{ "_purpose": "The public statement of the theory-level propositions: what each predicts, what would refute it, and the confidence stated or declined. Derived from the registration; analysis plans are not published.", "version": "1.98", "dated": "6 September 2026", "count": 22, "propositions": [ { "id": "P1", "statement": "Within the scope, usable capability is best described by a power law in modelled recursive depth, and the depth exponent exceeds the compute-matched and token-matched breadth exponent by the registered margin. Whether it also exceeds one is P8's separate verdict.", "instrument": "DESIGN DRAFT, the depth titration", "not_evaluable_until": "the crossed or off-path variation the direct boundary-mapping unit is designed to supply exists, and that is true whether P1 holds or fails.", "title": "Power-law conversion and recursive-depth advantage", "refuter": "a registered fit in which a rival form beats the power law under the registered model comparison across a majority of estimable cells.", "confidence": "high.", "group": "laws", "rung": 0, "rung_label": "0 draft, not yet registered", "evidential_status": "draft prediction; not yet registered or tested", "rung_public_label": "draft, not yet registered", "independent_replications": 0, "independent_implementations": 0, "peer_review": null }, { "id": "P2", "statement": "Within the scope, the sustained growth exponent does not rise without limit as reinvestment rises, and the profile has a maximum inside the administered range. This is a claim about the shape of that profile and is firewalled from the framework's boundary claim, which P16, P20 and P3 carry.", "instrument": "DESIGN DRAFT, the reinvestment-allocation titration", "not_evaluable_until": "", "title": "The sustainable growth profile has an interior maximum", "refuter": "a profile that rises throughout the administered range without turning over, where the registered shape adjudication returns monotone rather than unimodal. The adjudication rule is the titration design's registered rule and is restated here so it cannot drift: an interior maximum is declared only when the bootstrap interval on the location of the maximum excludes BOTH ADMINISTERED ENDPOINTS, the lowest as well as the highest, and the registered unimodality check passes; otherwise the profile is adjudicated monotone in whichever direction the registered shape rule returns, and a maximum located at either boundary refutes.", "confidence": "moderate.", "group": "laws", "rung": 0, "rung_label": "0 draft, not yet registered", "evidential_status": "draft prediction; not yet registered or tested", "rung_public_label": "draft, not yet registered", "independent_replications": 0, "independent_implementations": 0, "peer_review": null }, { "id": "P3", "statement": "The maximum growth exponent that a system holds while remaining correctable lies at or below the value the ceiling relation returns from the correction-leverage exponent measured on that same system, and where that exponent is one half the value is two.", "instrument": "DESIGN DRAFT, the paired frontier-and-exponent unit, which measures a frontier and the correction-leverage exponent on the same system so that the two enter the comparison above as a pair. It is named for that pairing rather than by a stem it would otherwise share with the direct boundary-mapping unit named in P16's and P20's entries, which is a different object: that unit reads a located zero crossing on held-out confirmatory cells, and one word between two names is not a distinction a scorer can be asked to hold", "not_evaluable_until": "the correction exponent is measured.", "title": "The corrected relation upper-bounds the sustainable frontier", "refuter": "an interval on the profile maximum lying entirely above the derived value, which replicates on fresh data at the same settings, and which is obtained while the system is still correctable, meaning its correction exponent out-scales its drift exponent with the lower bound of that margin above zero across a window fixed before the run.", "confidence": "", "group": "laws", "rung": 0, "rung_label": "0 draft, not yet registered", "evidential_status": "draft prediction; not yet registered or tested", "rung_public_label": "draft, not yet registered", "independent_replications": 0, "independent_implementations": 0, "peer_review": null }, { "id": "P4", "statement": "Within the registered minimal model, relative correctable burden tends to zero where the correction exponent exceeds the drift exponent, burden holds the advantage where it is the smaller, and at equality coefficients, delay, backlog and saturation decide any finite run.", "instrument": "DESIGN DRAFT, the stability unit, extended with the direct drift measurement and the comparison above", "not_evaluable_until": "", "title": "Correction out-scaling drift is what carries the asymptotic advantage", "refuter": "an observed system that remains aligned on the registered measure while its measured correction exponent sits below its measured drift exponent, over a horizon long enough for the shortfall to have shown.", "confidence": "moderate.", "group": "laws", "rung": 0, "rung_label": "0 draft, not yet