How many distinct explanations are needed for how culture spreads?

HERETICAL CANDIDATE SET: S1={U, a single transferable semantic-loss response law}; proposed minimum K=1. U jointly predicts within-source reconstruction and selection between supplied variants, rather than giving them independently adjustable response laws. For a finite, preregistered candidate-output set, P_U(y|x,c)=exp[-beta L(y,x,c)]/sum_z exp[-beta L(z,x,c)]. Here x is the available source, c the measured task/context, L is an independently specified semantic/function error plus production cost in common calibrated units, and beta is calibrated once per producer type on nonsocial trials. The same beta and loss differences must predict later between-variant choices, retellings and responses to source-frequency interventions; no free prestige, conformity, partner-history or feed-label coefficient can be added. Known delivery policy and measured opportunities enter as experimental inputs, not as an invented second cultural response law. The strong claim is cross-operation invariance, not that any arbitrarily flexible Bayesian program counts as one family. Selection and reconstruction are two observations of U, so S={R,S} overcounts; ecology, collective concurrency and kinetic intermediate dependencies add no held-out predictive benefit once the independently measured loss and source information are matched. Zero families are insufficient because randomized source availability and task-loss reversal cause reproducible nonzero descendant and adoption responses. The common-law count is limited to this bounded panel and would be rejected rather than universalized if one independent causal response remains.

In the same people, a randomized reversal of the independently specified functional loss must reverse both choice preference and semantic transformation in the quantitatively predicted amount, within epsilon_2 and epsilon_4, without fitting a choice-specific beta. Source prestige/frequency, third-party modifier and concurrent-update contrasts have residuals within their equivalence margins after the specified loss, knowledge and opportunities are matched. S1 is the minimal set only if this cross-operation restriction predicts every held-out block and removal of the single source-loss dependency causes out-of-margin failure. A reproducible choice-versus-reconstruction double dissociation at matched loss, or a genuine moderator/concurrency/kinetic residual, falsifies K=1 in favor of a split answer. If an unrestricted single kernel succeeds but this tied law fails, that does not support S1: it is relabeling a composition.

In held-out communities present the focal source i, competitor j and a third modifier k, keeping the focal producer's dose, selected parent, semantic facts and payoff constant. Change k's contextual relation to the i-versus-j contrast while preserving its surface salience and factual information; include independent-production and fixed-artifact-choice controls. Let D_M be the observed third-party change in the i-to-descendant semantic transition minus the prediction of the strongest calibrated established composition. S3 predicts |D_M|>epsilon_4, a prespecified direction for a given trained modifier relation, and loss of this residual when that relation is experimentally severed; restoring the relation rescues it in new source families. Fixed-artifact choice can show ordinary context effects without establishing M. The R and S removals separately impair source-specific feature transmission and fixed-variant selection, respectively, establishing the other two required dependencies. If the nonlinear established composition predicts D_M within margins, or if M survives only under one semantic meter, remove M as a distinct family and consolidate to the appropriate known R/S explanation. A significant three-way coefficient alone is expressly insufficient.

Condition-dependent scoring may create false extra families of cultural transmission predicts instead: Randomize the semantic coding pipeline on the same fully logged outputs, including meaning-reversed high-overlap pairs and meaning-preserved low-overlap pairs. Before calibration, the fitted family partition changes with coder and unit boundaries. After independent calibration of C_a and behavioral comprehension/enactment validation, the proposed modifier, concurrency and stage-split residuals all lie within epsilon_o and their added held-out predictive gain within eta_o; the source-removal versus fixed-variant-choice double dissociation persists, requiring exactly R and S. The one-law tie is rejected by a replicated difference between the reconstruction-calibrated and choice-calibrated response slopes. This is evidence for K=2 only with adequately powered equivalence and successful manipulation checks, not because a larger model has nonsignificant coefficients. A modifier or group-protocol residual that remains in behavioral outcomes, survives independent human rubrics and is selectively abolished by its own dependency removal falsifies the observation-channel account in favor of a larger candidate set. If the scoring effect is real but a biological/cultural residual remains too, S2 is not sufficient.

