From Problem Descriptions to Defensible Abstraction Links¶

A methodology for reconstructing trigger relationships between solution archetypes, prime abstractions, and domain-specific abstractions¶

A methodology companion to From Candidate to Catalog, which explains how prime entries are created, and Why Analogies Break, which develops the projection–residue boundary of cross-domain transfer.

Abstract¶

The Encyclopedia of Abstractions contains four distinct kinds of intellectual object: prime abstractions intended to express substrate-general structure, domain-specific abstractions whose invariants depend on bounded roles or substrates, solution archetypes describing reusable interventions, and mechanisms describing how effects are produced. A useful cross-domain retrieval system should allow a problem to be recognized in structural terms, linked to the abstractions it exhibits, and then connected to solution archetypes whose diagnostic situations contain those same structures.

The inherited source_primes field cannot support that use. It was generated in the forward discovery direction—asking which archetypes were associated with each prime—rather than in the diagnostic direction—asking which structures must be present in the problems an archetype addresses. A completed classification of 4,444 inherited links found that only 16.6% were genuine triggers. Most were conceptual ingredients, targets, discovery residue, tautologies, or wrong-sense matches, and 56% of archetypes had no trigger prime at all.

Reconstruction therefore requires a backward semantic analysis from each archetype's own problem description. This is not ordinary similarity matching. It is a constrained reasoning task involving predicate decomposition, condition typing, universal implication, counterexample search, role-preserving abstraction, open-world residuals, and construction of a diagnostic expression in disjunctive normal form. The task is not mathematically deterministic because its inputs are authored natural-language artifacts and the abstraction catalog is finite. It can nevertheless be made substantially reproducible by freezing the evidence surface, making every intermediate judgment explicit, separating structural and nonstructural functions, requiring counterexample-tested forward necessity, and preserving disagreement and residual uncertainty rather than erasing them.

This paper presents that methodology and its completed results. The prime reconstruction covered 1,080 normalized solution archetypes and all 6,600 source conditions. It produced 4,765 structural atoms, 1,591 diagnostic branches, 1,116 archetype-level prime trigger edges, and 3,434 explicit residual occurrences. A second, deliberately harder reconciliation then examined 1,555 residual occurrences against the existing domain-specific catalog. It produced 1,022 correction-aware DSA relationships, including 930 trigger groundings and 92 supporting groundings, while preserving 1,275 unmatched eligible atomic units as open research evidence.

After that population was frozen, 54 additional archetypes entered the catalog. An append-only extension applied the same semantic rules without rewriting the historical ledgers. The current publication projection therefore covers all 1,134 archetypes. Because the extension used one canonical pass plus a separate counterexample audit rather than a new blind double pass, its retained prime edges are explicitly provisional and do not inherit the earlier calibration's agreement statistics.

The result is best viewed as a defensible retrieval encoding and defect register—not a proof that an intervention is correct, complete, causal, or effective. Its public presentation therefore shows the complete diagnostic condition sets, the abstractions that ground each condition, the residual content that remains open, and the distinction between authoritative logic and generated explanatory prose. The method's value lies not in eliminating judgment, but in making judgment local, constrained, inspectable, and correctable.

1. The practical objective¶

The intended downstream use is analogical retrieval. A user or language model encounters a problem in some domain, recognizes several abstract structures in it, and asks which solution archetypes have been designed for situations containing those structures. The process can be represented informally as:

observed problem → recognized abstractions → candidate solution archetypes → contextual evaluation

The graph supports the middle transition. It should increase the chance that a useful intervention developed in one domain is considered in another domain that shares its structure but not its vocabulary.

This is a retrieval problem, not an automatic prescription problem. If a prime links to an archetype, the link should make the archetype worth inspecting. It should not imply that the archetype is sufficient, safe, feasible, or appropriate in the new case. A downstream reasoner must still evaluate the rest of the diagnostic route, application gates, constraints, residuals, and domain evidence.

That distinction controls the required standard of quality. The graph need not encode an impossible level of metaphysical certainty. It does need to be:

structurally meaningful rather than lexically convenient;
directionally correct;
explicit about what is and is not entailed;
conservative about universal claims;
useful enough to improve recall of plausible interventions;
inspectable after the fact; and
honest about incompleteness.

“Defensible” is therefore a better target than “perfectly deterministic.” A defensible edge has a stable rule, a role mapping, an implication argument, a checked prime record, a trace to source conditions, and a declared evidence tier. Another reviewer may still disagree at a scope boundary, but the disagreement can be localized and adjudicated rather than hidden.

2. Why the inherited links cannot simply be relabeled¶

The inherited source_primes field records discovery history. The mining process began with a prime and asked which solution archetypes tended to be associated with it. This produces a heterogeneous relation because “associated with” can mean many things:

the intervention is built from the prime;
the prime describes a situation that summons the intervention;
the intervention targets the prime or its effects;
the prime and archetype were near one another during discovery;
the prime restates the archetype;
the same word is used in a different sense; or
the relationship is simply wrong.

The classification pass quantified that heterogeneity: 51.6% of inherited links were employs, 16.6% were triggers, 9.9% were targets, 9.8% were discovery residue, 8.3% were tautological, and 3.3% were wrong-sense. More importantly, 56% of archetypes had no inherited trigger prime. A perfect relabeling of existing links could therefore never recover the missing situation side. The absent relationships were never recorded.

The reconstruction direction must be reversed. For each solution archetype, the reviewer starts from the problem it says it addresses, separates the problem from the remedy, and asks which supplied primes necessarily instantiate pieces of that problem.

This reversal changes the epistemic task. Forward mining is an association search. Backward relinking is a constrained implication analysis.

3. The ontology of objects and relations¶

3.1 Prime abstractions¶

A prime abstraction is intended to capture a reusable structural invariant across substrates. Its identity is not its title or one-line description alone. The mandatory record includes a structural signature, roles, relations, invariants, boundary conditions, and explicit what-it-is-not distinctions.

A valid instance of a prime must satisfy its mandatory structure. Optional examples and common manifestations do not define the prime. This matters because the relinking rule is universal: one counterexample admitted by the prime record is enough to defeat an implication.

3.2 Solution archetypes¶

A solution archetype is a reusable intervention pattern. Its entry normally contains at least four semantically different layers:

a structural problem;
trigger conditions or recognition cues;
a remedy or intervention logic; and
boundaries, trade-offs, or implementation constraints.

The relinking work concerns the first two layers. A prime describing the remedy may be highly similar to the archetype and still be the wrong kind of link.

3.3 Domain-specific abstractions¶

A domain-specific abstraction is reusable within a bounded substrate or practice but loses its identity when generalized too far. Examples can include statistical-study structures, protocol-specific failure modes, legal doctrines, or domain-bound physiological relations.

Domain specificity is not a defect. The distinction asks where the invariant lives:

If the roles and relations survive substrate substitution, a prime may be appropriate.
If removing domain roles destroys the important structure, the abstraction should remain domain-specific.
If the condition is composed from several primes plus a domain qualifier, the correct representation may be a composite with a residual rather than a new prime.

The method therefore permits DOMAIN_SPECIFIC residuals. It does not force every useful condition into a substrate-general prime merely to improve apparent coverage.

3.4 Mechanisms¶

Mechanisms describe how an effect is produced. A mechanism can participate in a trigger, a remedy, or both, but it should not automatically be treated as a prime trigger. The same mechanism may operate in many situations, only some of which make a particular archetype relevant.

3.5 Relation types¶

At minimum, the ontology needs to distinguish:

triggers: the prime necessarily exhibits a structural condition in a diagnostic route;
employs: the intervention uses the prime as conceptual or operational apparatus;
targets: the intervention acts on the prime, its bearer, or its consequence;
supports: the prime describes context, evidence, or a manifestation that helps recognize the case without constituting the structural trigger; and
typed residual or domain-specific relations where the prime catalog does not carry the needed structure.