registered", "evidential_status": "draft prediction; not yet registered or tested", "rung_public_label": "draft, not yet registered", "independent_replications": 0, "independent_implementations": 0, "peer_review": null }, { "id": "P5", "statement": "The growth exponent implied by a separately measured coupling agrees, within a registered tolerance, with the exponent fitted from the growth curve.", "instrument": "DESIGN DRAFT, the coupling-identification titration, written and dated as its own unit, not registered and not run. IT CARRIED NONE UNTIL THAT UNIT WAS WRITTEN AND THE CHANGE IS RECORDED RATHER THAN ABSORBED. This entry carried the words no instrument from the day it was written, with the note that building one later could not then be presented as a new idea. That note did its work: the design now drafted is the one this entry specified, it measures the coupling by manipulating the retained fraction of a system's own output at a fixed round on systems disjoint from those it predicts, it hash-commits the implied exponent before the sealed windows open, and it compares against the finite-window exponent of the complete solution rather than against its asymptote", "not_evaluable_until": "the scorer-validation units have passed.", "title": "The exponent is derived, not fitted", "refuter": "systematic disagreement beyond tolerance across a majority of estimable systems.", "confidence": "not stated, because the author has no measurement to be confident about.", "group": "derivation", "rung": 0, "rung_label": "0 draft, not yet registered", "evidential_status": "draft prediction; not yet registered or tested", "rung_public_label": "draft, not yet registered", "independent_replications": 0, "independent_implementations": 0, "peer_review": null }, { "id": "P6", "statement": "Where a system corrects itself using mechanisms of its own class, the correction exponent is at or below one half.", "instrument": "DESIGN DRAFT, BLOCKED ON A FROZEN CORRECTOR TAXONOMY, the correction-exponent estimator. The estimator is drafted; the population this proposition is universal over is not yet frozen, and the status names that rather than implying a runnable draft. WHICH AXIS AN AUDIT FREEZES, AND WHAT WOULD SUPPLY THE REST, said so that the freezing of one axis is not read as the unblocking of this proposition. The census of deployed correction named at P7 partitions correctors on the scaling axis, what a mechanism's strength may depend on. The two axes this bound actually rests on are access to external ground truth and failure-mode dependence, and a scaling partition settles neither. Freezing the scaling axis therefore removes one part of the block and leaves the population unfrozen on the two that carry the bound; what would supply them is a corrector-classification unit coding external grounding and failure-mode overlap on the same mechanisms, versioned and hash-pinned on the same rule before any corrector is measured against this proposition. Nothing in the proposition moves here, and what changes is the account of how much of the block one unit removes", "not_evaluable_until": "", "title": "The correction exponent is bounded for same-class correctors", "refuter": "a same-class corrector whose measured correction exponent interval lies entirely above one half.", "confidence": "low.", "group": "laws", "rung": 0, "rung_label": "0 draft, not yet registered", "evidential_status": "draft prediction; not yet registered or tested", "rung_public_label": "draft, not yet registered", "independent_replications": 0, "independent_implementations": 0, "peer_review": null }, { "id": "P7", "statement": "The correction mechanisms actually used in deployed alignment practice predominantly belong to the class whose strength is fixed by construction rather than the class that can scale with the capability it corrects.", "instrument": "DESIGN DRAFT, BLOCKED ON AN UNWRITTEN MAPPING FROM THE AUDIT'S CLASS DISTRIBUTION TO THIS PROPOSITION'S THREE VERDICTS, the corrector-class audit", "not_evaluable_until": "", "title": "Deployed correction is of the weaker class", "refuter": "a preregistered classification in which the scaling class predominates.", "confidence": "moderate.", "group": "surveys", "rung": 0, "rung_label": "0 draft, not yet registered", "evidential_status": "draft prediction; not yet registered or tested", "rung_public_label": "draft, not yet registered", "independent_replications": 0, "independent_implementations": 0, "peer_review": null }, { "id": "P8", "statement": "Across the admissible independent systems the pooled growth exponent exceeds the one-half null; an interval lying wholly below the LOWER EDGE of the registered equivalence region refutes rather than supports it, where an earlier wording said wholly below one half and so contradicted the four-outcome rule in P8's own entry, and whether it also exceeds one is the separate CLEARS UNITY verdict.", "instrument": "DESIGN DRAFT, the multi-system exponent estimation", "not_evaluable_until": "", "title": "Measured exponents exceed the null", "refuter": "a pooled interval on the growth exponent lying wholly below the LOWER EDGE of the registered equivalence region around one