Overlapping updates may transmit conflicting cultural rules despite accurate individual recall predicts instead: Run small communities learning an artificial reference system with two initially compatible rules. In an asynchronous arm two producers read the same earlier public version and issue individually valid but jointly incompatible updates; in a serialized arm the second update is produced after reading the first. Match numbers of messages, total time, word content available at final test, partner mix, payoff and aggregate feedback. A replay arm gives the identical final corpus to new individuals without joint updating; a yoked-delay arm controls staleness and recency. Fit ordinary CHAI-like partner learning, sequential priming, rule learning and allocator memory on matched histories before the test. Define D_C as the excess rate of jointly inconsistent but individually accurately recalled rule pairs over that full established composition. S4 predicts D_C>epsilon_4 specifically when overlapping writes target a shared rule, disappearance when the shared-update dependency is serialized or made nonconflicting, and rescue when conflict is reintroduced; the effect must persist beyond a mere last-item recall error. Independently resetting partner history while retaining a coherent shared record removes H's familiar-to-new-partner transfer, demonstrating H is also needed. Removing source access or choice feedback establishes R and S. If all C effects are predicted by established partner learning plus visible history and recency, delete C and reduce the proposed four-family answer; if H also merges with R under the panel, reduce again. The group label does not earn a family by itself.

Cultural transmission may require six distinct pathways that cannot be merged predicts instead: Use an intervention-and-rescue panel with timed, information-matched controls: E, move the same organizing context from before to after source presentation; U, add a retrieval-context cue after equal encoding; I, scramble the cross-source relation while preserving the same component facts and recall; A, swap experimentally known recipient knowledge while keeping the source and private recognition fixed; S, perturb choice information on fixed unchanged artifacts with exposure matched; F, reset versus preserve a logged allocator state and compare with exact exposure-history replay. Each full nonlinear model predicts the result of all removals before observing their held-out combination. Let Delta_f,o be the difference between the observed held-out effect of removal f and the best model in which f is merged into its nearest component. S6 predicts an out-of-margin Delta_f,o for every f on its prespecified primary outcome, successful mediator validation, and selective rescue; no five-family merge predicts all six. In contrast, no extra residual for the ecology modifier or concurrent-update dependency remains after these six established pathways and their calibrated compositions are included. If a single source-state model predicts both E and U removals and rescue, merge them; if I is explained by complementary facts or ordinary hierarchical reconstruction, merge I; if a logged exposure process fully explains F without an independent adaptive-state effect, merge F with S. Any such successful equivalence refutes exactly K=6 and narrows the admissible count downward. This must be tested with the actual nonlinear models, not a rank-six response matrix.

CROSS-DOMAIN CANDIDATE SET: S3={R, source-conditioned reconstruction; S, competition and selection among available variants; M, community-conditioned modification of the reconstruction rule}; proposed minimum K=3. R specifies the causal transition from a documented source to a descendant, including independently calibrated prior/uncertainty effects. S specifies opportunities and choice/reproduction of already available variants under independently calibrated source- and content-dependent selection, with ordinary measured learning and allocator history allowed. M adds an edge from the joint current competitor configuration to the source-to-descendant transition kernel itself: a third variant changes how one supplied variant is reconstructed relative to another, even after matching which source was seen and chosen, time, information, population mixture and the isolated priming effects of each competitor. Thus M is neither another selected variant nor a third source that simply contributes a missing premise. One and two families cannot predict the held-out three-way transformation/rescue contrast; splits into separate disciplinary accounts of the same M dependency are unnecessary. Three is a proposed size of this named set, not the number of terms in an ecological polynomial. A concrete test implementation is T_M(y|x,c,j,k)=T_null(y|x,c,j,k) exp[kappa g_y(x,j,k)]/sum_z T_null(z|x,c,j,k) exp[kappa g_z(x,j,k)]. T_null is the strongest independently calibrated nonlinear established composition, and g is a preregistered semantic relational-modifier code, zero in the relation-severed condition. Fit kappa on one stimulus family and predict its signed change on withheld families. Merely choosing g after inspecting failures is prohibited. kappa=0 removes the additional dependency, but the number of fitted kappa values never defines K.

