDITIONAL-ON-AP45 via D-CCC.4) and the divisor inherits KS-30.2's isotropy assumption, live in its parent. The landing itself, at −0.005σ, is weak evidence by the family's own standard: the paper is worth having for the structure and the falsification surface, not for the number.

0.5 — Epistemic status per section

Section 1: the family seat, orientation. Section 2: DEFINITIONAL — the scope, ruled. Section 3: DERIVED-AT-THE-STRUCTURAL-REGISTER — the mechanism, inherited and read on the mass face. Section 4: the process STATED and located; the order α² DERIVED-AT-THE-STRUCTURAL-REGISTER with riders. Section 5: the divisor 8π DERIVED, wearing its clauses and inheritance. Section 6: EMPIRICAL — one frozen row, reported once, never evidence of the structure. Section 7: deaths, shown. Section 8: RULED, with a declared null. Section 9: the census, open and honest about its size.

0.6 — Kill switch summary

KS-FLIP.1 — the frozen row dies if measurement departs beyond the bar. KS-FLIP.2 — forced structure; fires on any element shown selected by comparison with measurement; binding on author and desks. KS-FLIP.3 — the truncation; the absent α³ term is a prediction, dated at ~20× better B_d metrology. KS-FLIP.4 — the scope; dies if a ground state requires the cost or a domain member escapes it. KS-30.2 — inherited isotropy; both divisors move together. KS-NPP.1 — fired 2 August 2026, shown forever. Full statements in section 10.

0.7 — Items held open without claiming debt status

The lifetime dynamics of the window's snap — the free neutron's decay clock, including the standing beam-versus-bottle tension in its measurement — forward-register, no claim made. The census of section 9. The α³ silence until metrology reaches it. The ROAD v1.2's AP45 state-table line, corrected at that instrument's next revision (a v0.3 is recorded there that does not exist in the author's archive; v0.2.1 is the version of record by his word; should a file answering that entry ever surface, its four fence clauses are re-read before anything relies on it).

0.8 — Structural relationships

AP30: parent of the construction; KS-30.2 shared; no locked value touched (WP-FLIP.1 section 9's independence sentence superseded as stated in section 5). AP46: source of the mechanism and the pairs-balance ruling, both quoted verbatim; the one-base-rate reconciliation runs on its own thread ruling. AP45 (draft): source of the toll clauses and the grain's denomination; every inheritance conditional on its lock. AP44: source of the ε = α_em selection; D-CCC.4 carries the closure. AP06: the domain field. AP40: the conceptual development of the structural imbalance this paper prices. AP42/AP28 and the cosmology: untouched. The Assembly (AP48, forthcoming): none of its content is load-bearing here, and none of this paper's rows move on its verdict. One line is filed to the record-algebra programme (D-CCC.1): the availability field recomputes structurally, blind to energetic accessibility — section 8's ruling is an axiom of that algebra. No new debt books: D-FLIP.1 was reserved for an underived divisor and is not needed.

0.9 — Symbols and numbers

Δ_bare = 3(1 − 1/2π) + α(1 + 1/2π): the ideal neutron–proton difference in electron masses, the flip priced as free. Δ_real = Δ_bare/(1 + α²/8π): the realised difference, the claim of this paper. f₂ = α²/8π: the hold-cost fraction. α = 7.2973525643(11)×10⁻³, CODATA 2022. Δ_meas = 2.530988574, u = 7.4×10⁻⁷ (0.29 ppm) — CODATA 2022, the exact difference of m_n/m_e = 1838.68366200(74) and m_p/m_e = 1836.152673426(32), the uncertainty stated decade-safe because its parenthetical form caused one audited slip. The window: the held gap between a coupling's actual and ground orientations. The window's leak: the one process of section 4. ε, three postures: the arena's splinter (held forever), the Blink's slivers (spent per event), the flip's grain (held-and-leaking, terminally released at the snap-shut).