Asymmetric-Loss Equal-Born Test — Supplements 1 and 2: the Pre-Bench Closure with its postscripts, and the high-loss error-budget row with its adversarial referee report
Two working documents that the deposited paper (Draft 4, v1.0; DOI 10.5281/zenodo.22678044; printed title The Asymmetric-Loss Equal-Born Test: a pre-registered search for record-information-dependent optical loss) cites and undertakes to deposit alongside it. They are deposited here as they stood on September 7, 2026, the day Draft 4 was completed, each with a dated deposit note at its head; nothing beneath the note is altered. Supplement 1 — Pre-Bench Closure (September 4, 2026), with postscript layers of September 6 and 7. The arithmetic companion to the paper. Part A runs the no-signalling check on the programme's surviving statement, finds that the normalised form permits superluminal signalling and is excluded, and records the single repair — a loss channel — that leaves the bench prediction numerically unchanged and converts the hypothesis from a nonlinear modification of the Born rule into a linear one. Part B carries the consequences into the protocol: the turnover of −p ln p at p = 1/e and the extended scan that would see it, a fourth signature, the cost of the high-loss points, the total-rate observable, the absorber control with its prediction stated in advance, and the consolidated protocol amendments. Part C makes the structural repairs: locating the branching event, the J-conservation contradiction, and the cost functional, with both candidates carried and the location of the peak left to decide between them. Part D drafts the pre-registration and scores the open tasks. The September-6 layer, headed "Postscript — September 5–6", records the two independent referee passes (one blind, one adversarial), the photon-number-dependent loss map, the derivation of the record criterion put to a third referee instructed to kill it and killed on twelve counts, the pre-registered arms and the correction of a handover error; the addendum of September 7 records the closing of the high-loss row. 17 pages. Supplement 2 — The high-p row: proposal, adversarial pass, and the row as costed (September 7, 2026). The error-budget row for the extended scan (p = 10%, 36.8%, 60% and 70%) that the paper's §9 named as the single item blocking pre-registration of the extended points, kept in the three steps by which it was reached. Appendix A is the first-pass proposal exactly as written for review, errors included. Appendix B is the report of an independent adversarial referee instructed to kill it, verbatim: eight errors and six systematics the first pass had not carried. Appendix C is the row as costed after every finding was re-derived and accepted, with the seven pass criteria written into the pre-registration. Its findings: the reach at the turnover (5σ at λ* ≥ 0.0039, 95% exclusion to 0.0016) stands only under the seven criteria; the bright-phase thermal family has the sign of the predicted anomaly and is bounded by a power-dependence test stated in advance; the far point of the scan moves from 70% to 60%; and the extended scan is research-group metrology, not teaching-laboratory work. 25 pages with its deposit note. The coloured highlights in Supplement 1 are its dated layers (rose, September 6; periwinkle, September 7; sky, the deposit note of September 16, 2026), each explained at its head. The line "Not for deposit" on the cover of Supplement 2 recorded the authors' working practice on September 7 and is superseded by the deposit note above it; the paper's Draft-4 note undertakes to deposit the document. The reconciliation document the paper also cites is the programme's working record, still being expanded, and is available from the authors.