half.", "confidence": "", "group": "laws", "rung": 0, "rung_label": "0 draft, not yet registered", "evidential_status": "draft prediction; not yet registered or tested", "rung_public_label": "draft, not yet registered", "independent_replications": 0, "independent_implementations": 0, "peer_review": null }, { "id": "P9", "statement": "Where an effective dimension can be assigned to a domain, the growth exponent follows the dimensional relation with the dimension supplied by that domain's equation of state.", "instrument": "DESIGN DRAFT, BLOCKED ON A FROZEN DIMENSION-ASSIGNMENT RULE, on a correction made here. The surrounding design is written; the rule that assigns an effective dimension to a domain is not, and the status names that rather than implying a runnable draft", "not_evaluable_until": "the rule that assigns an effective dimension to a domain exists as a written procedure, for the same reason as the composition proposition below, which is blocked at the next stage of the same requirement: there the rule is written and its transmission to a third party is unmeasured, while here the rule is not written at all.", "title": "The cross-domain form", "refuter": "measured exponents disagreeing with the dimensional prediction across two or more independent domains.", "confidence": "low.", "group": "laws", "rung": 0, "rung_label": "0 draft, not yet registered", "evidential_status": "draft prediction; not yet registered or tested", "rung_public_label": "draft, not yet registered", "independent_replications": 0, "independent_implementations": 0, "peer_review": null }, { "id": "P10", "statement": "A material fraction of the results this programme has scored unblinded within a single model family, ten per cent, fixed in the entry below, fails to survive re-scoring by a different family.", "instrument": "DESIGN DRAFT, the cross-family re-scoring unit. The cheapest of the three cases named above as the ones that would decide most, because it generates no new model responses", "not_evaluable_until": "", "title": "Scorer-family dependence", "refuter": "a survival proportion whose interval excludes a material loss, where material is fixed now at ten per cent, which is a declared convention fixed before any result rather than a quantity this framework derives, so a fraction landing just either side of it is reported as a result at the margin: P10 is REFUTED when the 95 per cent interval on the fraction of earlier results that do not survive cross-family re-scoring lies entirely below ten per cent, SUPPORTED when it lies entirely above ten per cent, and INCONCLUSIVE otherwise. The re-scoring study's own registration carries the same threshold. A refutation here would mean this programme's blinding result does not reach its own earlier work, which is the one direction in which that result is convenient for its author.", "confidence": "moderate that some results do not survive.", "group": "instrument", "rung": 0, "rung_label": "0 draft, not yet registered", "evidential_status": "draft prediction; not yet registered or tested", "rung_public_label": "draft, not yet registered", "independent_replications": 0, "independent_implementations": 0, "peer_review": null }, { "id": "P11", "statement": "the residual-decay and correction-capacity exponents are not practically interchangeable, and the working practice of treating them as one is an assumption rather than a fact.", "instrument": "DESIGN DRAFT, on both sides of the comparison", "not_evaluable_until": "", "title": "The residual-decay and correction-capacity exponents are not practically interchangeable", "refuter": "measurements of the first two, taken on instruments that share no fitted quantity, agreeing within a registered tolerance across model families, which would license the identification the programme currently only assumes.", "confidence": "not stated.", "group": "derivation", "rung": 0, "rung_label": "0 draft, not yet registered", "evidential_status": "draft prediction; not yet registered or tested", "rung_public_label": "draft, not yet registered", "independent_replications": 0, "independent_implementations": 0, "peer_review": null }, { "id": "P12", "statement": "The order in which a system's components are built moves the correction-leverage exponent by at least the registered minimum effect.", "instrument": "NONE, and the reason is narrower than it looks. Registered without one for the same reason P5 was, before the design that entry specified was drafted. Several drafted units manipulate placement or build order, on gate position, on whether a value specification appears first or last, and on formation against a later rule, but none of them measures the correction-leverage exponent, which is this proposition's endpoint. This proposition is therefore one endpoint away from an instrument rather than lacking a design, and that is recorded here so a reader who finds those units does not conclude the statement was careless", "not_evaluable_until": "", "title": "Build order moves the correction-leverage exponent", "refuter": "a preregistered manipulation of build order producing no change in the correction-leverage exponent beyond the tolerance registered with that instrument, where