Conflating these relations produces a graph that is dense but semantically weak. The methodology deliberately sacrifices some apparent recall to preserve relation meaning.

4. The exact meaning of a trigger edge¶

Let:

P be a prime abstraction interpreted as the set of all its valid instances;
A be a canonical structural atom derived from an archetype's problem conditions; and
R be the solution archetype.

The local grounding claim is:

∀x (P(x) → A(x))

In words: every valid instance of the prime necessarily exhibits the atom under an explicit, legal role mapping.

A projected graph edge additionally requires that A occur in at least one diagnostic DNF route for R and that A be classified as a structural trigger rather than supporting context, a gate, a constraint, a goal, or feasibility condition.

The projected edge can be written:

P ─triggers→ R because P → A and A ∈ diagnostic_route(R)

The edge does not assert any of the following:

A → P;
P → R in the sense that the prime alone proves the whole diagnosis;
every problem suited to R contains P;
R will work whenever P is present;
the archetype's source text is externally correct;
the prime catalog is complete; or
no other prime could ground the same atom.

This is the most important interpretive boundary in the project. The edge is an indexed entry point into a diagnostic expression, not a sufficient-condition theorem for an intervention.

4.1 Why implication runs from prime to condition¶

The prime is usually narrower and more structured than the condition. A condition such as “several channels exceed a response apparatus” can be instantiated by many distinct primes. The condition does not identify which prime is present. But a sufficiently specific prime may guarantee that condition.

The direction also prevents loose thematic matching. It is not enough that a condition sounds like a prime, that the prime frequently co-occurs with it, or that the prime would be useful for addressing it. The prime must carry the condition in every valid instance.

4.2 Counterexample semantics¶

The operational test is adversarial:

Assume the exact prime record is satisfied.
Attempt to construct a valid instance in which the candidate atom is false.
If such an instance is admitted by the record, reject the implication.
If the only counterexample requires violating a mandatory role, relation, invariant, sign, scope, or boundary condition, retain the implication.

This makes the method stronger in the negative direction than the positive. A counterexample is decisive. Failure to imagine one is not itself proof, which is why exact records, independent review, and explicit role mappings matter.

5. Why the task is not fully deterministic¶

It is tempting to ask for a rule that produces one uniquely correct graph from the corpus. Several features of the inputs make that standard unrealistic.

5.1 Natural-language conditions are not formal predicates¶

Trigger conditions were written for readers, not theorem provers. They use ellipsis, examples, ordinary modal language, implicit comparison classes, and context-dependent scope. Two reasonable readers may initially disagree about whether a list is exhaustive, whether a clause is causal or merely evidential, or whether a consequence is part of the diagnosis or only a materiality gate.

5.2 Predicate boundaries are authored, not discovered by syntax¶

A sentence may contain multiple propositions joined by natural language. The correct split depends on what must be decided later. Splitting every grammatical conjunction produces fragments that no longer express the original relation. Refusing all splits forces one prime to entail unrelated functions at once.

Atomization therefore contains disciplined judgment. The goal is operational stability, not the claim that language has one metaphysically privileged parse.

5.3 Prime records define open categories¶

Prime records are rich authored descriptions. They can contain broad roles, nested qualifiers, representative examples, and boundary notes. Deciding which elements are mandatory and whether a cross-domain role mapping preserves them can require interpretation.

5.4 The catalog is finite and the population of possible abstractions is unknown¶

Even a perfect reviewer cannot assign a missing prime. More fundamentally, there is no reason to assume that every coherent condition must correspond one-to-one with some possible prime. Some conditions are composites, thresholds, domain-specific structures, contingent facts, or conjunctions whose residual content should remain explicit.

5.5 Retrieval limits and reasoning limits interact¶

A candidate may be absent because the embedding shortlist missed it, because the catalog lacks it, because the condition is poorly atomized, or because no prime should exist for it. Those failure modes are observationally confounded unless the ledger records shortlist scope, exact reviews, residual type, and any broader audit.

5.6 Reproducibility is therefore procedural¶

The attainable form of reproducibility is not “any reader immediately produces the same answer.” It is:

the same frozen source text;
the same frozen candidate evidence;
the same explicit atomization and function vocabulary;
the same direction of implication;
the same role-mapping restrictions;
the same counterexample protocol;
the same DNF and residual rules;
complete provenance; and
a documented process for reconciling the remaining judgment calls.

This is analogous to reproducible adjudication in other interpretive domains: the reasoning path is constrained, inspectable, and contestable even when the raw material does not yield a unique mechanical answer.

6. The end-to-end representation pipeline¶

The completed program used two linked semantic compilations followed by a presentation projection. The first compilation reconstructed prime trigger relationships. The second revisited the deliberately difficult residual population against the existing domain-specific catalog. The third joined those authoritative layers without altering either one:

flowchart LR
  S["Structural problem and source conditions"] --> H["Diagnostic head and obligations"]
  S --> A["Operational atoms"]
  A --> F["Function classification"]
  F --> D["Flat diagnostic DNF"]
  F --> C["Bounded prime-candidate adjudication"]
  C --> G["Prime grounding or explicit residual"]
  D --> P["Frozen prime authoritative ledger"]
  G --> P
  P --> R["Candidate-blind residual re-atomization"]
  R --> M["Double-pass DSA matching and third-reader reconciliation"]
  M --> U["Direct, guarded, supporting, or still-open DSA result"]
  P --> J["Correction-aware presentation join"]
  U --> J
  J --> W["Human-readable condition sets and machine-readable projection"]

Each stage prevents a different class of error. Skipping the diagnostic head loses the target meaning. Skipping atomization confounds functions. Skipping function classification projects remedies as triggers. Skipping DNF loses conjunction and alternative-route structure. Skipping residuals invents completeness. Skipping exact-record adjudication replaces implication with similarity. Treating the original domain-specific residual label as a known catalog match confuses a hypothesis with evidence. Flattening a guarded DSA relationship into the DSA alone launders the missing qualifier. Skipping provenance makes later review impossible.

7. Constructing the diagnostic head¶

The diagnostic head is a remedy-free statement of the complete structural relation that makes the archetype relevant. It is derived primarily from structural_problem, checked against the essence, invariants, anti-signatures, and conditions.

A good head:

names the roles involved;
preserves causal or relational direction;
preserves sign, scope, time, and modality;
excludes the desired outcome and intervention;
distinguishes the archetype from nearby problems; and
is strong enough that satisfying it would make inspection of the archetype reasonable.

The head is then decomposed into obligations H1 … Hn. Obligations make hidden load paths visible. For example, an audience-spillover head can require:

a sender targets audience A;
the carrier exposes adjacent audience B;
B interprets the signal through a different calculus; and
B's response overloads an apparatus sized only for A.

Conditions and atoms are mapped to these obligations. Any obligation not supplied by source conditions becomes an explicit head residual. This prevents the conditions from quietly redefining the archetype more weakly than its own structural problem.

8. Operational atomization¶

8.1 Why atomization is necessary¶

A condition can contain several semantically different elements:

a structural state;
a comparison;
a consequence;
a materiality qualifier;
an application rule;
a feasibility judgment;
a remedy;
a goal; and
a list of manifestations.

The original condition-level necessity test made many partially covered conditions appear wholly unmatched. If a prime entailed the structural state but not an attached threshold or recommendation, the entire candidate was rejected.

8.2 Operational, not grammatical, atoms¶

The method splits a condition only when separation can change at least one of:

semantic function;
prime grounding;
DNF placement;
residual type; or
a dedicated nontrigger field.

Operands of one relation remain together. “A planned bundle may work at cross purposes” is not usefully split into “there is a bundle” and “cross-purpose interaction”; the relation is the proposition. Conversely, “reports and measurements diverge, and neither can responsibly be ignored” contains a structural divergence and an application rule, so it should be split.