Two working documents that the deposited paper (Draft 4, v1.0; DOI 10.5281/zenodo.22678044; printed title The Asymmetric-Loss Equal-Born Test: a pre-registered search for record-information-dependent optical loss) cites and undertakes to deposit alongside it. They are deposited here as they stood on September 7, 2026, the day Draft 4 was completed, each with a dated deposit note at its head; nothing beneath the note is altered. Supplement 1 — Pre-Bench Closure (September 4, 2026), with postscript layers of September 6 and 7. The arithmetic companion to the paper. Part A runs the no-signalling check on the programme's surviving statement, finds that the normalised form permits superluminal signalling and is excluded, and records the single repair — a loss channel — that leaves the bench prediction numerically unchanged and converts the hypothesis from a nonlinear modification of the Born rule into a linear one. Part B carries the consequences into the protocol: the turnover of −p ln p at p = 1/e and the extended scan that would see it, a fourth signature, the cost of the high-loss points, the total-rate observable, the absorber control with its prediction stated in advance, and the consolidated protocol amendments. Part C makes the structural repairs: locating the branching event, the J-conservation contradiction, and the cost functional, with both candidates carried and the location of the peak left to decide between them. Part D drafts the pre-registration and scores the open tasks. The September-6 layer, headed "Postscript — September 5–6", records the two independent referee passes (one blind, one adversarial), the photon-number-dependent loss map, the derivation of the record criterion put to a third referee instructed to kill it and killed on twelve counts, the pre-registered arms and the correction of a handover error; the addendum of September 7 records the closing of the high-loss row. 17 pages. Supplement 2 — The high-p row: proposal, adversarial pass, and the row as costed (September 7, 2026). The error-budget row for the extended scan (p = 10%, 36.8%, 60% and 70%) that the paper's §9 named as the single item blocking pre-registration of the extended points, kept in the three steps by which it was reached. Appendix A is the first-pass proposal exactly as written for review, errors included. Appendix B is the report of an independent adversarial referee instructed to kill it, verbatim: eight errors and six systematics the first pass had not carried. Appendix C is the row as costed after every finding was re-derived and accepted, with the seven pass criteria written into the pre-registration. Its findings: the reach at the turnover (5σ at λ* ≥ 0.0039, 95% exclusion to 0.0016) stands only under the seven criteria; the bright-phase thermal family has the sign of the predicted anomaly and is bounded by a power-dependence test stated in advance; the far point of the scan moves from 70% to 60%; and the extended scan is research-group metrology, not teaching-laboratory work. 25 pages with its deposit note. The coloured highlights in Supplement 1 are its dated layers (rose, September 6; periwinkle, September 7; sky, the deposit note of September 16, 2026), each explained at its head. The line "Not for deposit" on the cover of Supplement 2 recorded the authors' working practice on September 7 and is superseded by the deposit note above it; the paper's Draft-4 note undertakes to deposit the document. The reconciliation document the paper also cites is the programme's working record, still being expanded, and is available from the authors.
Standard linear optics requires that the transmittance of an optic be independent of photon number: for a linear element the input–output relation a_out = t·a_in + r·b_in is an operator identity, so single-photon and bright-light transmission are equal as a theorem rather than as an approximation. We are not aware of a dedicated test of that equality with a controlled scatterer at the 10⁻⁴ level. We state a hypothesis in which the equality fails in the single-quantum sector by a fixed dimensionless coupling λ*, and specify the tabletop experiment that would exclude it. The observable is Δ = D_quantum − D_classical, where D is the half-difference of a two-arm log-ratio under an ABBA swap of a weak scatterer, measured once with counting detectors and once with photodiodes through identical geometry. Standard quantum mechanics fixes Δ = 0 exactly; the hypothesis predicts Δ = −λ*·(−p ln p), or −0.046·λ* at a 1% transmission deficit. The loss map is stated as a photon-number-dependent Kraus channel, K = Σ exp[−½λ*·I_R(n)]|n⟩⟨n| with P_R(n) = 1 − (1−p)^n, which is linear, completely positive, local and non-signalling; invariance of a remote marginal is verified explicitly on a two-mode squeezed vacuum to 3×10⁻¹⁷. An earlier thermal formulation of the same idea is excluded by published SNSPD efficiency data at 2 K by a factor of 2×10⁵ and is withdrawn. An attempt to derive the criterion distinguishing which optical elements incur the cost failed under independent adversarial review and is reported as a failure; the surviving readings are converted into five pre-registered experimental arms with their nulls stated in advance. A borrowed teaching bench at 780 nm reaches a total uncertainty of 2.9×10⁻⁴ per operating point at 2×10⁸ counts, giving 5σ sensitivity at λ* ≥ 0.031 and 95% exclusion to 0.013 at a 1% scatterer; an extended scan through the turnover at p = 36.8% reaches 0.0039 and 0.0016 respectively, subject to a costed high-loss error-budget row and seven stated pass criteria. Five signatures distinguish the effect from systematics, including a −p ln p scaling and a maximum located at p = 0.368. The cheapest arm needs no interferometer: the single-photon versus bright transmission of one 50/50 beam splitter at 10⁻³, which bounds one reading of the hypothesis below λ* = 0.003 in an afternoon’s run on a prepared bench. The protocol is pre-registered before any bench is borrowed. The result will be published in either direction; a null is reported as the best bound in this sector.