the instrument has shown from its own sensitivity that a change of that size would have been detected. A manipulation too weak to move anything is not a refutation of this prediction; it is a failed instrument, and condition D above says so in advance.", "confidence": "low.", "group": "engineering", "rung": 0, "rung_label": "0 draft, not yet registered", "evidential_status": "draft prediction; not yet registered or tested", "rung_public_label": "draft, not yet registered", "independent_replications": 0, "independent_implementations": 0, "peer_review": null }, { "id": "P13", "statement": "Where an automated alignment researcher post-trains a target model against alignment benchmarks, a researcher from a different model family than the target reduces held-out misalignment more than a researcher from the same family, at matched data and compute, and the panels differ in measured pairwise error correlation in the direction that would explain it. The two halves are one conjunctive proposition, and an advantage arriving without the correlation difference is reported as unexplained by this framework rather than as support for it.", "instrument": "NONE, corrected here from a value the neighbouring unit could not carry", "not_evaluable_until": "", "title": "Same-family automated correction underperforms cross-family at matched resources, and through the measured error correlation", "refuter": "the interval on the cross-family minus same-family difference in held-out misalignment reduction sitting wholly at or below zero, with data and compute matched and with scoring blind to condition.", "confidence": "moderate.", "group": "engineering", "rung": 0, "rung_label": "0 draft, not yet registered", "evidential_status": "draft prediction; not yet registered or tested", "rung_public_label": "draft, not yet registered", "independent_replications": 0, "independent_implementations": 0, "peer_review": null }, { "id": "P14", "statement": "Where an automated researcher's method is re-scored by a scorer that cannot see the condition and comes from a different model family than either the researcher or its target, the alignment gain it returns is smaller than the gain the unblinded same-family scoring reported.", "instrument": "DESIGN DRAFT, the blinding-evaluation design", "not_evaluable_until": "", "title": "Gains shrink under blinded cross-family scoring", "refuter": "the interval on the blinded minus unblinded gain sitting wholly at or above zero across the same items.", "confidence": "moderate.", "group": "instrument", "rung": 0, "rung_label": "0 draft, not yet registered", "evidential_status": "draft prediction; not yet registered or tested", "rung_public_label": "draft, not yet registered", "independent_replications": 0, "independent_implementations": 0, "peer_review": null }, { "id": "P15", "statement": "Gains installed by external post-training erode under later capability-directed training that embeds no correction of its own, and more than half of what was installed is lost once the capability-training budget matches the alignment budget that installed it.", "instrument": "NONE, corrected here from a value this document's own definition made false. The designs previously named against this proposition cross correction regimes with recursive depth on frozen provider endpoints and update no weights anywhere, while this proposition is about the persistence of a gain installed by post-training, so nothing in this programme measures its endpoint and the honest status is the one reserved for that state", "not_evaluable_until": "", "title": "Externally installed gains decay under subsequent capability training", "refuter": "an interval on the retained fraction of the installed gain, after matched capability training without embedded correction, lying entirely above one half.", "confidence": "moderate.", "group": "engineering", "rung": 0, "rung_label": "0 draft, not yet registered", "evidential_status": "draft prediction; not yet registered or tested", "rung_public_label": "draft, not yet registered", "independent_replications": 0, "independent_implementations": 0, "peer_review": null }, { "id": "P16", "statement": "A system does not hold both at once: a growth exponent above the point at which its own measured correction margin reaches zero, and a correction margin whose lower bound stays above zero, sustained across a window fixed before the run.", "instrument": "DESIGN DRAFT, BLOCKED ON CANONICAL IDENTITY AND ON DECISIONS THE AUTHOR HAS NOT YET TAKEN, the direct boundary-mapping unit taken jointly with the exponent measurement", "not_evaluable_until": "", "title": "The prohibition itself", "refuter": "a run holding the exponent above that point with the lower bound of the correction margin above zero across the registered window, replicated on fresh data at the same settings.", "confidence": "low to moderate.", "group": "laws", "rung": 0, "rung_label": "0 draft, not yet registered", "evidential_status": "draft prediction; not yet registered or tested", "rung_public_label": "draft, not yet registered", "independent_replications": 0, "independent_implementations": 0, "peer_review": null }, { "id": "P17", "statement": "Within