8.3 Preserving logical content¶

Atomization must preserve:

negation;
causality;
temporal order;
quantifiers such as all, some, most, or repeated;
modality such as can, may, must, or will;
comparisons and baselines;
thresholds and materiality;
role restrictions; and
whether an enumeration is exhaustive or illustrative.

Dropping any of these can manufacture an implication. For example, a prime entailing a generic bottleneck does not entail “leadership attention is the bottleneck for decisions.” The latter restricts both the resource and the governing process.

9. Function classification¶

Every atom receives exactly one primary function. The current function vocabulary is:

Function	Meaning	Prime-groundable?	Projects trigger edge?
`STRUCTURAL_TRIGGER`	Part of the problem structure that makes the archetype relevant	Yes	Yes
`SUPPORTING_CONTEXT`	Context, manifestation, evidence, or indicator that helps recognize the case	Yes	No
`APPLICATION_GATE`	Condition controlling whether the archetype should be considered or prioritized	No	No
`DEPLOYMENT_CONSTRAINT`	Constraint on safe or legitimate implementation	No	No
`GOAL`	Desired outcome	No	No
`SOLUTION_FEASIBILITY`	Claim that the intervention can be performed or is preferable to alternatives	No	No
`MALFORMED`	No stable proposition can be recovered	No	No

This stage is load-bearing because textual similarity often points toward the wrong function. nonparametric_methods is highly similar to an assumption-light inference archetype, but it describes the remedy rather than the unstable evidence condition. eventual_consistency describes a convergence contract; it can ground supporting facts about replicas and local writes, but it should not automatically become a trigger for the absence of such a contract.

Function classification also clarifies why some archetypes legitimately receive zero trigger edges. Their supplied conditions may consist mainly of gates, feasibility requirements, or positive solution properties, while the actual failure asserted by the structural problem is missing from the condition list.

10. Candidate generation and bounded recall¶

Each packet supplies a top-15 candidate shortlist per condition, produced by embedding similarity, plus a deduplicated archetype-level candidate pool with one-line descriptions. Production adjudication does not search the full catalog.

This bounded evidence surface serves several purposes:

controls cost;
prevents reviewers from opportunistically searching until they find a favored match;
makes recall limitations measurable;
keeps independent passes comparable; and
allows negative judgments to have a defined scope.

Embedding similarity is only a candidate generator. It cannot decide implication because word overlap and structure frequently diverge. commutativity can entail order independence without sharing the same vocabulary. Conversely, a prime with nearly identical wording may describe the intervention rather than the situation.

10.1 The candidate ledger¶

For each groundable atom, every permitted condition-shortlist candidate receives one of four dispositions:

QUALIFIES: the exact mandatory record establishes forward necessity;
EXACT_RECORD_REJECT: the full record admits a counterexample;
ONE_LINER_VETO: the one-liner positively establishes a different relation, role, polarity, scope, or function; and
NOT_REVIEWED: no semantic decision has yet been made.

Omission from a one-liner is never sufficient for a veto. A terse one-liner may omit a mandatory detail present in the structural signature. Exact review is required whenever the one-liner could satisfy any atom disjunct under a legal role mapping.

Under method v1.1, a production-complete condition shortlist has zero NOT_REVIEWED candidates.

10.2 The packet-pool escape scan¶

The unseen batch-005 confirmation revealed that condition-level top-15 completeness is not the same as packet-level recall. Two exact matches were absent from the relevant condition's top 15 but present elsewhere in the same archetype's candidate pool:

habituation_to_repeated_signal for alerts multiplying into an ignore equilibrium; and
training_serving_skew for training-environment success followed by deployment failure.

Method v1.2 therefore adds one bounded cross-condition scan of the archetype-level candidate pool. Qualifying candidates are recorded as OTHER_ESCAPE_PACKET_POOL. The method still does not search the catalog.

In batch 005, the base condition top 15 recovered 14 of the final 16 unique edges; the packet-pool escape recovered the remaining two. This is an observed 87.5% condition-list edge recall within that packet, not a general estimate of catalog recall.

10.3 What “complete” means under bounded evidence¶

The 72-batch production run completed 84,678 candidate-to-atom dispositions: 2,445 QUALIFIES, 2,128 EXACT_RECORD_REJECT, 80,105 ONE_LINER_VETO, and zero NOT_REVIEWED. Completion therefore means that every candidate the frozen method permitted was dispositioned and every surviving candidate received the required exact-record review. It does not mean the complete 1,402-prime catalog was exhaustively compared against every atom.

This scope distinction governs all negative claims. A residual can establish that the frozen evidence did not provide a qualifying prime. Depending on its later audits, it may also provide evidence of a catalog gap, composite, source problem, domain-bound relation, or legitimate non-abstraction. It cannot establish that no possible abstraction could ever represent the condition.

11. Exact-record necessity adjudication¶

11.1 Mandatory versus optional structure¶

Review uses the prime's complete mandatory record. A candidate qualifies only if all valid instances carry the atom. Examples, common applications, and optional manifestations cannot support a universal implication.

For instance, selection_bias explicitly includes loss to follow-up as one subtype. It does not therefore entail a condition about preliminary dropout rates diverging between treatment groups, because many valid selection-bias instances arise through initial recruitment, publication, collider conditioning, or other mechanisms.

11.2 Legal role mapping¶

A role mapping may rename mandatory roles and bind substrate objects to them. It may not:

choose a convenient subtype of the prime;
add a role the prime does not require;
delete a condition qualifier;
reverse sign or direction;
change a modal claim;
convert an optional example into a mandatory role; or
treat a generic input as one of an atom's enumerated object types without support.

Legal mappings are what make cross-domain transfer possible. channel_capacity can map an information medium to a response channel because channelhood and finite reliable throughput are mandatory. bottleneck cannot automatically map to “leadership attention,” because a valid bottleneck may be a machine, material, dependency, or approval stage unrelated to leadership.

11.3 Quantifier discipline¶

Quantifiers frequently decide the case:

A prime describing some public/private divergence does not entail public unanimity.
One local optimum does not entail multiple local optima.
A pressure that could suppress challenge does not entail actual groupthink.
A common pattern does not become universal because it is typical.

The confirmation recheck reversed four initial qualifications for exactly these reasons:

a consensus fault model need not place failure in participants rather than channels;
an unowned known risk may still be monitored or partly safeguarded;
substrate-general attentional capacity does not entail the atom's enumerated human roles;
regime change does not universally require a distinct reverse threshold.

11.4 Disjunctive atoms¶

For an atom A ∨ B ∨ C, a prime qualifies when every valid prime instance satisfies the disjunction. It need not always satisfy the same disjunct, but the reviewer must show that no valid instance lies outside all disjuncts. If the mapping relies on only a favorable subset of prime instances, it fails.

11.5 Polarity discipline¶

Positive apparatus is not evidence of its absence. authority, legitimacy, consent, accountability, and procedural_fairness_due_process do not trigger conditions about unclear mandate, eroding legitimacy, absent voice, lost accountability, or overlapping jurisdiction merely because they share vocabulary. Their mandatory structures often have the opposite polarity.

12. Diagnostic DNF¶

12.1 Why a list of conditions is insufficient¶

An archetype can be summoned through alternative diagnostic routes. Some conditions are jointly necessary; others are alternative manifestations; still others are gates or supporting evidence. A flat list cannot distinguish:

all conditions required together;
any one of several alternatives;
mixed expressions such as (A AND B) OR C; or
a partly prime-grounded route that also requires uncataloged content.

The method therefore represents the diagnostic expression in flat disjunctive normal form:

D_R = B1 ∨ B2 ∨ ... ∨ Bm

where each branch is a conjunction:

Bj = L_j1 ∧ L_j2 ∧ ... ∧ L_jk

and each literal is a structural atom or positive residual. The expression is an OR of ANDs and is never nested.

