{ "$schema": "urn:kingdom:schema:number-isness-theology-atlas:0.1", "protocol": "kingdom.number-isness-theology-atlas/0.1", "atlas_id": "number-isness-theology-atlas-2026-08-14", "title": "Number, Isness & Theology Atlas", "compiled_on": "2026-08-14", "evidence_through": "2026-08-14", "source_bindings": [ { "id": "kingdom-being-access-aftermath-v0-2", "protocol": "kingdom.being-access-aftermath-atlas/0.2", "revision": "a22a88f8be3387fed199b5d746a6b3c5f1e4d81d", "url": "https://thekingdom.dev/atlases/being-access-aftermath-atlas-2026-08-13-v0-2.json", "raw_digest": "sha256:9678e5269e8db62beb36abee691087cddbc4f98703190c5fa3788b68c89ab29e", "semantic_digest": "sha256:505a1e3aef6116430dccf49b327c4cce2ac5d6fb6b6b9bf68e529272f989cde8", "relation": "typed-isness-and-karma-boundary-precedent", "mutated": false, "authority_imported": false }, { "id": "kingdom-exploration-deep", "protocol": "kingdom.explore-phenomena-deep-wing/0.1", "revision": "013e9f4619029e9ccbb7442dfd0311dfa473bd8d", "url": "https://thekingdom.dev/wings/explore-phenomena-deep-2026-08-14.json", "raw_digest": "sha256:3eff9952a2013e011946d37db4316f82081fab992438b003bb6241ff7a775d55", "semantic_digest": "sha256:f57af0a832a1e7a7c601d5186291131a7750db69e106be0934e25d816973ae6c", "relation": "cross-domain-transfer-gate-precedent", "mutated": false, "authority_imported": false }, { "id": "kingdom-karma-definition", "protocol": "kingdom.karma/0.1", "revision": "e4e84a67d7ee1ae0dd9c9c23762e6ecd03597212", "url": "https://thekingdom.dev/definitions/kingdom-karma/e4e84a67/NEN.md", "raw_digest": "sha256:14b7d210d320fd716553992a7b874747b299f8907d15da14ac405cbfc496c446", "semantic_digest": null, "relation": "immutable-public-definition-mirror", "mutated": false, "authority_imported": false }, { "id": "kingdom-karma-receipt-schema", "protocol": "kingdom.karma/0.1", "revision": "e4e84a67d7ee1ae0dd9c9c23762e6ecd03597212", "url": null, "repository_locator": "schemas/karma-receipt-v0.1.schema.json", "public_availability": "UNAVAILABLE_AT_EVIDENCE_HORIZON", "raw_digest": "sha256:888e81fa0d29b71512525a40e88f9aef678046c40fcdf22c2039507d9d13267b", "semantic_digest": null, "relation": "repository-local-receipt-contract-input", "verification_note": "The revision-pinned GitHub URL inherited by predecessor atlases returned 404 on 2026-08-14. This atlas makes no public-access claim; the digest was checked against the repository-local path and revision object.", "mutated": false, "authority_imported": false } ], "scope": { "question": "How can changes in mathematical expression illuminate number, zero, symmetry, being, negation, creation, God-language, and religious compatibility without turning analogy into proof?", "intended_use": "Read-only education, typed question design, source comparison, and bounded opt-in philosophical reflection.", "excluded_use": "No proof or disproof of God, revelation, creation doctrine, religious truth, cosmic purpose, or karma; no religion, culture, community, or person ranking; no persuasion, governance, invocation, event, receipt, or action.", "method": "Keep formal mathematics, historical scholarship, source attribution, school-specific theology, metaphysical proposal, comparative relation, and analogy in separate registers; every bridge records what it does not transfer.", "central_boundary": "A mathematical structure can sharpen the form of a question. It does not supply the theological premises, translation, interpretation, soundness, actuality, or authority required to answer that question.", "currentness": "selected-sources-observed-through-compilation" }, "claim_typing": { "rule": "Every reviewed claim has a discourse register, review target, review status, support descriptors, and source scope. Source attribution can be supported without the attributed proposition becoming a world fact.", "registers": [ "MATHEMATICAL_DEFINITION", "MATHEMATICAL_CONVENTION", "MATHEMATICAL_CONSTRUCTION", "MATHEMATICAL_THEOREM", "OPEN_MATHEMATICAL_CONJECTURE", "HISTORICAL_SCHOLARSHIP", "EMPIRICAL_SCIENCE", "SCIENTIFIC_MODEL", "PRIMARY_TRADITION_TEXT", "SCHOOL_SPECIFIC_THEOLOGY", "METAPHYSICAL_PROPOSAL", "COMPARATIVE_RELIGION", "INTERPRETIVE_BRIDGE", "BOUNDARY", "OPEN_QUESTION" ], "review_targets": [ "FORMAL_DERIVATION", "WORLD_CLAIM", "SOURCE_ATTRIBUTION", "INTERNAL_COHERENCE" ], "review_statuses": [ "SUPPORTED_AS_SCOPED", "NOT_ESTABLISHED", "UNKNOWN_TO_REVIEW" ], "support_descriptors": [ "SOURCE_BOUND", "MODEL_ASSUMPTION", "DERIVED", "PROVED", "FINITE_EXACT", "NUMERICAL_APPROXIMATION" ], "support_guard": "Descriptors are non-exclusive and never upgrade review status. A theorem proves only its exact statement under its assumptions; a primary text establishes what that text says under a declared edition and interpretation, not that its claim is true.", "translation_guard": "A translated term remains indexed by source language, edition, translator, context, school, and interpretive loss; lexical resemblance never establishes shared reference." }, "typed_isness": { "rule": "Replace is, is not, no, and no-no with a typed predicate before drawing a mathematical, historical, metaphysical, or theological inference.", "isness_record": "ISNESS(x;c,t)=", "predicates": [ {"id":"formal-membership","signature":"FORMAL_MEMBER(x,structure,model)","meaning":"x belongs to a declared formal carrier under a named model.","not_equivalent_to":["physical-existence","theological-being","moral-worth"]}, {"id":"typed-as","signature":"TYPED_AS(x,type)","meaning":"x is classified under one declared type rule.","not_equivalent_to":["identity","essence","actuality"]}, {"id":"identity-under-invariant","signature":"IDENTICAL_UNDER(x,y,invariant)","meaning":"x and y agree under one named invariant.","not_equivalent_to":["unqualified-sameness","interchangeability","shared-ontology"]}, {"id":"embedded-as","signature":"EMBEDS_AS(source,target,map,x,y)","meaning":"A structure-preserving map sends x to y.","not_equivalent_to":["literal-identity-of-constructions","historical-supersession","spiritual-inclusion"]}, {"id":"property-predication","signature":"HAS_PROPERTY(x,property,context,time,method)","meaning":"A named method supports one property attribution in scope.","not_equivalent_to":["identity","timeless-essence","global-predication"]}, {"id":"domain-existence","signature":"EXISTS_INSTANCE(form,domain,context,time)","meaning":"At least one witness in a named domain instantiates the form in context and time.","not_equivalent_to":["metaphysical-necessity","continuous-existence","observation"]}, {"id":"defined-in","signature":"DEFINED_IN(term,theory,conventions)","meaning":"The term receives a formation and interpretation rule in a formal theory.","not_equivalent_to":["actual-existence","unique-reference","empirical-instantiation"]}, {"id":"proved-in","signature":"PROVED_IN(formula,theory,logic,proof)","meaning":"A checked derivation establishes a formula relative to premises, rules, and logic.","not_equivalent_to":["premise-truth","soundness-about-the-world","revelation"]}, {"id":"asserted-by-source","signature":"ASSERTED_BY(claim,source,edition,interpretation)","meaning":"A source is attributed a bounded claim under an edition and interpretation.","not_equivalent_to":["world-truth","whole-tradition-consensus","endorsement"]}, {"id":"interpreted-by","signature":"INTERPRETED_BY(interpreter,expression,concept,tradition,as_of)","meaning":"A named interpreter offers one scoped reading.","not_equivalent_to":["literal-translation","sole-reading","formal-equivalence"]}, {"id":"compatible-under","signature":"COMPATIBLE_UNDER(claims,translation,logic,assumptions)","meaning":"A bounded formalization has at least one model under declared choices.","not_equivalent_to":["doctrinal-identity","truth","practical-coexistence","whole-religion-compatibility"]}, {"id":"predicate-negation","signature":"NEGATES(logic,phi)","meaning":"A logic-specific negation is applied to a proposition.","not_equivalent_to":["numeric-zero","refusal","absence-of-witness","unknown"]}, {"id":"quantified-absence","signature":"ABSENT(domain,predicate) iff not exists x in domain: predicate(x)","meaning":"No