a corrector panel named in advance by model lineage, substrate, training provenance and scaling class, pairwise joint misses on a frozen fault set are practically equivalent to the conditional-independence baseline; failure-mode overlap is the outcome rather than the entry criterion, and this is the cross-sectional claim the instrument can decide rather than the temporal premise it bears on.", "instrument": "DESIGN DRAFT, the correlated-failure unit", "not_evaluable_until": "", "title": "Panel corrector failures are conditionally independent on a frozen fault set", "refuter": "a registered panel drawn from the population above, whose joint failure rate exceeds the independence baseline by the equivalence margin registered with that instrument, which that unit fixes at 0.20 on the log scale of the ratio of observed to predicted joint misses, an inflation of about 22 per cent over independence, on a frozen fault set whose type is stated. The panel and the fault set carry their type, checkable or judged, because P22 predicts the answer differs between them and a panel reported without its type cannot be read against either.", "confidence": "low to moderate.", "group": "laws", "rung": 0, "rung_label": "0 draft, not yet registered", "evidential_status": "draft prediction; not yet registered or tested", "rung_public_label": "draft, not yet registered", "independent_replications": 0, "independent_implementations": 0, "peer_review": null }, { "id": "P18", "statement": "Classified in advance by how a domain composes its inputs and outputs, the scaling family that best fits that domain's data is the family the classification predicts, and not one chosen after the curve is seen.", "instrument": "DESIGN DRAFT, BLOCKED ON A COMPOSITION-CLASSIFICATION RULE WHOSE THIRD-PARTY REPRODUCIBILITY IS UNMEASURED, the domain-catalogue units. The surrounding design is written and so is the rule: the deciding unit carries a written external-assessor packet, prepared and never issued, together with a registered agreement test comparing an external human classification against the frame's own locked class at a stated threshold. What is missing is the measurement and not the writing, and an earlier wording of this line said no such rule was written at all. This is a correction of the status and not a relaxation of it: until the agreement test reports at or above its registered threshold, the rule is not shown to transmit to a third party, and the five-value status vocabulary exists precisely to tell a runnable draft from a blocked one", "not_evaluable_until": "the classification rule this proposition requires is shown to transmit to a third party.", "title": "The composition operator predicts the family", "refuter": "the predicted family failing to beat, by the margin registered with the deciding instrument and across the registered domain set, the comparator that belongs to the draw actually used: the balanced rate where the domains are drawn balanced across families, and the empirical prevalence where they are drawn unstratified.", "confidence": "low to moderate.", "group": "laws", "rung": 0, "rung_label": "0 draft, not yet registered", "evidential_status": "draft prediction; not yet registered or tested", "rung_public_label": "draft, not yet registered", "independent_replications": 0, "independent_implementations": 0, "peer_review": null }, { "id": "P19", "statement": "Alignment achieved by mechanisms outside a system's own recursion does not improve as the capability of the system it governs rises.", "instrument": "DESIGN DRAFT, BLOCKED ON A REGISTERED MAPPING FROM THE INTEGRITY-INDEX REGRESSION SCALE TO THE EXPONENT SCALE, the integrity-index scaling units, named here for what they measure rather than for the quantity they would need a mapping to reach. They estimate the slope of an operational integrity index against a capability score and register their own flat bound on that regression scale, and their own text says the estimand is not an exponent margin; an earlier wording called them the alignment-exponent units, which named them for the one scale this instrument line exists to say they do not report on. The units are drafted; the mapping this proposition's own rule requires before their result can be scored against it is not, and the status names that rather than implying a runnable verdict. Those units bear on the zero-scaling axis alone. The keep-pace axis has no deciding design registered anywhere in this programme and is NOT EVALUABLE, stated here beside the other axis so that a split verdict is not read as two live axes when one of them has no instrument", "not_evaluable_until": "", "title": "External alignment does not scale with capability", "refuter": "on the zero-scaling axis, which is this proposition as worded, an alignment exponent whose interval lies entirely outside the registered equivalence region of plus or minus 0.10 about zero, in either direction; and on the keep-pace axis, reported beside it, an interval lying entirely above one half.", "confidence": "low to moderate.", "group": "surveys", "rung": 0, "rung_label": "0 draft, not yet registered", "evidential_status": "draft prediction; not yet registered or