12.2 Branch sufficiency¶

Each branch must imply the diagnostic head. The operational test is:

hold every condition outside the proposed branch false;
assume every literal in the branch true; and
ask whether the complete head follows.

If not, the branch needs another atom or a residual. A condition cannot become a standalone branch merely because it is a vivid symptom.

12.3 Greedy minimality¶

After a branch is sufficient, literals are removed one at a time. A literal is deleted when the remaining branch still entails the head. The process repeats until no single deletion preserves sufficiency.

This is greedy minimality, not exhaustive subset enumeration. The goal is an auditable, operationally minimal branch without combinatorial search or a false claim of globally unique logical factorization.

12.4 Example: fully grounded conjunction¶

The audience-boundary spillover archetype has four structural obligations:

A1: bounded signaling is attempted;
A2: the audience boundary is porous;
A3: the adjacent audience interprets differently; and
A4: the response apparatus is capacity-limited or overloaded.

Its route is:

D = A1 ∧ A2 ∧ A3 ∧ A4

boundary_signal_spillover necessarily exhibits all four atoms, while channel_capacity grounds only A4. Both project useful retrieval edges, but they have different diagnostic coverage. The first nearly names the complete structural pattern; the second is a partial entry point requiring the other branch obligations.

12.5 Example: alternative routes with a residual¶

An assumption-light inference archetype can be reached through several alternatives:

(changing process ∧ ρ) ∨ (outlier-dominated sample ∧ ρ) ∨ sensitivity-to-assumptions ∨ ...

Here ρ states that the identified hazard actually carries load in the formal conclusion. concept_drift can ground the changing-process atom and outlier_leverage can ground the outlier atom, but neither alone proves that the current decision depends materially on that failure. The residual preserves the missing relation.

12.6 DNF is an encoding, not a proof assistant¶

The DNF is a disciplined representation of the authored diagnostic logic. It is not a claim that the corpus has been translated into a complete decidable formal system. Its value is that conjunction, alternative routes, residual content, and prime coverage are explicit enough for inspection and retrieval.

13. Residuals and open-world semantics¶

13.1 Why residuals are necessary¶

Without residuals, a partially grounded route creates a false choice:

reject every useful prime because it does not cover the whole sentence; or
accept the prime and silently pretend it covers omitted content.

The open-world representation permits:

prime-grounded atom ∧ positive residual

The residual is not “unknown noise.” It is a named predicate that remains necessary to the branch but is not currently grounded by an accepted prime.

13.2 Residual types¶

The ledger distinguishes:

SOURCE_GAP: the diagnostic head requires content absent from source conditions;
UNRESOLVED_RETRIEVAL: the bounded evidence did not establish a prime;
CATALOG_GAP_CANDIDATE: a broader catalog audit found no prime;
DOMAIN_SPECIFIC: the structure remains useful but cannot be generalized without loss;
NON_PRIME_QUALIFIER: a threshold, materiality, admissibility, or modal clause should not become a prime;
COMPOSITE_UNRESOLVED: several abstractions appear necessary but the composition is not yet stabilized;
SOURCE_AMBIGUITY: the source supports materially different readings; and
CONTINGENT_FACT: the literal is case-specific rather than reusable.

13.3 A residual is not a percentage error¶

It is tempting to calculate “80% of the condition is covered” by counting atoms. Such a number can be useful as a rough coverage descriptor, but it is not a probability or semantic error rate. One small residual may carry the decisive causal link, polarity, or threshold. Ten grounded descriptive atoms do not compensate for one missing load-bearing relation.

The ledger may report counts such as:

grounded structural atoms / structural atoms;
fully grounded DNF branches / total branches;
branches containing source residuals; and
zero-edge archetypes.

These are coverage diagnostics. They do not measure truth, intervention validity, or the importance of the residual.

13.4 When residuals are the main result¶

The method is intentionally strong in the negative direction. A stable residual can show that:

the trigger condition is too composite;
the source conditions omit the archetype's defining relation;
the candidate generator missed a clear prime;
the catalog lacks a reusable abstraction;
the structure belongs at domain-specific level; or
the archetype itself needs editorial repair.

This makes the output a defect register as well as a graph encoding.

13.5 Residual status after DSA reconciliation¶

The original residual kind and the later research disposition are separate facts. In particular, DOMAIN_SPECIFIC initially meant “the prime evidence failed and the remaining predicate appears domain-bound.” It did not mean that an existing encyclopedia DSA had been found, or even checked.

The completed DSA stage re-atomized 1,555 residual occurrences into 1,888 units. It classified 1,812 as eligible relational units, 64 as non-abstractions, and 12 as source defects. Among the eligible units, 537 received at least one accepted existing-DSA grounding and 1,275 remained open. This produces four importantly different reader-facing states:

DSA grounded: every eligible relational unit represented by the condition received an accepted trigger grounding;
partially DSA grounded: one or more eligible units received a grounding while another load-bearing unit remained open;
non-abstraction reclassified: the remainder is a threshold, parameter, materiality test, admissibility qualifier, or other fact that should not be turned into an abstraction merely to increase coverage; and
source review required: the source wording lacks the relation needed by its diagnostic interpretation.

These dispositions prevent two symmetrical errors. The first is leaving a condition labeled “missing DSA” after an existing DSA has been defensibly found. The second is claiming that every unmatched remainder is evidence that a new DSA should be created. The unresolved population is heterogeneous by construction and remains a research population, not a queue of preapproved catalog additions.

14. Prime and domain-specific grounding¶

The decision between prime and domain-specific representation should be based on structural survival under substrate substitution. The two catalogs are not ranked levels of quality. They encode different scopes of invariance.

14.1 Prime test¶

Ask whether the atom can be restated so that:

its roles are substrate-neutral;
its relation and failure mode remain intact;
the same intervention-relevant inference survives; and
the abstraction is not merely a broad label.

If yes, a prime may be appropriate.

14.2 Domain-specific test¶

Ask whether removing the domain role destroys the structure. Loss to follow-up in a study, for example, can be related to generic selection, but its treatment-arm, endpoint, exchangeability, censoring, and estimand roles may form a domain-specific abstraction whose identity is not preserved by calling it generic selection bias.

The first prime pass treated such cases conservatively. It recorded a domain-specific hypothesis instead of forcing a substrate-general prime through an illegal subtype mapping. The later DSA pass then asked a different question: does an abstraction with the necessary domain roles already exist in the encyclopedia?

14.3 Why the DSA stage required a new method¶

The DSA population consisted of hard remainders from the prime run. Its source predicates were often long, enumerative, domain-bound, and only partly relational. A binary “existing DSA matches / does not match” rule reproduced the earlier atomization problem and added another: a candidate often supplied the correct structural spine but not one threshold, timing fact, branch selection, or domain restriction.

The DSA method therefore separated three decisions that a single judgment could not safely carry:

candidate-blind atomization of the residual;
necessity testing of each eligible atomic unit against a frozen DSA shortlist; and
explicit adjudication of whether one narrow qualifier legitimately completes a nearly sufficient DSA.

Each residual occurrence was reprocessed before candidate evidence was visible. A proposer chose PRESERVE, CLARIFY, SPLIT, or REWRITE_REQUIRED. A challenger reviewed the proposal using the same source but still without candidates, and an adjudicator froze the result before matching began.

Each resulting unit received one semantic scope:

ELIGIBLE_RELATIONAL: a reusable role-and-relation structure that an abstraction could represent;
NON_ABSTRACTION: a threshold, generic existence fact, recurrence fact, adjustable parameter, feasibility condition, case-contingent fact, or materiality test; or
SOURCE_DEFECT: wording that lacks the relation its diagnostic interpretation requires.