Why this measurement is worth a bench: see section 2 of the proposal, "Why anyone should want to measure it". Contact: concursion.alebt@gmail.com. Two companion documents to the deposited paper, doi:10.5281/zenodo.22678044, and its pre-registration, osf.io/3h6yf. The question: does a 50/50 beam splitter transmit a single photon in exactly the same proportion as it transmits bright light? Standard linear optics says yes, exactly. The first run compares the two to one part in a thousand, with one source; only a calibrated attenuator changes between the bright phase and the single-photon phase. ALEBT_proposal_paper_v1_oct20.pdf: the proposal written for a host laboratory (the observable, the hypothesis, the error budget, the stages, the equipment and the open problems). ALEBT_equipment_list_v2_oct26.pdf: the first-run equipment list, with answers to the questions raised by groups we have written to (existing measurements, fibre-coupled detectors, differences between detectors).
This paper is the forty-fourth in a sequence developing an interpretive framework that redescribes physical reality as a causally consistent history of information updates rather than as a collection of independently existing objects. It is the closing panel of the twelfth grouping — the U3 construction program — and its genre was fixed by Paper 43's closure before its first sentence: a design-and-feasibility paper for new configurations, barred from re-interpreting existing proposals, executing no measurement, scoring no datum, and moving no band. Paper 43's verdict (iii-c) — a surviving, laboratory-reachable-in-part window with reachable sub-window [1.7e-1, 2.1] at the conservative probe corner — unlocked this panel as a conditional discriminant-and-design unlock, not a claim that the generic-CQ collapse branch was avoided. What this paper supplies is the readiness layer: everything short of the measurement itself, arranged so that whichever outcome the world someday returns is already a typed verdict. Three feasibility verdicts are computed, each by a criterion declared before the computation, each with a named failure branch carrying a pre-committed publishable consequence. F_A — the photonic probe (flagship): Paper 43's symmetric dual-rail tapped-switch circuit is completed to pre-registration grade — a six-row confound budget with every row closing at its declared floor, an executable lambda-blind instrument-validity protocol at a declared tap ramp, the statistics/systematics split displayed (statistics never bind; every binding floor is a systematic), and a pre-committed outcome map on which a null carves a named region of the band while an excess is held un-interpreted pending the differential. F_A closes as a pre-registration-grade design — explicitly not an execution pass: every systematic either closes algebraically or carries an executable pass/fail gate whose failure branch is pre-committed, and the instrument-validity gate remains future laboratory work. F_B — the circuit-QED co-location envelope: the Paper 42 benchmark environment with one structural upgrade no existing device is claimed to instantiate — the monitored register is the order-control register — scored against five host-envelope criteria under a two-regime protocol (a validity regime that certifies the controlled-order resource, and a monitored regime in which the measured destruction rate of that resource is itself the observable). F_B is established as a design at declared floors, explicitly not a device claim, and the environment carries the named status-audit instruments (sector-exhibition, Clausius-defect protocol, co-location gravimetry option), specified and never executed. F_C — the recorded-versus-unrecorded differential at execution readiness: the declared toggle is the retention-step toggle — the entire analog chain runs identically in both arms; only persistent retention of the during-window monitoring stream differs, with both arms' rates estimated from identically-retained end-of-sequence readout, and the unrecorded arm's zero-export status fixed a priori at architecture level (transient buffer dwell time far below the retention floor, no persistent branch, effective redundancy below threshold — audited before the arm is admitted, with audit failure failing the verdict rather than mislabeling the arm). The comparator-blindness certificate is computed in the comparator class's own normal form to pass with about forty orders of magnitude of margin: the sole physical difference between arms — branch-correlated persistent-memory writes at meters — induces ~1e-36 per second of comparator contrast against an audit floor of ~1e4 per second, robust to twenty orders of transcription generosity. Ordinary write systematics are closed by an equalized dummy-write/dummy-load protocol, and the declared rate-matching floor closes from its own five-row decomposed budget; at that floor the discriminable sub-band covers the entire reachable window even at the conservative certified fraction. F_C is implementable. The realized corner of the pre-declared verdict architecture is (P_exec, D_disc) = (yes, yes): a band-motion-capable probe design exists, and the distinctness discriminant exists. The lasting artifact is the execution map: the single pre-registered decision tree from every feasibility verdict and every possible future measured outcome to its Paper-43 pre-committed consequence — null: carve; certified contrast tracking the recorded arm: distinctness earned and the first FrameworkForcedShift candidate; certificate failure in situ: confounded row, nothing carved, collapse at the audit frontier. The title's "Gate-VII signature" is typed exactly and nowhere exceeded: it names the designed observable pair whose executed measurement could first move the force axes of U3Status off pending — the paper claims no crossing, no measurement, no confirmation, no probability. The retired authority is the Global Experimenter: the assumption that empirical adjudication of an adopted dynamics requires a privileged, external certifying authority. Its methodological face is retired with the levels typed — world-level results come only from executed measurement, program-level results from pre-committed design, and nothing further is needed; its substantive face is declined, not refuted. The retirement is enforced by the subject matter itself: the probe's heralded detection records are certified export events — the very quantity that sources the predicted excess — so any apparatus that measures the kernel is made of what the kernel rates, and no experimenter stands outside the physics even in principle. U3Status is restated, not re-scored; Gate VII is claimed by nobody; the twelfth grouping ends with every branch disposed and the program handed to the laboratory.
Version 1 (first deposit, 2026-08). 19 pages. Every quantitative claim traces to a pre-registered evidence block with an archived log in the companion zip; the ledger of failed predictions is an appendix of the paper. A long-running dispute asks whether a quantum world selects its own decomposition into subsystems from the Hamiltonian and the state alone. Stoica (Adv. Theor. Math. Phys. 26, 3895 (2022)) proves that a structure so constructed cannot be both essentially unique and physically relevant, the non-uniqueness being modulo the unitaries commuting with H; Soulas, Franzmann and Di Biagio (arXiv:2512.07468) object that producing a second structure that way modifies the input pair, and prove a positive uniqueness theorem under two hypotheses. Both are correct, about different groups, and this paper makes the difference arithmetic. Working inside the collision architecture of the companion flagship (doi:10.5281/zenodo.22014601, all versions), where an interior memory writes records of a system and audits itself from them, the two invariance groups an interior audit actually has are measured. FIRST, the audit's Hamiltonian-side content is exactly constant on the orbits of the commutant of H, the fibres of the transport map are exactly those orbits, and the resulting gauge has the closed form sum_i m_i^2 - 1 in the eigenvalue multiplicities: the degeneracy has a computable size, three dimensions inside sixteen for a generic four-level Hamiltonian, five at (2,3), and larger exactly when the symmetry group is NON-ABELIAN (Heisenberg gives nine; abelian symmetry forces no spectral degeneracy). SECOND, the audit's total content is invariant not under that commutant but under the stabiliser of the PAIR (H, psi), which is trivial precisely under the Soulas hypotheses: the orbit holds the Hamiltonian side fixed to 2.7e-15 and pays for the second structure entirely on the state side, 1.14. The stabiliser formula quantifies exactly when their free-action condition holds and by how many dimensions it fails otherwise. THIRD, the record statistics carry their own blindness: the directions invisible to the census, whatever the state and the time, form a group, and for a register read in one basis per cell it is exactly span{I, T} at every fragment count, proved by a symplectic argument over F_2 requiring no induction -- in this deposit, by two algorithmically independent F_2 implementations plus a dense-matrix verification. That scope is the result rather than a caveat: the one-bit blindness is the price of a one-basis readout, and it is the only thing that price buys; reading a second basis on every cell collapses the group to the identity and credentials the full matrix algebra. The twist is the product of the observer's own precession with all of its own readouts, T = P R_1 ... R_k exactly, so the blindness group is the CENTRE of the credentialed algebra: an interior observer cannot see the centre its own operations generate. The credentialed algebra is everything commuting with that one bit, of dimension d^2/2. Blindness under this reading is an identity and not a similarity: for T in the blindness group the census under rho and under T rho T-dagger agrees exactly at trace distance 0.740, so no additional sampling can separate them. The paper prints the response functional every margin and census count is computed from, together with its grid and state. Around the group sit its measured collapse conditions: the price list of restorations (menus that eject the twist restore visibility at costs that double register by register, 10/20/40 contexts on the z-menu and 4/8/16 on the y/z-menu at k = 2, 3, 4, stated as observed at three points, not derived); the sorting condition for which twist configurations a restoration menu revives, named as reach membership of the displacement in the Krylov closure of the menu (63/63 exact at k = 2 in three independent engines, 255/255 at k = 3 in exact rational arithmetic; an all-time reach lemma proves the decision grid decision-faithful and shows it deliberately not span-complete); the genericity of visibility (the blindness locus is a union of alignment strata