In held-out communities present the focal source i, competitor j and a third modifier k, keeping the focal producer's dose, selected parent, semantic facts and payoff constant. Change k's contextual relation to the i-versus-j contrast while preserving its surface salience and factual information; include independent-production and fixed-artifact-choice controls. Let D_M be the observed third-party change in the i-to-descendant semantic transition minus the prediction of the strongest calibrated established composition. S3 predicts |D_M|>epsilon_4, a prespecified direction for a given trained modifier relation, and loss of this residual when that relation is experimentally severed; restoring the relation rescues it in new source families. Fixed-artifact choice can show ordinary context effects without establishing M. The R and S removals separately impair source-specific feature transmission and fixed-variant selection, respectively, establishing the other two required dependencies. If the nonlinear established composition predicts D_M within margins, or if M survives only under one semantic meter, remove M as a distinct family and consolidate to the appropriate known R/S explanation. A significant three-way coefficient alone is expressly insufficient.

In the same people, a randomized reversal of the independently specified functional loss must reverse both choice preference and semantic transformation in the quantitatively predicted amount, within epsilon_2 and epsilon_4, without fitting a choice-specific beta. Source prestige/frequency, third-party modifier and concurrent-update contrasts have residuals within their equivalence margins after the specified loss, knowledge and opportunities are matched. S1 is the minimal set only if this cross-operation restriction predicts every held-out block and removal of the single source-loss dependency causes out-of-margin failure. A reproducible choice-versus-reconstruction double dissociation at matched loss, or a genuine moderator/concurrency/kinetic residual, falsifies K=1 in favor of a split answer. If an unrestricted single kernel succeeds but this tied law fails, that does not support S1: it is relabeling a composition.

Condition-dependent scoring may create false extra families of cultural transmission predicts instead: Randomize the semantic coding pipeline on the same fully logged outputs, including meaning-reversed high-overlap pairs and meaning-preserved low-overlap pairs. Before calibration, the fitted family partition changes with coder and unit boundaries. After independent calibration of C_a and behavioral comprehension/enactment validation, the proposed modifier, concurrency and stage-split residuals all lie within epsilon_o and their added held-out predictive gain within eta_o; the source-removal versus fixed-variant-choice double dissociation persists, requiring exactly R and S. The one-law tie is rejected by a replicated difference between the reconstruction-calibrated and choice-calibrated response slopes. This is evidence for K=2 only with adequately powered equivalence and successful manipulation checks, not because a larger model has nonsignificant coefficients. A modifier or group-protocol residual that remains in behavioral outcomes, survives independent human rubrics and is selectively abolished by its own dependency removal falsifies the observation-channel account in favor of a larger candidate set. If the scoring effect is real but a biological/cultural residual remains too, S2 is not sufficient.

Overlapping updates may transmit conflicting cultural rules despite accurate individual recall predicts instead: Run small communities learning an artificial reference system with two initially compatible rules. In an asynchronous arm two producers read the same earlier public version and issue individually valid but jointly incompatible updates; in a serialized arm the second update is produced after reading the first. Match numbers of messages, total time, word content available at final test, partner mix, payoff and aggregate feedback. A replay arm gives the identical final corpus to new individuals without joint updating; a yoked-delay arm controls staleness and recency. Fit ordinary CHAI-like partner learning, sequential priming, rule learning and allocator memory on matched histories before the test. Define D_C as the excess rate of jointly inconsistent but individually accurately recalled rule pairs over that full established composition. S4 predicts D_C>epsilon_4 specifically when overlapping writes target a shared rule, disappearance when the shared-update dependency is serialized or made nonconflicting, and rescue when conflict is reintroduced; the effect must persist beyond a mere last-item recall error. Independently resetting partner history while retaining a coherent shared record removes H's familiar-to-new-partner transfer, demonstrating H is also needed. Removing source access or choice feedback establishes R and S. If all C effects are predicted by established partner learning plus visible history and recency, delete C and reduce the proposed four-family answer; if H also merges with R under the panel, reduce again. The group label does not earn a family by itself.