Eligible units preserved typed obligations for role, relation, polarity, modality, quantifier, timing, causality, comparison, domain, and true disjunction. The atomization also distinguished a complete logical alternative from an illustrative list. A candidate may satisfy a true disjunction through one complete branch; it may not select a convenient example from an illustrative list and treat that example as the predicate.

14.5 Direct and guarded DSA relationships¶

Each blind matcher evaluated the top 30 frozen DSA candidates for an eligible unit. Four classifications were permitted:

DIRECT: every complete DSA instance entails every obligation;
GUARDED_CONTEXT: the DSA supplies the same structural spine and one atomic contingent fact makes the remaining obligation necessary;
GUARDED_BRIDGE: the DSA supplies the same spine and one general type- or relation-subsumption axiom completes it; or
REJECTED: no expression within the one-qualifier limit is defensible.

A guard is part of the relationship expression, not an explanatory footnote. If bus_factor grounds a condition only when the relevant steward capability has a bus-factor count equal to one, the published relationship is:

bus_factor ∧ [bus-factor count = 1]

It is not bus_factor alone. Removing the guard would reintroduce valid bus-factor instances with an available substitute and would falsify the condition.

14.6 The qualifier-laundering prohibition¶

One qualifier can improve practical coverage, but it can also restate the entire target and make any candidate appear sufficient. The method rejects a qualifier if it:

repeats the source predicate in different words;
introduces a missing principal role or unrelated relation;
selects an unnamed favorable manifestation;
substitutes the intervention for the trigger;
combines two independent facts; or
invokes a bridge that is not generally true outside the edge.

After adding a valid qualifier, no complete instance may preserve both the DSA and qualifier while falsifying an obligation. This is the guarded equivalent of the prime counterexample test.

14.7 Double pass, mandatory reconciliation, and final edge audit¶

Two mutually blind matching passes evaluated the same frozen atomization and exact candidate records without seeing one another's judgments. Reconciliation then reviewed every candidate retained by either pass, every candidate-level disagreement, every proposed guard, and a deterministic sample of shared negatives. Neither the union nor intersection of the passes was treated as truth.

The authoritative decision preserved both raw classifications and rationales, the source of disagreement, the adjudicator's reasoning, the counterexample attempt, and the final relationship clause. An independent final auditor then reviewed every retained expression. Failed expressions were retracted through append-only correction files; committed ledgers were never silently rewritten.

This design was necessary because the rare positive decisions were much less reproducible than the large background of shared rejections. Across 54,360 candidate slots per pass, raw four-way agreement was 0.981 and Cohen's κ was 0.494, while retained-edge pooled Jaccard was 0.372. The high raw agreement mostly records that both readers rejected the same candidates. The lower positive overlap localizes the real difficulty: role scope, guards, branch semantics, and entailment boundaries.

14.8 Composite representation¶

Some conditions remain best represented as:

P1 ∧ P2 ∧ domain qualifier

or:

P1 ∧ residual

or, at domain-specific level:

DSA ∧ explicit guard ∧ residual

This is preferable to minting a new abstraction whose only function is to restate one archetype condition. Catalog creation should be driven by recurring missing structure across residual clusters, not by a coverage target.

15. Provenance, evidence tiers, and reconciliation¶

15.1 The authoritative ledger¶

The ledger records, per archetype:

diagnostic head and obligations;
every source condition;
atomization and bidirectional condition mapping;
class, function, and head role;
DNF branches and removal arguments;
residuals and coverage state;
candidate universe and every disposition;
exact prime-record hashes;
accepted role mappings and implication arguments;
rejected counterexamples;
projected edges;
review flags; and
correction history.

The graph is a projection of this richer record. The ledger is the evidence.

The DSA layer adds, per atomic unit:

candidate-blind repair and coverage accounting;
enumeration semantics and typed obligations;
both independent candidate judgments;
disagreement dimensions;
the mandatory third-reader disposition;
any context guard or interpretive bridge;
a complete counterexample attempt;
final audit status; and
append-only retractions.

15.2 Edge tiers and authoritative provenance¶

Prime edges are not flattened into one unsupported truth status:

CONSENSUS_TRIGGER: independent reviews agree;
HUMAN_ADJUDICATED_TRIGGER: reconciliation resolves a disagreement;
PROVISIONAL_TRIGGER: one canonical pass establishes the edge;
SCOPE_CONTESTED_TRIGGER: a useful relation is supported but atom or role scope remains unresolved.

Consumers can rank tiers differently depending on whether precision or recall matters more.

DSA edges use a more granular provenance because every positive decision passed through the double-pass reconciliation. Provenance distinguishes agreed direct expressions, agreed guarded expressions, adoption of reader A or B, adjudicated synthesis, audited shared negatives, and rejected-both decisions. Final publication additionally reflects the edge audit and correction overlays. The visible website does not need to expose this machinery beside every condition, but the downloadable record must preserve it.

15.3 Reconciliation¶

When independent passes disagree, reconciliation should identify the exact source:

different atom boundaries;
different function classification;
different head or residual scope;
different interpretation of a prime's mandatory structure;
illegal versus legal role mapping;
missed candidate; or
different DNF factorization.

The reconciler does not average judgments. It chooses or constructs an authoritative result with a reason, while preserving both raw passes. In the DSA stage, 6,152 mandatory reconciliation records covered 2,218 material disagreements, 618 guard audits, and 3,613 sampled shared negatives.

15.4 Immutable raw judgments and additive corrections¶

Committed results are not silently rewritten. If later evidence changes a judgment, an additive correction records:

the frozen artifact hash;
the reason for reopening;
the previous and new disposition;
any edge addition or removal; and
the updated summary.

This distinction matters because a changing methodology can otherwise erase the evidence needed to understand why the graph changed.

The completed DSA run illustrates why this rule matters. The final edge audit passed 1,025 edges and failed or retracted 159 proposed authoritative edges. Supplemental review later retracted three more. The effective result contains 1,022 relationships, and the history still shows why the 162 removed relationships were once proposed and why they no longer project.

16. Review design and error control¶

The project ultimately used two different review designs because the two evidence populations had different difficulty profiles.

16.1 Prime production review¶

Full double-pass review of all prime candidates would have duplicated a large population of obvious negatives. After blind calibration stabilized the representation, prime production used:

one canonical primary pass;
complete condition-shortlist one-line triage;
exact review of every plausible survivor;
one bounded packet-pool escape scan;
targeted semantic recheck of risky decisions;
a random audit of otherwise unflagged archetypes; and
immutable ledgers with additive corrections.

Targeted review was triggered by multiple surviving primes, non-obvious mappings, load-bearing scalar or modal qualifiers, mixed functions, residual-only branches, source/head gaps, escape use, and any close decision whose reversal would add or remove an edge.

The unseen confirmation demonstrated that this review was substantive. It reversed four of 34 initially qualifying atom-candidate dispositions before freeze. Two reversals removed unique edges; two removed redundant groundings while the same prime remained linked through another atom.

16.2 DSA production review¶

The residual population justified a more expensive design. It was selected precisely because prime matching had failed, and guarded DSA expressions created a new qualifier-laundering risk. The DSA stage therefore used:

candidate-blind proposer, challenger, and final atomization;
two independent matching passes across all frozen candidate slots;
mandatory third-reader reconciliation of every positive, disagreement, guard, and sampled shared negative;
an independent final audit of every retained expression; and
correction-aware projection rather than rewriting frozen decisions.

The decisive quality measure is not whether the reviewers agreed. It is whether the process made disagreement visible and then subjected every proposed positive expression to an adversarial, candidate-local resolution. A review stage that never changes an answer is not evidence of quality; in this run, the audit and correction layers removed 162 proposed edges.