computed in part: a QND family at the minimal codimension 2 and twist families indexed by subsets of cells at codimension 2k, with a bounded search that surfaced a mixed partial-twist family the hand count had missed); and both branches of the open-world dichotomy reproduced from the group definition alone. The transport side is independently rebuilt: the W-alone computation the framework's kill switch depends on was reconstructed from the printed setting alone and the switch does not fire. A closing section isolates the mechanism shared with an earlier half-space result and shows, against the natural reading, that the two halves are distinct subspaces meeting in a quarter: one lemma, distinct instances. All quantitative claims were pre-registered before their runs. The ledger of failed predictions is an appendix and is kept in full, including a posted mechanism that died, a symmetry law corrected to Schur's criterion, a numerics trap caught only because a posted claim came back wrong, engine deaths from the exact-census campaign convicted by their own gates, and errors printed in earlier drafts and caught in review. The delineation of what is inherited from the literature is stated throughout; the paper asserts no priority claims.
Paper 44 of this sequence closed its U3 construction program at readiness: two budgeted experimental designs — a photonic tapped-switch probe and a circuit-QED recorded-versus-unrecorded differential — and an execution map, a pre-registered decision tree assigning every future measured outcome its pre-committed consequence, with scoring left "by whoever holds the data." Paper 47 then closed the theory-side debt ledger, leaving the executed-measurement route as the corpus's only live route to a framework-forced world-side shift. What 44 did not freeze is the layer between data-in-hand and leaf-adjudicated: shot schemas, exclusion policy, blinding order, stopping rule, claim authority. That unfrozen layer is where a post-data analysis authority could still sit — the researcher degrees of freedom and forking paths of the methodological literature, answered in precision physics by blind analysis and pre-registration. This paper — the forty-eighth in the sequence, opening panel of its Execution Program (Papers 48-50) — freezes exactly that layer, before any laboratory exists, as the template of a handover package executable and adjudicable by strangers: every analysis decision the package will ever need is either frozen here or typed as a named pre-data slot behind a failable acceptance gate, so that once a design-specific instance is accepted, no one — including the author, who operates no laboratory and has made that fact load-bearing — retains a seat from which a future outcome could be re-interpreted. Four document-level layers are delivered. Record layer: field-level shot schemas for both designs, with every field and every raw source typed into an audit or scoring partition; an add-only extension rule; ledger, provenance, and dataset-role conventions; and an exclusion grammar under which every excluded run is a first-class recorded event and every exclusion predicate is outcome-unread by construction. Statistics layer: the estimators, the null-carving formula, a leaf-decision normal form (frozen statistics, thresholds, tie rules per leaf), and the stopping rule, inherited verbatim from Papers 43/44 with the arithmetic re-checked; and a four-stage blinding architecture ending in a scoring stage at which everything is readable and nothing is choosable. Authority layer: a claim-authority table over the map's seven leaves and four post-data speaking roles — the data holder scores; the series designer holds no scoring cell; the decisive leaf is licensed only to the data holder's own successor paper — plus the handover normal form H with a seven-condition acceptance gate, a data-existence certificate with a public deposit obligation, a mock-data challenge typed as non-evidence, and pre-committed unlock conditions for the reserved data papers 49-D/50-D. Verdict layer: a six-check closure audit (leaf coverage; arithmetic consistency; partition admissibility; blinding soundness; exclusion soundness; authority totality), each check mechanical against the delivered artifacts, with the pre-committed either-way verdict ProtocolStatus in {closed, gapped} scoring template closure — an executable package exists per design only as an accepted H-instance. The audit is run and every check passes: closed at the template layer, quarantine register empty. Papers 49 (tap-channel exclusion protocol) and 50 (recorded-unrecorded differential protocol) are unlocked to instantiate H per design; only the unlock-conditioned data papers 49-D/50-D will ever score a datum. The retired authority is the Global Statistician — post-data analytic discretion personified: its authority reading is retired by construction (no analysis decision has a post-data seat left to occupy, the per-design property conferred by each accepted H-instance), its innocence reading by the imported methodological record, and its substantive face — one uniquely correct inference framework — is declined, not refuted. Nothing world-side moves: no datum is scored, no band or floor shifts, the feasibility verdicts stay 44's, U3Status is restated not re-scored; if no laboratory ever executes, the program rests where 44 left it — undecided, with an implementable and now administrable discriminant — a complete record, not a failure.