Cultural transmission may require six distinct pathways that cannot be merged predicts instead: Use an intervention-and-rescue panel with timed, information-matched controls: E, move the same organizing context from before to after source presentation; U, add a retrieval-context cue after equal encoding; I, scramble the cross-source relation while preserving the same component facts and recall; A, swap experimentally known recipient knowledge while keeping the source and private recognition fixed; S, perturb choice information on fixed unchanged artifacts with exposure matched; F, reset versus preserve a logged allocator state and compare with exact exposure-history replay. Each full nonlinear model predicts the result of all removals before observing their held-out combination. Let Delta_f,o be the difference between the observed held-out effect of removal f and the best model in which f is merged into its nearest component. S6 predicts an out-of-margin Delta_f,o for every f on its prespecified primary outcome, successful mediator validation, and selective rescue; no five-family merge predicts all six. In contrast, no extra residual for the ecology modifier or concurrent-update dependency remains after these six established pathways and their calibrated compositions are included. If a single source-state model predicts both E and U removals and rescue, merge them; if I is explained by complementary facts or ordinary hierarchical reconstruction, merge I; if a logged exposure process fully explains F without an independent adaptive-state effect, merge F with S. Any such successful equivalence refutes exactly K=6 and narrows the admissible count downward. This must be tested with the actual nonlinear models, not a rank-six response matrix.

PHENOMENON-DOESN'T-EXIST CANDIDATE SET: S2={R, source-conditioned reconstructive transmission; S, exposure-conditioned selection/reproduction}; proposed minimum K=2, with zero additional families created by the apparent clustering of semantic effects. The alleged multiplication into several irreducible cultural families is generated by a condition-dependent observation channel: the same latent change is split differently by lexical-overlap, embedding, entailment or lineage coders because sentence roles, unit boundaries and provenance are treated inconsistently. Write P(observed code v|do(a))=sum_y C_a(v|y) P_{R,S}(true state y|do(a)); C_a is estimated on blinded known-origin, known-meaning challenge material and is not silently assumed invariant across a. Nonlinearity and ordinary learning are allowed in the frozen R/S composition, but it cannot receive a separate arbitrary kernel for every intervention. R and S remain irreducible because source removal and fixed-artifact menu/choice changes produce different validated causal effects. The nonexistent phenomenon is the additional discrete-family structure in the current meters, not cultural transmission, source-specific inheritance or all forms of mechanistic diversity. One common-law family is insufficient because R and S do not satisfy IH_01's parameter-tying equality; three, four or six are unnecessary if their residual signatures arise in C_a alone.

Before calibration, the fitted family partition changes with coder and unit boundaries. After independent calibration of C_a and behavioral comprehension/enactment validation, the proposed modifier, concurrency and stage-split residuals all lie within epsilon_o and their added held-out predictive gain within eta_o; the source-removal versus fixed-variant-choice double dissociation persists, requiring exactly R and S. The one-law tie is rejected by a replicated difference between the reconstruction-calibrated and choice-calibrated response slopes. This is evidence for K=2 only with adequately powered equivalence and successful manipulation checks, not because a larger model has nonsignificant coefficients. A modifier or group-protocol residual that remains in behavioral outcomes, survives independent human rubrics and is selectively abolished by its own dependency removal falsifies the observation-channel account in favor of a larger candidate set. If the scoring effect is real but a biological/cultural residual remains too, S2 is not sufficient.

In the same people, a randomized reversal of the independently specified functional loss must reverse both choice preference and semantic transformation in the quantitatively predicted amount, within epsilon_2 and epsilon_4, without fitting a choice-specific beta. Source prestige/frequency, third-party modifier and concurrent-update contrasts have residuals within their equivalence margins after the specified loss, knowledge and opportunities are matched. S1 is the minimal set only if this cross-operation restriction predicts every held-out block and removal of the single source-loss dependency causes out-of-margin failure. A reproducible choice-versus-reconstruction double dissociation at matched loss, or a genuine moderator/concurrency/kinetic residual, falsifies K=1 in favor of a split answer. If an unrestricted single kernel succeeds but this tied law fails, that does not support S1: it is relabeling a composition.

A third cultural variant may change how competing variants are reconstructed predicts instead: Measure lower-order source/competitor conditions first and freeze both the actual nonlinear R+S composition and its mixture-selection, causal-source-inference and complementary-information extensions. In held-out communities present the focal source i, competitor j and a third modifier k, keeping the focal producer's dose, selected parent, semantic facts and payoff constant. Change k's contextual relation to the i-versus-j contrast while preserving its surface salience and factual information; include independent-production and fixed-artifact-choice controls. Let D_M be the observed third-party change in the i-to-descendant semantic transition minus the prediction of the strongest calibrated established composition. S3 predicts |D_M|>epsilon_4, a prespecified direction for a given trained modifier relation, and loss of this residual when that relation is experimentally severed; restoring the relation rescues it in new source families. Fixed-artifact choice can show ordinary context effects without establishing M. The R and S removals separately impair source-specific feature transmission and fixed-variant selection, respectively, establishing the other two required dependencies. If the nonlinear established composition predicts D_M within margins, or if M survives only under one semantic meter, remove M as a distinct family and consolidate to the appropriate known R/S explanation. A significant three-way coefficient alone is expressly insufficient.