16.3 Mechanical validation¶

Semantic review was paired with mechanical checks. All 72 prime ledgers and 104 DSA packets were schema-validated, hash-frozen, and checked for complete source coverage. The final presentation projection additionally verifies that:

all 1,134 current normalized archetypes appear exactly once, with the 54 post-freeze records hash-linked to their append-only extension authority;
every diagnostic head, DNF branch, and predicate is byte-for-byte preserved;
every authoritative prime and DSA expression is projected exactly;
all typed catalog references resolve;
supporting-context groundings never enter the trigger graph; and
every condition and diagnostic problem has reader-facing explanatory copy.

Mechanical validation cannot decide whether a semantic judgment is good. It prevents the implementation layer from quietly changing or losing the judgments that were made.

16.4 Division of labor and the meaning of review statistics¶

The bulk semantic work was performed by language-model agents under curator-directed rules, calibration gates, stop conditions, and publication decisions. Independent passes were kept blind at the judgment stage, and later agents performed reconciliation and audit against the frozen evidence. The curator determined the project objective, accepted or revised the method, interpreted calibration failures, authorized scale-up, and set the standard of defensibility.

The resulting agreement statistics are therefore machine-reviewer reproducibility measures inside this procedure. They are not estimates of agreement among human domain experts. Nor does third-reader adjudication become “human adjudication” merely because older tier names use that phrase. Where the machine-readable provenance preserves such historical labels, the paper interprets them as adjudicated process roles rather than claims about reviewer biology.

This distinction does not make the measurements uninformative. Blind disagreement identified unstable atom boundaries, role mappings, and guard semantics, and the audit layer removed relationships that survived earlier passes. It does limit the claim: the procedure is an auditable LLM-assisted semantic compilation supervised by a curator, not a human-annotated gold standard.

17. Calibration history and empirical results¶

The method was developed through bounded rounds rather than scaled immediately. Early rounds showed that condition-level adjudication produced excessive unmatched rates and unstable DNF because source conditions were not atomic and their functions were mixed.

The final five-archetype v3.11 blind regression achieved:

100% agreement on condition class;
100% agreement on condition structure;
100% agreement on atom function, head role, and grounding type;
exact prime-set agreement on 75% of aligned grounded atoms;
mean prime-set Jaccard of 0.870;
projected-edge mean Jaccard of 0.711;
agreement on all five head/residual scopes; and
equivalent DNF in three of five cases.

The remaining disagreement localized to five projected edges and two mixed-clause boundaries. This showed that broad semantic categories had stabilized while role scope and some DNF boundaries still required reconciliation.

17.2 Five-archetype authoritative reconciliation¶

Reconciliation produced 18 authoritative edges:

14 CONSENSUS_TRIGGER;
4 HUMAN_ADJUDICATED_TRIGGER; and
one explicitly rejected disputed candidate.

The disputed role mappings were resolved using mandatory role coverage rather than permissive similarity. Four edges were accepted and one was rejected because the prime's generic focal input admitted valid instances outside the condition's enumerated object roles.

17.3 First 15-archetype efficiency trial¶

Batch 003 contained 15 archetypes and 93 source conditions. The frozen pass produced 20 provisional edges in 16.27 minutes, but left 1,041 of 1,095 candidate-to-atom dispositions as NOT_REVIEWED. A post-freeze comparison surfaced two plausible candidates. Exact review:

accepted echo_chamber → alienation_reconnection; and
rejected release_from_controlling_context → agentic_control_loop_design.

The corrected edge count became 21. The lesson was not that the necessity rule failed; the candidate triage had stopped too early. Method v1.1 therefore made complete condition- shortlist disposition mandatory.

17.4 Unseen 15-archetype confirmation¶

Batch 005 was selected before its contents were read because no prior batch-005 result artifact existed. Inputs and outputs were hash-frozen. The confirmation represented:

15 archetypes;
99 source conditions and 99 operational atoms;
54 structural atoms;
24 prime-grounded structural atoms;
16 unique provisional trigger edges;
five zero-edge archetypes;
1,037 candidate-to-atom dispositions;
30 qualifying dispositions;
61 exact-record rejections;
946 positive one-line vetoes;
zero NOT_REVIEWED candidates;
55 unique exact prime records;
eight targeted rechecks and one random audit;
four pre-freeze review corrections;
two accepted packet-pool escapes;
14 archetypes with at least one source/head residual;
ten archetypes with at least one residual-only branch; and
two domain-specific residual atoms.

The observed semantic pass occupied 17.1 wall-clock minutes in the instrumented task. This time should be treated as an execution observation, not a promise: difficulty varies and the environment does not expose reliable model-token totals.

The confirmation supports four conclusions:

complete shortlist triage is operationally feasible;
exact-record and role-scope recheck materially improves precision;
condition-level top 15 alone is not sufficient recall, but the bounded packet-pool escape recovers clear misses without catalog search; and
high residual prevalence persists after improved candidate review, so much of it is a property of the authored source conditions and catalog boundary rather than unperformed work.

17.5 Completed prime reconstruction¶

The production run applied the frozen method to all 72 packets, including a uniform backfill of the first 75 archetypes that had originally lived in calibration artifacts. The resulting prime layer contains:

Measure	Completed result
Normalized solution archetypes	1,080
Source conditions	6,600
Operational atoms	6,671
Structural atoms	4,765
Prime-grounded structural atoms	2,214
Archetype-level prime trigger edges	1,116
Diagnostic DNF branches	1,591
DNF literal occurrences	5,092
Fully prime-grounded branches	275
Explicit residual occurrences	3,434
Archetypes with no prime trigger edge	252

The structural-atom grounding rate was 46.5%. This does not mean the graph is 46.5% correct, or that 53.5% of its meaning is missing. It means that 2,214 of 4,765 structural atoms received at least one accepted prime grounding under the stated necessity rule. Only 17.3% of complete DNF branches were fully prime-grounded, because a branch is counted as complete only when every literal is grounded. At the archetype level, 237 had at least one fully prime-represented route, 591 were partially represented, and 252 had no prime representation.

The shape of the authored diagnostic logic was predominantly conjunctive: 889 archetypes were classified as conjunctive, 116 as mixed, and 75 as disjunctive. The typical archetype had 1.47 DNF branches, and the typical branch contained 3.20 literals. Those averages should not be read as a recommended authoring template; they describe the logic recovered from the existing corpus.

The completed candidate ledger contains 84,678 atom-candidate dispositions: 2,445 accepted qualifications, 2,128 exact-record rejections, 80,105 one-line vetoes, and no unreviewed candidates. This is what permits a bounded negative claim: no supplied candidate was silently left undecided. It does not permit the stronger claim that no unsupplied prime could qualify.

17.6 Completed DSA reconciliation¶

The DSA stage began with 1,555 selected residual occurrences from 636 archetypes. Candidate- blind atomization expanded these into 1,888 authoritative units: 1,812 eligible relational units, 64 non-abstractions, and 12 source defects. The matching and correction layers produced:

Measure	Completed result
Effective DSA relationships	1,022
Direct relationships	644
Guarded-context relationships	354
Guarded-bridge relationships	24
Trigger groundings	930
Supporting-context groundings	92
Eligible units receiving a grounding	537
Eligible units remaining open	1,275
Existing DSA records used	381
Source occurrences receiving any edge	502
Archetypes receiving any DSA edge	342

The unresolved eligible share remained 70.4%. This high number is not a failed completion check. The population was deliberately selected from material the prime pass could not ground, so it is an enriched sample of hard, composite, domain-bound, or inadequately authored predicates. Completion meant adjudicating the bounded candidate evidence and preserving the remainder accurately, not forcing a positive edge.

The DOMAIN_SPECIFIC residual label was therefore only a research hypothesis at the start of the second stage. Of 1,174 source occurrences bearing that label, 395 received at least one existing DSA edge. The rest cannot be described as known encyclopedia DSAs. They may represent missing DSAs, composites, non-abstraction qualifiers, shortlist misses, or source problems, depending on the atomic disposition.

