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.