Overlapping updates may transmit conflicting cultural rules despite accurate individual recall predicts instead: Run small communities learning an artificial reference system with two initially compatible rules. In an asynchronous arm two producers read the same earlier public version and issue individually valid but jointly incompatible updates; in a serialized arm the second update is produced after reading the first. Match numbers of messages, total time, word content available at final test, partner mix, payoff and aggregate feedback. A replay arm gives the identical final corpus to new individuals without joint updating; a yoked-delay arm controls staleness and recency. Fit ordinary CHAI-like partner learning, sequential priming, rule learning and allocator memory on matched histories before the test. Define D_C as the excess rate of jointly inconsistent but individually accurately recalled rule pairs over that full established composition. S4 predicts D_C>epsilon_4 specifically when overlapping writes target a shared rule, disappearance when the shared-update dependency is serialized or made nonconflicting, and rescue when conflict is reintroduced; the effect must persist beyond a mere last-item recall error. Independently resetting partner history while retaining a coherent shared record removes H's familiar-to-new-partner transfer, demonstrating H is also needed. Removing source access or choice feedback establishes R and S. If all C effects are predicted by established partner learning plus visible history and recency, delete C and reduce the proposed four-family answer; if H also merges with R under the panel, reduce again. The group label does not earn a family by itself.

Cultural transmission may require six distinct pathways that cannot be merged predicts instead: Use an intervention-and-rescue panel with timed, information-matched controls: E, move the same organizing context from before to after source presentation; U, add a retrieval-context cue after equal encoding; I, scramble the cross-source relation while preserving the same component facts and recall; A, swap experimentally known recipient knowledge while keeping the source and private recognition fixed; S, perturb choice information on fixed unchanged artifacts with exposure matched; F, reset versus preserve a logged allocator state and compare with exact exposure-history replay. Each full nonlinear model predicts the result of all removals before observing their held-out combination. Let Delta_f,o be the difference between the observed held-out effect of removal f and the best model in which f is merged into its nearest component. S6 predicts an out-of-margin Delta_f,o for every f on its prespecified primary outcome, successful mediator validation, and selective rescue; no five-family merge predicts all six. In contrast, no extra residual for the ecology modifier or concurrent-update dependency remains after these six established pathways and their calibrated compositions are included. If a single source-state model predicts both E and U removals and rescue, merge them; if I is explained by complementary facts or ordinary hierarchical reconstruction, merge I; if a logged exposure process fully explains F without an independent adaptive-state effect, merge F with S. Any such successful equivalence refutes exactly K=6 and narrows the admissible count downward. This must be tested with the actual nonlinear models, not a rank-six response matrix.

SCOUT 1 — DISTRIBUTED DATABASE SYSTEMS CANDIDATE SET: S4={R, individual source-conditioned reconstruction; S, variant choice/reproduction; H, partner-to-population hierarchical convention inference; C, concurrent incompatible-update reconciliation}; proposed minimum K=4. H is the already established kind of dependency in which a local partner's meaning is distinguished from a population prior. C is the new candidate dependency: individually adequate local updates to a shared meaning system can jointly violate a cross-partner semantic constraint when each is produced against an older version; subsequent transmissions inherit the inconsistent public version even when each person's source recall is accurate. H cannot replace C because tracking partner identities and local beliefs does not by itself specify which mutually incompatible updates become jointly authoritative in the shared record. C cannot replace H because the same correctly serialized public record can generalize differently to familiar and new partners. The transmitted system includes relationships among labels, referents and interpretation rules, with propositions nested inside it. R/S suffice for neither a held-out partner-generalization contrast nor a residual dependency on update overlap; a finer kinetic split is unnecessary if the four causal modules predict it. Four is a candidate set cardinality, not a count of computers, participants or messages. Formally, H updates separate partner lexicons theta_p under a population parameter eta using p(theta_p,eta|history), rather than one undifferentiated source prior. C adds a shared accepted-version state V whose transition depends jointly on the read-version and write-set of overlapping updates; the otherwise matched composition updates V only through a serial order. This is a causal-state distinction, not a claim that the cultural process is a literal database.