17.7 Combined publication projection¶

The correction-aware presentation join now contains all 1,134 archetypes and 4,953 unique structural conditions. It preserves 5,194 condition occurrences across the DNF because the same condition can legitimately appear in more than one branch. At the unique-condition level, the final statuses are:

Condition status	Unique conditions
Prime grounded	2,236
DSA grounded	421
Partially DSA grounded	38
Open	2,216
Non-abstraction reclassified	31
Source review required	11

At the archetype level, 311 have at least one fully catalog-grounded condition set, 664 have partial catalog grounding, and 159 have no catalog grounding. These categories describe the best available route through the diagnostic expression. They do not assign confidence scores or say whether the archetype itself is valid.

17.8 Post-freeze new-archetype extension¶

The extension population was defined mechanically as the exact difference between the current 1,134-record archetype catalog and the frozen 1,080-record projection. It contained 54 archetypes and 187 normalized conditions: 102 structural triggers, 19 supporting-context conditions, and 66 goals, gates, feasibility clauses, or deployment constraints. Fourteen archetypes already had authored trigger conditions. For forty, the minimum proposition-sized condition set was reconstructed from authored structural-problem, problem-state, structural-signature, and when-to-use fields without changing the source files.

The extension disposed all 1,815 prime shortlist candidates and all 2,880 DSA candidates on live prime residuals. Twenty-two structural conditions received prime grounding, seven more received existing-DSA grounding, and 73 remained open. The retained expressions add 26 condition-level prime edges—22 distinct archetype-to-prime relations—and 12 DSA relationships, of which nine are trigger groundings and three are supporting-context groundings. Eleven DSA relationships are direct; one uses a single explicit context guard. Every retained expression passed the extension's separate counterexample audit.

These figures should not be pooled into a new agreement statistic. The historical production run used calibrated independent review, while the extension used one canonical pass plus a mandatory counterexample audit. The public graph can combine their effective relationships, but the research record preserves the different review designs and evidence tiers.

18. Scaling behavior and workload¶

The completed run confirms that calibration cost cannot be extrapolated linearly to production. Calibration included invention of the representation, repeated rule revisions, blind duplicate passes, disagreement diagnosis, and tooling. Once the method was frozen, production became a packetized semantic compilation with bounded evidence and mechanical validation.

The prime layer was completed in 72 packets and the DSA layer in 104 packets organized into 18 monitored waves. Packets bounded failure, permitted checkpointing, and made it possible to pause on a genuinely new semantic ambiguity without treating ordinary residual prevalence as a crisis. Waves allowed distributions and corrections to be monitored without requiring a human decision after every packet.

The principal intellectual workload was not reading every negative candidate at equal depth. It was finding plausible survivors, opening their exact records, constructing role mappings, attempting counterexamples, deciding whether qualifiers were legal, and reconciling positive or near-positive judgments. The data reflect that asymmetry: the prime run rejected 80,105 candidates at the one-line stage and opened a much smaller exact-review population, while the DSA run concentrated its expensive reconciliation on positives, disagreements, guards, and sampled shared negatives.

No authoritative total token count or end-to-end wall-clock telemetry is preserved in the artifact set, so this paper does not present an invented productivity estimate. The durable workload measures are the completed source coverage, candidate dispositions, reconciliation records, audits, corrections, and validation manifests. Those measures make future reruns estimable even when execution infrastructure changes.

19. How to read the resulting graph¶

19.1 Read condition sets, not isolated edges¶

The human unit of interpretation is a condition set. Conditions inside one set are joined by AND; multiple sets are alternatives joined by OR. A prime or DSA link explains one condition within that expression. It rarely means that the linked abstraction, by itself, fully diagnoses the archetype.

A compact reader-facing rendering can therefore take this form:

Diagnostic problem
  [concise statement of the complete problem]

Condition set 1 — all conditions required
  grounded condition
  AND grounded condition
  AND open residual condition

Catalog grounding
  primes: ...
  domain-specific abstractions: ...

Representation status
  partial catalog grounding

The words “all conditions required” are scoped to a single displayed set, not to every condition anywhere on the page. If a second set exists, it supplies an alternative route. This is why the website should avoid calling branches “routes” without first explaining the logical relationship; “condition set” is less technical and easier to interpret locally.

19.2 Grounding and residuals describe different parts of one predicate¶

A grounded condition has an accepted catalog expression that necessarily exhibits it. An open condition is still part of the diagnostic expression but lacks an accepted catalog grounding under the bounded evidence. A partially DSA-grounded condition has both: one or more relational units are represented by existing DSAs, while another load-bearing unit remains open.

Neither state is a confidence percentage. “Three of four structural atoms grounded” is a coverage count. The fourth atom may be a minor qualifier or the decisive causal relation. The interface should therefore show counts and exact open predicates, not convert them into a probability-like score.

19.3 Guards belong in the visible expression¶

When a DSA qualifies only with a context guard or interpretive bridge, the guard must remain beside it. Displaying only the linked DSA would overstate the catalog record. A reader should see the difference between:

bus_factor

and:

bus_factor AND [the relevant capability has a bus-factor count of one]

The second is the adjudicated relationship. The bracketed clause is not optional explanatory copy.

19.4 Reader-facing explanations are not new evidence¶

The projection adds concise labels and expandable paragraphs so a reader can understand an abstract diagnostic problem or condition. Those explanations have explicit provenance. Some are syntheses of authored context; some preserve a source condition; and some are conservative logic clarifications generated solely for presentation. None can create a new edge, alter a guard, strengthen a predicate, or change branch membership.

The same rule applies to material displayed as other requirements and context. Goals, application gates, deployment constraints, solution-feasibility conditions, supporting context, and source-review items remain outside the trigger expression because they do not state the structural situation that summons the archetype. The publication projection may give each item a clearer display label, an expandable explanation of its role, and a short explanation of why it is separate from trigger logic. It must also preserve the original classified text and source-condition reference. These explanations make the boundary legible; they do not silently promote contextual material into a trigger edge.

19.5 Supported uses¶

The graph can support:

cross-domain retrieval of potentially relevant solution archetypes;
explanation of why an archetype was retrieved;
inspection of the other conditions that must hold;
ranking or filtering by provenance and representation status;
discovery of recurring prime- and DSA-catalog gaps;
editorial diagnosis of malformed or incomplete trigger conditions;
training examples for structural reasoning; and
research on abstraction-mediated analogical transfer.

For a query problem with observed abstraction set Q, a retrieval system can collect archetypes linked from members of Q, then present the unsatisfied conditions and residuals as questions. This is more informative than returning an archetype solely because its prose is semantically similar to the query.

20. What the graph cannot establish¶

The graph does not establish:

real-world causal validity of the source archetype;
intervention efficacy;
safety in a particular domain;
completeness of the prime catalog;
completeness of the domain-specific catalog;
completeness of the candidate shortlist;
absence of a better solution archetype;
uniqueness of atomization or DNF;
calibrated probability that an edge is correct; or
independent validation, because both compared artifacts originate in the same authored encyclopedia pipeline.

The last limitation is especially important. A clean match can show internal structural compatibility while both the prime and archetype share the same upstream misconception. This is why the output is strong as a defect register and retrieval index but weak as external validation.

The same caution applies to the DSA layer. Mandatory reconciliation and final edge audit make the accepted expressions more defensible; they do not turn agreement inside one encyclopedia into evidence that the represented relation holds in the world. External evaluation would require independent cases, independent domain experts, or downstream retrieval studies.

21. Common failure modes¶

21.1 Similarity substituted for necessity¶

The candidate shares vocabulary or topic but admits valid instances outside the atom.

21.2 Remedy projected as trigger¶

A prime describes how the archetype works and is accepted because it is highly similar.