witness satisfies a predicate in a named domain.","not_equivalent_to":["absolute-nonbeing","not-observed","impossibility"]}, {"id":"zero-value","signature":"ZERO_VALUE(value,structure)","meaning":"A value is the distinguished zero of one declared structure.","not_equivalent_to":["metaphysical-nothingness","undefined","false","unknown"]}, {"id":"null-observation","signature":"NULL_OBSERVATION(operator,window)","meaning":"An observation operator returned zero reports in a bounded window.","not_equivalent_to":["zero-event-rate","nonexistence","refusal"]}, {"id":"refusal","signature":"REFUSES(subject,proposal,time)","meaning":"A subject declines a proposal at a time.","not_equivalent_to":["nonexistence","incapacity","falsehood","silence"]}, {"id":"prohibition","signature":"FORBIDDEN(norm,action,context)","meaning":"A norm disallows an action in context.","not_equivalent_to":["physical-impossibility","refusal","zero"]}, {"id":"unknown-at-horizon","signature":"UNKNOWN_AT(claim,evidence_horizon)","meaning":"This bounded review cannot determine the claim.","not_equivalent_to":["false","nonexistent","unknowable"]}, {"id":"withheld-predication","signature":"WITHHOLDS(speaker,predicate,subject,context)","meaning":"A speaker does not apply a predicate in context.","not_equivalent_to":["predicate-negation","denial","agreement"]} ], "no_family": { "members": ["not P(x)","not exists x in D: P(x)","v=0 in a structure","count(O,W)=0","REFUSES(a,p,t)","FORBIDDEN(n,p,c)","WITHHOLDS(s,p,x,c)","UNKNOWN_AT(phi,H)"], "guard": "These expressions have different types and no default conversion.", "double_negation_guard": "No-no returns affirmation only in a declared logic that validates double-negation elimination. Apophatic restraint, tetralemma, refusal, and silence are not hidden applications of that formal rule." } }, "historical_expression": { "rule": "Formal inclusion order is not chronological history. Mathematical expression developed nonlinearly across cultures through notation, calculation, transmission, rejection, reuse, and later formalization.", "relation_types": ["INTRODUCED_SYMBOL","USED_OPERATION","BORROWED_OR_TRANSLATED","ACCEPTED_AS_NUMBER","FORMALIZED_AS","EMBEDDED_IN"], "cards": [ { "id": "zero-placeholder-and-number", "claim": "The positional placeholder and zero as a number are historically distinguishable uses; their development was neither a single invention event nor an inevitable straight line.", "register": "HISTORICAL_SCHOLARSHIP", "review_target": "SOURCE_ATTRIBUTION", "review_status": "SUPPORTED_AS_SCOPED", "support_descriptors": ["SOURCE_BOUND"], "source_ids": ["mactutor-zero"], "nonclaims": ["one culture alone explains every zero practice","mathematical zero is Buddhist emptiness","notation history proves metaphysics"] }, { "id": "division-by-zero-theological-analogy", "claim": "MacTutor records Bhaskara using divine immutability as an analogy while treating division by zero; the historical analogy does not make division by zero valid in an ordinary field.", "register": "HISTORICAL_SCHOLARSHIP", "review_target": "SOURCE_ATTRIBUTION", "review_status": "SUPPORTED_AS_SCOPED", "support_descriptors": ["SOURCE_BOUND"], "source_ids": ["mactutor-zero"], "nonclaims": ["theology caused the mathematical error","Indian mathematics is reducible to this episode","metaphor can replace an inverse law"] }, { "id": "complex-from-impossible-to-structural", "claim": "Rules for complex arithmetic, geometric rotation, and later field language emerged through distinct historical stages; imaginary was a contested name, not a proof of lesser mathematical reality.", "register": "HISTORICAL_SCHOLARSHIP", "review_target": "SOURCE_ATTRIBUTION", "review_status": "SUPPORTED_AS_SCOPED", "support_descriptors": ["SOURCE_BOUND"], "source_ids": ["mactutor-complex"], "nonclaims": ["complex numbers prove an unseen realm","historical acceptance establishes Platonism","formal extension is cosmic creation"] }, { "id": "formal-tower-not-history", "claim": "N0 to Z to Q to R to C is a modern structural presentation of embeddings, closure, and completion needs, not a complete chronology of how people expressed number.", "register": "BOUNDARY", "review_target": "INTERNAL_COHERENCE", "review_status": "SUPPORTED_AS_SCOPED", "support_descriptors": ["DERIVED"], "source_ids": ["mactutor-zero","mactutor-complex"], "nonclaims": ["civilizations form a progress ranking","later systems replace earlier practices","religions follow the same tower"] } ] }, "number_systems": { "natural_convention": "N0={0,1,2,...