tested", "rung_public_label": "draft, not yet registered", "independent_replications": 0, "independent_implementations": 0, "peer_review": null }, { "id": "P20", "statement": "Where a stability boundary can be located and a correction exponent measured on the same system, the boundary follows one over one minus the correction exponent rather than one over the correction exponent or a fitted constant.", "instrument": "DESIGN DRAFT, the form-discrimination unit", "not_evaluable_until": "the crossed variation the direct boundary-mapping unit is designed to supply exists, and that holds whether P1 holds or fails.", "title": "The ceiling relation takes the corrected form", "refuter": "the discrimination registered with the deciding instrument selecting a rival over the registered relation across a majority of admissible cells, on systems held out of the fitting.", "confidence": "low to moderate.", "group": "laws", "rung": 0, "rung_label": "0 draft, not yet registered", "evidential_status": "draft prediction; not yet registered or tested", "rung_public_label": "draft, not yet registered", "independent_replications": 0, "independent_implementations": 0, "peer_review": null }, { "id": "P21", "statement": "Correction that participates in each subsequent revision round outperforms correction that sees only the finished output, and the advantage widens as recursive depth rises rather than staying constant.", "instrument": "DESIGN DRAFT, the embedded-versus-external correction designs. That unit's registered sensitivity was measured on a smaller design than the one registered, and its negative-slope hypothesis has no operating characteristic; both are recorded against that unit and are closed before this proposition is scored", "not_evaluable_until": "", "title": "In-loop correction pulls away with depth", "refuter": "no interaction between correction placement and depth beyond the tolerance registered with that instrument, in a design whose own sensitivity shows an interaction of that size would have been detected. A design too small to find the interaction is a failed instrument and not a refutation, as condition D already provides.", "confidence": "low to moderate.", "group": "engineering", "rung": 0, "rung_label": "0 draft, not yet registered", "evidential_status": "draft prediction; not yet registered or tested", "rung_public_label": "draft, not yet registered", "independent_replications": 0, "independent_implementations": 0, "peer_review": null }, { "id": "P22", "statement": "The checkable correction-leverage exponent exceeds the judged correction-leverage exponent on the same systems under the same instrument, so the ceiling is strictly lower for judged correction.", "instrument": "NONE, and a typed extension of the correction-exponent estimator is required. It does not exist. This entry is a correction of an earlier one that named the correlated-failure unit, and the correction matters more than the change of name: that unit estimates the excess of joint misses over a conditional-independence baseline across a panel of correctors, which is a dependence between failures and is not an elasticity of correction against capability. An instrument measuring correlation cannot decide an inequality between two exponents. What would decide this proposition is the correction-exponent estimator, which fits corrective strength against overseen capability per corrector family, run over two matched fault populations of stated type on the same capability ladder, with the two exponents estimated under one instrument so their difference carries a joint interval. That extension is not built, does not exist anywhere in this programme's own work, and will be registered as its own unit or as a recorded amendment to the estimator's own registration before any outcome is examined. The correlated-failure unit remains named here as mechanism evidence: it can show whether the failure-mode overlap this proposition's reasoning invokes differs by type, and it cannot supply the exponents. FALLS WITH IT: the reading of the value two as a single number that holds across correction types. P6 survives as a statement about whichever type its own instrument measures, and the ceiling relation is untouched", "not_evaluable_until": "", "title": "Checkable correction carries the higher exponent, so the ceiling is lowest where the safety claim lives", "refuter": "a measured judged correction-leverage exponent exceeding the checkable one on the same systems under the same instrument, with the reversal replicating on fresh data at the same settings.", "confidence": "low to moderate.", "group": "laws", "rung": 0, "rung_label": "0 draft, not yet registered", "evidential_status": "draft prediction; not yet registered or tested", "rung_public_label": "draft, not yet registered", "independent_replications": 0, "independent_implementations": 0, "peer_review": null } ], "ladder": [ "0 written and dated", "1 author-run support", "2 independently reproduced", "3 independently replicated", "4 independently reimplemented", "5 generalised across architectures", "6 prospectively predictive", "7 validated within the tested domain" ], "result_chain_record_version": "1.85" }