After an experiment runs, exactly two decisions could still be made by a person: does this outcome exclude the theory's declared region, or did an auxiliary — source, tap, detector, calibration — fail, voiding the run instead; and who is licensed to say so. Any protocol that leaves either decision open after data exist has left a seat for a post-hoc refutation authority — the Global Falsifier, the imagined adjudicator who owns the modus tollens. Paper 44 of this sequence closed its photonic tapped-switch probe F_A at pre-registration-grade design ("the IV gate itself remains future laboratory work"); Paper 48 froze the shared adjudication layer as a handover template, typing everything design-specific as named pre-data slots behind a failable acceptance gate. What stands between that design and a laboratory's first shot is a single object: a completed, gate-passing handover instance. This paper — the forty-ninth in the sequence, centre panel of its Execution Program (Papers 48-50) — builds that object, the reference instance H_A, at the executable level the template promised. Delivered: the delta specification from the cited apparatus class (the Goswami-type photonic quantum switch) to 44's tapped configuration, component by component against the frozen budget rows; the schema completion with field-level primitives for every field, extensions add-only and partition-admissible; the frozen analysis pipeline in algorithmic normal form — IV gate, measured-calibration transfer, estimators, and the leaf router implementing 48's tap rows verbatim, under a language-independent rounding convention so floating-point artifacts cannot flip a frozen boundary direction — with the reference implementation shipped as a hash-anchored code appendix (deposited companion file) behind a declared production-scoring boundary; the concrete exclusion rule list with its veto-impact report and a frozen post-exclusion N rule disposing shortfall, surplus, and stopping at once; the S1-S4 blinding runbook; and the mock-data challenge, executed in three parts — a deterministic core exhaustive over every router branch and both tie directions, an adversarial set generated through a recorded, deposited exchange by a party in the auditor role that did not implement the scoring code, and a public-beacon-seeded bulk for totality and determinism. All three parts pass; the routing tables are generated by executing the shipped implementation and are typed non-evidence in the sentence that reports them. The acceptance gate is then run condition by condition on the deposited pair. One finding is published along the way: 48's coverage condition, read literally, would force every per-design instance to claim all seven leaves; the pre-committed completion evaluates coverage over the design's assigned leaf subset plus the shared non-execution leaf — an annotation to 48, never a retro-edit. The verdict is InstanceStatus_A = reference-complete, with an empty instance gap register: every gate condition passes, and what remains is ownership — acceptance transfers when a laboratory signs, auditor-reproducibly, over the instance plus its re-gated extensions; reference-complete never shortens to accepted, and an immutable core guarantees that no admissible extension can change what a null excludes, who may say so, or how boundary cases route. Displayed at the close is the channel's frozen exclusion content — the carve a future null already names, [1.7e-1, 2.1] at the conservative corner — beside the pre-priced Duhem escape map. Nothing is carved, scored, or measured; no band or feasibility verdict moves; the data paper 49-D stays reserved behind its unlock conditions. What retires is the interpretive seat: refutation content as a public, frozen, executable object — falsifiability without a Falsifier.