In an asynchronous arm two producers read the same earlier public version and issue individually valid but jointly incompatible updates; in a serialized arm the second update is produced after reading the first. Match numbers of messages, total time, word content available at final test, partner mix, payoff and aggregate feedback. A replay arm gives the identical final corpus to new individuals without joint updating; a yoked-delay arm controls staleness and recency. Fit ordinary CHAI-like partner learning, sequential priming, rule learning and allocator memory on matched histories before the test. Define D_C as the excess rate of jointly inconsistent but individually accurately recalled rule pairs over that full established composition. S4 predicts D_C>epsilon_4 specifically when overlapping writes target a shared rule, disappearance when the shared-update dependency is serialized or made nonconflicting, and rescue when conflict is reintroduced; the effect must persist beyond a mere last-item recall error. Independently resetting partner history while retaining a coherent shared record removes H's familiar-to-new-partner transfer, demonstrating H is also needed. Removing source access or choice feedback establishes R and S. If all C effects are predicted by established partner learning plus visible history and recency, delete C and reduce the proposed four-family answer; if H also merges with R under the panel, reduce again. The group label does not earn a family by itself.

In the same people, a randomized reversal of the independently specified functional loss must reverse both choice preference and semantic transformation in the quantitatively predicted amount, within epsilon_2 and epsilon_4, without fitting a choice-specific beta. Source prestige/frequency, third-party modifier and concurrent-update contrasts have residuals within their equivalence margins after the specified loss, knowledge and opportunities are matched. S1 is the minimal set only if this cross-operation restriction predicts every held-out block and removal of the single source-loss dependency causes out-of-margin failure. A reproducible choice-versus-reconstruction double dissociation at matched loss, or a genuine moderator/concurrency/kinetic residual, falsifies K=1 in favor of a split answer. If an unrestricted single kernel succeeds but this tied law fails, that does not support S1: it is relabeling a composition.

A third cultural variant may change how competing variants are reconstructed predicts instead: Measure lower-order source/competitor conditions first and freeze both the actual nonlinear R+S composition and its mixture-selection, causal-source-inference and complementary-information extensions. In held-out communities present the focal source i, competitor j and a third modifier k, keeping the focal producer's dose, selected parent, semantic facts and payoff constant. Change k's contextual relation to the i-versus-j contrast while preserving its surface salience and factual information; include independent-production and fixed-artifact-choice controls. Let D_M be the observed third-party change in the i-to-descendant semantic transition minus the prediction of the strongest calibrated established composition. S3 predicts |D_M|>epsilon_4, a prespecified direction for a given trained modifier relation, and loss of this residual when that relation is experimentally severed; restoring the relation rescues it in new source families. Fixed-artifact choice can show ordinary context effects without establishing M. The R and S removals separately impair source-specific feature transmission and fixed-variant selection, respectively, establishing the other two required dependencies. If the nonlinear established composition predicts D_M within margins, or if M survives only under one semantic meter, remove M as a distinct family and consolidate to the appropriate known R/S explanation. A significant three-way coefficient alone is expressly insufficient.

Condition-dependent scoring may create false extra families of cultural transmission predicts instead: Randomize the semantic coding pipeline on the same fully logged outputs, including meaning-reversed high-overlap pairs and meaning-preserved low-overlap pairs. Before calibration, the fitted family partition changes with coder and unit boundaries. After independent calibration of C_a and behavioral comprehension/enactment validation, the proposed modifier, concurrency and stage-split residuals all lie within epsilon_o and their added held-out predictive gain within eta_o; the source-removal versus fixed-variant-choice double dissociation persists, requiring exactly R and S. The one-law tie is rejected by a replicated difference between the reconstruction-calibrated and choice-calibrated response slopes. This is evidence for K=2 only with adequately powered equivalence and successful manipulation checks, not because a larger model has nonsignificant coefficients. A modifier or group-protocol residual that remains in behavioral outcomes, survives independent human rubrics and is selectively abolished by its own dependency removal falsifies the observation-channel account in favor of a larger candidate set. If the scoring effect is real but a biological/cultural residual remains too, S2 is not sufficient.