}; authors using N={1,2,3,...} must declare that alternate convention.", "tower": "N0 embeds in Z embeds in Q embeds in R embeds in C", "embedding_guard": "Write iota_NZ(1_N)=1_Z rather than an untyped literal identity. Canonically embedded roles may agree while set-theoretic constructions differ.", "cards": [ {"id":"natural-succession","symbol":"N0","construction":"A model of the Peano-style zero-and-successor structure.","door":"finite counting, iteration, and induction","equations":["S(0)=1","n+0=n"],"limit":"not closed under additive inverses or nonzero division","register":"MATHEMATICAL_CONVENTION","review_target":"FORMAL_DERIVATION","review_status":"SUPPORTED_AS_SCOPED","support_descriptors":["DERIVED"],"source_ids":[],"nonclaims":["natural in mathematics means metaphysically natural","one counts divine unity","successor causes ontological creation"]}, {"id":"integer-group-completion","symbol":"Z","construction":"(N0 x N0)/~, where (a,b)~(c,d) iff a+d=b+c","door":"additive inverses and signed difference","equations":["[(a,b)]+[(c,d)]=[(a+c,b+d)]","iota_NZ(n)=[(n,0)]"],"limit":"not closed under division by every nonzero element","register":"MATHEMATICAL_CONSTRUCTION","review_target":"FORMAL_DERIVATION","review_status":"SUPPORTED_AS_SCOPED","support_descriptors":["DERIVED"],"source_ids":[],"nonclaims":["negative number is moral negation","construction chronology follows this quotient","completion increases worth"]}, {"id":"rational-fraction-field","symbol":"Q","construction":"{(a,b):a in Z,b in Z\\{0}}/~, where (a,b)~(c,d) iff ad=bc","door":"fractions, ratios, and division by nonzero elements","equations":["a/b=c/d iff ad=bc","(a/b)/(c/d)=ad/bc when c is nonzero"],"limit":"dense and ordered but not complete; rational does not mean reasonable or revelatory","register":"MATHEMATICAL_CONSTRUCTION","review_target":"FORMAL_DERIVATION","review_status":"SUPPORTED_AS_SCOPED","support_descriptors":["DERIVED"],"source_ids":[],"nonclaims":["God is ratio","rational number measures rationality","proportion proves harmony is divine"]}, {"id":"real-completion","symbol":"R","construction":"A completion of Q, for example by Cauchy sequences modulo zero-distance equivalence or Dedekind cuts.","door":"limits and completeness of the ordered field","equations":["every Cauchy sequence in R converges in R","sqrt(2) is in R but not Q"],"limit":"the construction choice is not the unique ontology of real numbers","register":"MATHEMATICAL_CONSTRUCTION","review_target":"FORMAL_DERIVATION","review_status":"SUPPORTED_AS_SCOPED","support_descriptors":["DERIVED"],"source_ids":[],"nonclaims":["real means more existent than complex","completion means theological perfection","continuum proves divine infinity"]}, {"id":"complex-adjoin-i","symbol":"C","construction":"R[x]/(x^2+1), isomorphic to {a+bi:a,b in R and i^2=-1}.","door":"roots of polynomials and plane rotations","equations":["i^2=-1"],"theorem_claims":[{"id":"complex-rotation","statement":"For theta in R and z in C, multiplication by exp(i theta) rotates z through angle theta in the standard complex plane.","conditions":["theta is real","z is complex","the standard complex exponential and Euclidean plane identification are used"],"register":"MATHEMATICAL_THEOREM","review_target":"FORMAL_DERIVATION","review_status":"SUPPORTED_AS_SCOPED","support_descriptors":["DERIVED"],"source_ids":[]},{"id":"fundamental-theorem-of-algebra","statement":"Every nonconstant polynomial with complex coefficients has a root in C.","conditions":["the polynomial is nonconstant","coefficients lie in