21.3 Optional manifestation promoted to invariant¶

A prime sometimes appears in the condition's role but does not require it.

21.4 Illegal subtype mapping¶

A generic prime role is restricted to the convenient subtype named by the condition.

21.5 Qualifier deletion¶

A reviewer silently removes “most,” “repeated,” “critical,” “because,” “after,” or a material threshold to make the match work.

21.6 Positive/negative polarity confusion¶

A prime for due process is linked to absence of due process; a prime for legitimacy is linked to eroding legitimacy.

21.7 Residual treated as failure or erased as success¶

The reviewer either discards a useful partial grounding or pretends it covers the entire condition.

21.8 DNF branch under-specification¶

A symptom becomes a standalone route even though the diagnostic head does not follow.

21.9 Candidate absence treated as rejection¶

NOT_REVIEWED or shortlist omission is silently interpreted as “no prime exists.”

21.10 Apparent precision from one authoritative binary¶

Consensus, adjudicated, provisional, and contested evidence are collapsed into identical edges with no trace of their origin.

21.11 Guard laundering¶

A DSA supplies the right structural spine only with an explicit qualifier, but the qualifier is omitted when the relationship is projected. The published DSA then appears to entail more than its record supports.

21.12 Illustrative enumeration treated as disjunction¶

A source lists several examples of one broader requirement. A reviewer selects the one example a candidate happens to satisfy and treats it as a complete alternative branch.

21.13 A residual label treated as a catalog match¶

DOMAIN_SPECIFIC is interpreted as “this existing DSA applies” rather than “the unresolved structure appears domain-bound.” The later DSA stage exists precisely because the former does not follow from the latter.

21.14 Generated explanation promoted to authority¶

Reader-facing prose is allowed to add a cause, example, qualifier, or consequence that does not occur in the frozen predicate, and that prose is later used to infer an edge. Explanatory copy must remain a projection of the authority, never a second semantic source.

22. Governance and versioning¶

The method is versioned independently from corpus content. A production run records:

policy version;
schema version;
packet hash;
prime-record hashes;
adjudicator identity or process role;
output freeze manifest;
validation result;
review and audit outcomes; and
corrections.

Method changes should be additive and explicit. The current sequence illustrates the pattern:

v1.0 established atoms, functions, DNF, residuals, role mapping, and tiers;
v1.1 required complete condition-shortlist triage;
v1.2 added the bounded packet-pool escape scan;
DSA production v2 froze candidate-blind atomization, enumeration semantics, exact matching, direct and one-qualifier guarded expressions, and mandatory reconciliation;
append-only DSA audit corrections removed relationships that failed the final adversarial check; and
presentation projection v2 joined the frozen prime and DSA authorities without changing their predicates, branches, edges, guards, or residual decisions; and
presentation projection v2.1 added provenance-bearing explanations for non-trigger requirements and context while preserving their classifications and source text exactly.

Earlier raw results remain interpretable because their policies and limitations are preserved. The website projection is disposable and reproducible; the ledgers, manifests, pass outputs, reconciliation records, and corrections are the durable evidence.

23. Publication posture¶

The publication should expose several layers rather than forcing every audience into the raw ledger.

The default solution-archetype page should show:

a concise diagnostic problem;
one or more numbered condition sets, with AND inside each set and alternatives separated clearly;
linked primes and DSAs beside the conditions they ground;
every necessary guard beside its DSA;
an explicit open residual wherever catalog grounding is incomplete;
a plain-language representation status; and
an optional expanded explanation for the diagnostic problem and each condition; and
separately labeled goals, gates, constraints, feasibility conditions, supporting context, and source-review items, each with an optional explanation of its meaning and why it is not part of the trigger expression.

The default page should not show candidate ledgers, blind-pass agreement, adjudicator choices, or audit mechanics. Those details explain the method, not the archetype. They belong in this paper and in a downloadable research packet that preserves the machine-readable authority, raw judgments, disagreement rationales, correction history, schemas, and manifests.

The interface must distinguish three kinds of text:

authoritative logic: diagnostic head, condition predicate, DNF placement, guard, and residual;
catalog authority: the linked prime or DSA record and its accepted relationship; and
presentation copy: concise descriptions and expanded explanations added for human comprehension.

Progressive disclosure is appropriate because these predicates are abstract. The concise line should support scanning; an expansion can explain roles, relations, and why the catalog grounding fits. Provenance remains machine-readable even when it is not displayed by default.

The resulting publication has two complementary products: a usable encyclopedia interface for recognizing structural problems, and an auditable research record for inspecting how those recognitions were encoded.

24. Conclusion¶

Reconstructing links between solution archetypes, prime abstractions, and domain-specific abstractions was not a labeling exercise. It was a form of controlled semantic compilation. Authored problem prose was turned into a diagnostic head, operational atoms, typed functions, a flat DNF, explicit residuals, bounded candidate judgments, and correction-aware edges. Each transformation could introduce error, so each remained recoverable in the authoritative record.

The method cannot make natural-language interpretation mathematically deterministic, and it should not pretend that the finite prime catalog can eliminate every residual. What it can do is constrain judgment enough that disagreements become local, arguments become inspectable, false positives face adversarial counterexamples, and missing structure becomes data rather than embarrassment.

The completed graph covers all 1,134 normalized archetypes. It establishes 1,138 distinct archetype-to-prime trigger relations and 1,034 correction-aware or extension-audited DSA relationships while preserving thousands of explicit open predicates. Those residuals are not an embarrassment or an unfinished percentage bar. They are an empirical map of where the present catalogs, source conditions, and one-to-one abstraction model cease to explain the diagnostic structure.

The graph is useful precisely because its claim is modest. It does not say which solution must be used. It says why a solution archetype is structurally worth examining, what additional facts remain to be checked, and how the association was reasoned from the corpus. That is a defensible foundation for analogical retrieval—and a much stronger one than the discovery-history links it replaces.

Appendix A. Compact formal specification¶

For archetype R:

Construct diagnostic head H_R with obligations {H1 … Hn}.
Atomize source conditions into atoms {A1 … Ak}.
Assign each atom one function f(Ai).
Construct flat DNF:

D_R = ⋁j ⋀l L_jl

where each literal is a structural atom or positive residual and every branch entails H_R. 5. For supplied prime candidate P and groundable atom Ai, accept only if:

∀x (P(x) → Ai(x))

under a legal role mapping. 6. Project P ─triggers→ R only when f(Ai) = STRUCTURAL_TRIGGER and Ai occurs in D_R. 7. Preserve evidence tier, role mapping, exact-record hash, argument, counterexamples, residuals, and correction history. 8. For a candidate domain-specific abstraction D and eligible residual unit Ai, accept a direct expression only if:

∀x (D(x) → Ai(x))

Accept a guarded expression only if one legal atomic qualifier g completes the implication:

∀x ((D(x) ∧ g(x)) → Ai(x))

and g neither restates Ai nor introduces a second independent relation. 10. Project a DSA expression as trigger grounding only when the unit is a structural trigger. Preserve supporting-context groundings separately. 11. Apply reconciliation, audit, and append-only correction overlays before constructing the reader-facing projection.

Appendix B. Interpretation checklist for a retrieved edge¶

When a consumer follows a catalog grounding into archetype R, ask:

What is the exact grounding expression: a prime, a direct DSA, or a DSA plus guard?
Which structural condition does that expression entail?
Which DNF condition set contains that condition?
What other conditions or residuals must hold in the same set?
Is the grounding a trigger or supporting context?
Are application gates satisfied?
Are feasibility and deployment constraints satisfied?
What evidence tier and reconciliation provenance does the relationship carry?
Does the role mapping fit the current domain without illegal subtype restriction?
Is the abstraction instance—and every required guard—actually present in the problem?
What external evidence supports using the archetype here?

Only after those questions should the retrieved archetype move from candidate to proposed intervention.