Cultural transmission may require six distinct pathways that cannot be merged predicts instead: Use an intervention-and-rescue panel with timed, information-matched controls: E, move the same organizing context from before to after source presentation; U, add a retrieval-context cue after equal encoding; I, scramble the cross-source relation while preserving the same component facts and recall; A, swap experimentally known recipient knowledge while keeping the source and private recognition fixed; S, perturb choice information on fixed unchanged artifacts with exposure matched; F, reset versus preserve a logged allocator state and compare with exact exposure-history replay. Each full nonlinear model predicts the result of all removals before observing their held-out combination. Let Delta_f,o be the difference between the observed held-out effect of removal f and the best model in which f is merged into its nearest component. S6 predicts an out-of-margin Delta_f,o for every f on its prespecified primary outcome, successful mediator validation, and selective rescue; no five-family merge predicts all six. In contrast, no extra residual for the ecology modifier or concurrent-update dependency remains after these six established pathways and their calibrated compositions are included. If a single source-state model predicts both E and U removals and rescue, merge them; if I is explained by complementary facts or ordinary hierarchical reconstruction, merge I; if a logged exposure process fully explains F without an independent adaptive-state effect, merge F with S. Any such successful equivalence refutes exactly K=6 and narrows the admissible count downward. This must be tested with the actual nonlinear models, not a rank-six response matrix.

SCOUT 2 — CHEMICAL REACTION ENGINEERING CANDIDATE SET: S6={E, source organization during encoding; U, access and updating during retrieval; I, cross-source relational integration; A, audience-conditioned expression and generalization; S, choosing among already available variants; F, adaptive allocation of future exposure}; proposed minimum K=6. The imported mechanism is the failure of kinetic lumping when distinct intermediate pathways respond differently to a localized perturbation. In the cultural realization, an encoded source representation, its accessible retrieval state, an integrated relational representation and an audience-specific emitted version are experimentally distinguishable intermediate states; the selection and allocation processes act on different stages. A scalar 'reconstruction strength' or a single selection kernel cannot predict all localized-removal and rescue responses. E is needed when context before encoding changes later organization; U when retrieval cues change access with the source representation held constant; I when paired premises change a novel relation without changing premise recall; A when recipient knowledge changes the emitted descendant while private recognition is stable; S when fixed-artifact choice changes without semantic editing; F when policy-state reset changes later opportunities while immediate human responses are fixed. Neither six stage names nor six fitted states suffices: each of these six dependency classes must have a transferable, independently necessary intervention signature. M and C from the other candidates are predicted compositions of these intermediates, rather than seventh and eighth mechanisms. The program exposes intermediate distributions z_E,z_U,z_I,z_A: z_E=E(x,c_pre), z_U=U(z_E,c_retrieval,delay), z_I=I(z_U,other_sources), z_A=A(z_I,recipient_state), followed by S over outputs and F over later delivery opportunities. Each operator is a calibrated nonlinear probability kernel. A candidate merge is an actual reduced kernel that must predict both isolated and combined timed removals, including order changes, rather than a label deletion. If the same composed kernel has identical intervention predictions, it is one admissible partition regardless of the number of drawn boxes.

Each full nonlinear model predicts the result of all removals before observing their held-out combination. Let Delta_f,o be the difference between the observed held-out effect of removal f and the best model in which f is merged into its nearest component. S6 predicts an out-of-margin Delta_f,o for every f on its prespecified primary outcome, successful mediator validation, and selective rescue; no five-family merge predicts all six. In contrast, no extra residual for the ecology modifier or concurrent-update dependency remains after these six established pathways and their calibrated compositions are included. If a single source-state model predicts both E and U removals and rescue, merge them; if I is explained by complementary facts or ordinary hierarchical reconstruction, merge I; if a logged exposure process fully explains F without an independent adaptive-state effect, merge F with S. Any such successful equivalence refutes exactly K=6 and narrows the admissible count downward. This must be tested with the actual nonlinear models, not a rank-six response matrix.