C"],"register":"MATHEMATICAL_THEOREM","review_target":"FORMAL_DERIVATION","review_status":"SUPPORTED_AS_SCOPED","support_descriptors":["PROVED","SOURCE_BOUND"],"source_ids":["mactutor-complex"]}],"limit":"C admits no field order compatible with its field operations; adjoining elements does not preserve every structure of R","register":"MATHEMATICAL_CONSTRUCTION","review_target":"FORMAL_DERIVATION","review_status":"SUPPORTED_AS_SCOPED","support_descriptors":["DERIVED"],"source_ids":[],"nonclaims":["imaginary means unreal","complex numbers evidence spirits","algebraic closure is metaphysical completeness"]} ], "embeddings": [ {"id":"N0-to-Z","map":"n maps to [(n,0)]","preserves":["zero","one","addition","multiplication"],"does_not_establish":["literal identity of underlying encodings","historical replacement","higher worth"]}, {"id":"Z-to-Q","map":"a maps to a/1","preserves":["zero","one","addition","multiplication","order"],"does_not_establish":["all rational numbers are embedded integers","division by zero","rational membership measures reason"]}, {"id":"Q-to-R","map":"q maps to the equivalence class of its constant Cauchy sequence or to the matching Dedekind cut","preserves":["field operations","order","rational values"],"does_not_establish":["chronological inevitability","one unique construction","theological completion"]}, {"id":"R-to-C","map":"a maps to a+0i","preserves":["zero","one","addition","multiplication","absolute value on embedded reals"],"does_not_establish":["compatible field order on C","literal identity of carriers","ontological ascent"]} ] }, "zero": { "rule": "Zero is role-indexed. A representation may identify a zero with an empty set, as in the von Neumann encoding 0=empty set, without making the number-role semantically identical to an empty collection or to metaphysical nothingness.", "field_boundary": "No field element z satisfies 0*z=1; therefore zero has no multiplicative inverse and division by zero is not a field operation.", "roles": [ {"id":"number-zero","signature":"0 in a declared number structure","equation":"x+0=x","not":"absolute nothingness"}, {"id":"additive-identity","signature":"0_A for an additive structure A","equation":"for all x in A: x+0_A=x","not":"absence of structure"}, {"id":"absorbing-multiplier","signature":"0_R in a ring or semiring R","equation":"for all x in R: x*0_R=0_R","not":"universal annihilation outside the operation"}, {"id":"positional-digit","signature":"0 in a base-b numeral","equation":"205_base10=2*10^2+0*10+5","not":"the number zero in every historical notation"}, {"id":"empty-cardinality","signature":"cardinality(empty set)=0","equation":"|empty set|=0","not":"the empty set is metaphysical nothing"}, {"id":"origin-or-zero-vector","signature":"0_V in a vector space V","equation":"v+0_V=v","not":"no space or no vector structure"}, {"id":"zero-probability","signature":"P(E)=0 in a probability space","equation":"P({x})=0 for a point under a continuous distribution","not":"logical impossibility without further assumptions"}, {"id":"initial-object-in-Set","signature":"empty set is initial in Set","equation":"for every set X there is a unique function empty set -> X","not":"a causal process creating X from nothing"}, {"id":"zero-observation-count","signature":"count(O,W)=0","equation":"zero reports in window W under operator O","not":"zero event rate, nonexistence, refusal, or impossibility"} ], "non_equivalences": [ "numeric zero is not metaphysical nothingness", "numeric zero is not theological creation ex nihilo", "numeric zero is not Buddhist sunyata", "numeric zero is not Daoist wu", "numeric zero is not falsehood", "numeric zero is not undefinedness", "numeric zero is not an unknown review status", "numeric zero is not silence or refusal", "cardinality zero does not erase the existence of the carrier, rule, or discourse", "a chosen encoding such as 0=empty set does not transfer set-theoretic identity into a universal ontology" ] }, "symmetry": { "definitions": { "group_action": "A group action is a map G x X -> X satisfying e*x=x and (g*h)*x=g*(h*x) for all g,h in G and x in X", "orbit": "Orbit_G(x)={g*x:g in G}", "stabilizer": "Stab_G(x)={g in G:g*x=x}", "invariant": "I(g*x)=I(x) for declared g,x", "quotient": "X/G identifies points only up to the declared action" }, "cards": [ {"id":"group-action-invariance","claim":"Symmetry is invariance under specified transformations, not beauty or sameness without a transformation group.","register":"MATHEMATICAL_DEFINITION","review_target":"FORMAL_DERIVATION","review_status":"SUPPORTED_AS_SCOPED","support_descriptors":["DERIVED"],"source_ids":["sep-symmetry"],"nonclaims":["group action is agency","invariance is authority","equivalence is identity in every respect"]}, {"id":"noether-conditional","claim":"For a variational problem satisfying the theorem's hypotheses, continuous invariance yields corresponding conservation structure.","register":"MATHEMATICAL_THEOREM","review_target":"FORMAL_DERIVATION","review_status":"SUPPORTED_AS_SCOPED","support_descriptors":["PROVED","SOURCE_BOUND"],"source_ids":["noether-1918"],"nonclaims":["every visual symmetry yields a conserved quantity","conservation proves a creator","conservation is moral or karmic balance"]}, {"id":"symmetry-breaking","claim":"A law or model can have a symmetry while a realized state has lower symmetry; asymmetry and history remain mathematically meaningful.","register":"SCIENTIFIC_MODEL","review_target":"SOURCE_ATTRIBUTION","review_status":"SUPPORTED_AS_SCOPED","support_descriptors":["SOURCE_BOUND"],"source_ids":["sep-symmetry"],"nonclaims":["all asymmetry has one cause","broken symmetry is moral fall","model symmetry is world ontology"]}, {"id":"sacred-order-reflection","claim":"Geometric repetition, balance, and invariant form can support source-bound aesthetic or theological reflection without constituting a designer proof.","register":"INTERPRETIVE_BRIDGE","review_target":"SOURCE_ATTRIBUTION","review_status":"SUPPORTED_AS_SCOPED","support_descriptors":["SOURCE_BOUND"],"source_ids":["met-islamic-geometry","quran-55-7-9","met-buddhist-mandalas"],"nonclaims":["Islamic geometry is mandated by scripture","mandalas and Islamic patterns share theology","symmetry proves divine perfection"]} ] }, "logics": { "rule": "Negation, contradiction, proof, and existence claims are logic-indexed. A logic is a formal consequence relation, not a religion or a complete metaphysics.", "cards": [ {"id":"classical-double-negation","equations":["not not phi iff phi","from phi and not phi, arbitrary psi follows"],"meaning":"Classical logic validates double-negation elimination and explosion.","source_ids":["sep-intuitionistic-logic"],"not_equivalent_to":["every natural-language no-no","apophatic theology","refusal"]}, {"id":"intuitionistic-double-negation","equations":["phi implies not not phi","not generally: not not phi implies phi"],"meaning":"Intuitionistic logic does not validate unrestricted double-negation elimination.","source_ids":["sep-intuitionistic-logic"],"not_equivalent_to":["denial of truth","paraconsistency","agnosticism"]}, {"id":"paraconsistent-non-explosion","equations":["not generally: {phi,not phi} entails psi"],"meaning":"A paraconsistent consequence relation is non-explosive; there are many such logics.","source_ids":["sep-paraconsistent-logic"],"not_equivalent_to":["every contradiction is true","anything goes","Buddhist tetralemma"]}, {"id":"belnap-dunn-information-states","equations":["status(phi) in {true-only,false-only,both,neither}"],"meaning":"Four statuses can represent supported truth, supported falsity, conflicting information, or no information in the Belnap-Dunn setting.","source_ids":["sep-many-valued-logic"],"not_equivalent_to":["four metaphysical states","catuskoti identity","religious truth classification"]} ], "tetralemma_boundary": "A fourfold religious or philosophical discourse may challenge a question's presupposition or suspend predication. Similar cardinality to a four-valued logic is not a translation or formal equivalence." }, "creation": { "rule": "Construction, causation, cosmogenesis, theological creation, manifestation, dependent arising, and grammatical command are separate relations with no default adapter.", "types": [ {"id":"formal-construction","signature":"CONSTRUCTS(formal_system,object,rules)","register":"MATHEMATICAL_CONSTRUCTION","meaning":"Rules introduce or characterize an object in a formal system.","not_equivalent_to":["temporal beginning","physical manufacture","theological creation"]}, {"id":"physical-causation","signature":"CAUSES_TO_EXIST(cause,entity,model,conditions,time)","register":"SCIENTIFIC_MODEL","meaning":"A causal model attributes production under explicit conditions and evidence.","not_equivalent_to":["formal definition","ultimate explanation","divine act"]}, {"id":"theological-creation","signature":"CREATES_THEOLOGICALLY(tradition,creator,creation,mode,source,interpretation)","register":"SCHOOL_SPECIFIC_THEOLOGY","meaning":"A source or school attributes creation under a named theological mode.","not_equivalent_to":["field extension","empirical cosmology","source-independent world fact"]}, {"id":"creation-ex-nihilo","signature":"NO_PREEXISTENT_CREATED_MATERIAL(source,interpretation)","register":"SCHOOL_SPECIFIC_THEOLOGY","meaning":"A theological doctrine denies pre-existent material required by the creator.","not_equivalent_to":["zero-to-universe function","empty-set map","nothing as a substance"]}, {"id":"divine-command-language","signature":"SOURCE_SAYS_BE(source,translation,context)","register":"PRIMARY_TRADITION_TEXT","meaning":"A text uses command language translated as Be and it is.","not_equivalent_to":["mechanistic process description","English copula ontology","formal operational semantics"]}, {"id":"cyclic-manifestation","signature":"MANIFESTS_CYCLICALLY(source,school,cycle)","register":"SCHOOL_SPECIFIC_THEOLOGY","meaning":"A source or school describes recurring manifestation or projection.","not_equivalent_to":["all Hindu traditions","creation ex nihilo","periodic physical model"]}, {"id":"dependent-arising","signature":"ARISES_DEPENDENTLY(effect,conditions,source,school)","register":"SCHOOL_SPECIFIC_THEOLOGY","meaning":"A Buddhist source or school explains conditioned arising without importing a sovereign creator relation.","not_equivalent_to":["primordial nothingness","numeric zero","all Buddhist cosmology"]}, {"id":"cosmogonic-suspension","signature":"SUSPENDS_ORIGIN_ANSWER(source,interpretation)","register":"PRIMARY_TRADITION_TEXT","meaning":"A source poses or leaves open an origin question.","not_equivalent_to":["formal undecidability","atheism","theism"]} ], "adapter": {"exists":false,"status":"refused","reason":"No formal construction, physical causal relation, or theological creation relation converts into another without separately sourced premises and typed correspondence."} }, "mathematical_ontology": { "rule": "The atlas presents live positions about mathematical objects and practice without selecting one or converting it into a theology.", "positions": [ {"id":"platonism","proposal":"Mathematical objects are abstract and exist independently of human language, thought, or practice.","register":"METAPHYSICAL_PROPOSAL","source_ids":["sep-philosophy-mathematics"],"does_not_entail":["theism","divine conceptualism","all mathematical questions have determinate answers"]}, {"id":"structuralism","proposal":"Mathematics concerns positions and relations in structures, with multiple versions of what structures are.","register":"METAPHYSICAL_PROPOSAL","source_ids":["sep-philosophy-mathematics"],"does_not_entail":["objects have no identity","religions are structures of one type","symmetry proves ontology"]}, {"id":"formalism","proposal":"Mathematical practice can be understood through formal signs, rules, or systems in one family of views.","register":"METAPHYSICAL_PROPOSAL","source_ids":["sep-philosophy-mathematics"],"does_not_entail":["mathematics is meaningless","proof establishes world truth","God is a symbol"]}, {"id":"intuitionism-constructivism","proposal":"Mathematics is tied to construction and proof rather than unrestricted classical