In the same people, a randomized reversal of the independently specified functional loss must reverse both choice preference and semantic transformation in the quantitatively predicted amount, within epsilon_2 and epsilon_4, without fitting a choice-specific beta. Source prestige/frequency, third-party modifier and concurrent-update contrasts have residuals within their equivalence margins after the specified loss, knowledge and opportunities are matched. S1 is the minimal set only if this cross-operation restriction predicts every held-out block and removal of the single source-loss dependency causes out-of-margin failure. A reproducible choice-versus-reconstruction double dissociation at matched loss, or a genuine moderator/concurrency/kinetic residual, falsifies K=1 in favor of a split answer. If an unrestricted single kernel succeeds but this tied law fails, that does not support S1: it is relabeling a composition.

A third cultural variant may change how competing variants are reconstructed predicts instead: Measure lower-order source/competitor conditions first and freeze both the actual nonlinear R+S composition and its mixture-selection, causal-source-inference and complementary-information extensions. In held-out communities present the focal source i, competitor j and a third modifier k, keeping the focal producer's dose, selected parent, semantic facts and payoff constant. Change k's contextual relation to the i-versus-j contrast while preserving its surface salience and factual information; include independent-production and fixed-artifact-choice controls. Let D_M be the observed third-party change in the i-to-descendant semantic transition minus the prediction of the strongest calibrated established composition. S3 predicts |D_M|>epsilon_4, a prespecified direction for a given trained modifier relation, and loss of this residual when that relation is experimentally severed; restoring the relation rescues it in new source families. Fixed-artifact choice can show ordinary context effects without establishing M. The R and S removals separately impair source-specific feature transmission and fixed-variant selection, respectively, establishing the other two required dependencies. If the nonlinear established composition predicts D_M within margins, or if M survives only under one semantic meter, remove M as a distinct family and consolidate to the appropriate known R/S explanation. A significant three-way coefficient alone is expressly insufficient.

Condition-dependent scoring may create false extra families of cultural transmission predicts instead: Randomize the semantic coding pipeline on the same fully logged outputs, including meaning-reversed high-overlap pairs and meaning-preserved low-overlap pairs. Before calibration, the fitted family partition changes with coder and unit boundaries. After independent calibration of C_a and behavioral comprehension/enactment validation, the proposed modifier, concurrency and stage-split residuals all lie within epsilon_o and their added held-out predictive gain within eta_o; the source-removal versus fixed-variant-choice double dissociation persists, requiring exactly R and S. The one-law tie is rejected by a replicated difference between the reconstruction-calibrated and choice-calibrated response slopes. This is evidence for K=2 only with adequately powered equivalence and successful manipulation checks, not because a larger model has nonsignificant coefficients. A modifier or group-protocol residual that remains in behavioral outcomes, survives independent human rubrics and is selectively abolished by its own dependency removal falsifies the observation-channel account in favor of a larger candidate set. If the scoring effect is real but a biological/cultural residual remains too, S2 is not sufficient.

Overlapping updates may transmit conflicting cultural rules despite accurate individual recall predicts instead: Run small communities learning an artificial reference system with two initially compatible rules. In an asynchronous arm two producers read the same earlier public version and issue individually valid but jointly incompatible updates; in a serialized arm the second update is produced after reading the first. Match numbers of messages, total time, word content available at final test, partner mix, payoff and aggregate feedback. A replay arm gives the identical final corpus to new individuals without joint updating; a yoked-delay arm controls staleness and recency. Fit ordinary CHAI-like partner learning, sequential priming, rule learning and allocator memory on matched histories before the test. Define D_C as the excess rate of jointly inconsistent but individually accurately recalled rule pairs over that full established composition. S4 predicts D_C>epsilon_4 specifically when overlapping writes target a shared rule, disappearance when the shared-update dependency is serialized or made nonconflicting, and rescue when conflict is reintroduced; the effect must persist beyond a mere last-item recall error. Independently resetting partner history while retaining a coherent shared record removes H's familiar-to-new-partner transfer, demonstrating H is also needed. Removing source access or choice feedback establishes R and S. If all C effects are predicted by established partner learning plus visible history and recency, delete C and reduce the proposed four-family answer; if H also merges with R under the panel, reduce again. The group label does not earn a family by itself.