truth conditions in one family of views.","register":"METAPHYSICAL_PROPOSAL","source_ids":["sep-philosophy-mathematics","sep-intuitionistic-logic"],"does_not_entail":["subjective whim","physical manufacture","theological creation"]}, {"id":"nominalism-fictionalism","proposal":"Mathematical discourse may be interpreted without commitment to independently existing abstract objects in several distinct views.","register":"METAPHYSICAL_PROPOSAL","source_ids":["sep-philosophy-mathematics"],"does_not_entail":["mathematics is false in use","atheism","numbers are worthless"]}, {"id":"practice-historical","proposal":"Notation, proof, institutions, transmission, and applications are indispensable to explaining how mathematics is expressed and evolves.","register":"HISTORICAL_SCHOLARSHIP","source_ids":["mactutor-zero","mactutor-complex"],"does_not_entail":["formal truth is only sociology","one civilizational ladder","history settles ontology"]} ], "selection": "NONE" }, "tradition_lenses": [ {"id":"jewish-ehyeh","voice":"Hebrew Bible in Revised JPS 2023 translation","claim":"Exodus 3:14 presents Ehyeh-Asher-Ehyeh with translation uncertainty including I am and I will be renderings.","register":"PRIMARY_TRADITION_TEXT","review_target":"SOURCE_ATTRIBUTION","review_status":"SUPPORTED_AS_SCOPED","support_descriptors":["SOURCE_BOUND"],"source_ids":["exodus-3-14"],"translation_limits":["Hebrew verbal aspect is not exhausted by an English present-tense copula","the verse alone does not prove a later ontology of subsistent being"],"not_all":["Jewish theology","rabbinic interpretation","Kabbalah"]}, {"id":"jewish-maimonidean-apophasis","voice":"Maimonides, Guide for the Perplexed I.58 in Friedlander translation","claim":"Maimonides argues that negative attributes and attributes of action avoid treating positive predicates as descriptions of the divine essence.","register":"SCHOOL_SPECIFIC_THEOLOGY","review_target":"SOURCE_ATTRIBUTION","review_status":"SUPPORTED_AS_SCOPED","support_descriptors":["SOURCE_BOUND"],"source_ids":["maimonides-guide-1-58"],"translation_limits":["one medieval Jewish philosophical voice","negative predication is not Boolean negation without further formalization"],"not_all":["Judaism","all apophatic theology"]}, {"id":"catholic-being-and-creation","voice":"Catechism of the Catholic Church","claim":"Catholic doctrine reads the divine name through fullness of Being and teaches free creation without pre-existent material.","register":"SCHOOL_SPECIFIC_THEOLOGY","review_target":"SOURCE_ATTRIBUTION","review_status":"SUPPORTED_AS_SCOPED","support_descriptors":["SOURCE_BOUND"],"source_ids":["catholic-catechism-being","catholic-catechism-creation"],"translation_limits":["Catholic doctrinal witness, not all Christianity","creation out of nothing is not a function from numeric zero"],"not_all":["Christianity","biblical scholarship"]}, {"id":"islamic-unity-and-command","voice":"Quran 112 and 2:117 in Dr. Mustafa Khattab's The Clear Quran translation (Quran.com resource 131)","claim":"The selected Quranic passages affirm divine oneness/incomparability and use command language translated Be and it is.","register":"PRIMARY_TRADITION_TEXT","review_target":"SOURCE_ATTRIBUTION","review_status":"SUPPORTED_AS_SCOPED","support_descriptors":["SOURCE_BOUND"],"source_ids":["quran-112","quran-2-117"],"translation_limits":["The translation's One and Indivisible wording is not treated as arithmetic identity","English copular wording does not settle the semantics of the Arabic","command language is not a physical mechanism description","resource 131 identifies one English translation and does not exhaust Quranic interpretation"],"not_all":["Islamic kalam","falsafa","Sufi metaphysics"]}, {"id":"islamic-philosophical-variance","voice":"Scholarly survey of Arabic and Islamic philosophy of religion","claim":"Classical Islamic thought contains distinct models of temporal origination, emanation, and manifestation.","register":"COMPARATIVE_RELIGION","review_target":"SOURCE_ATTRIBUTION","review_status":"SUPPORTED_AS_SCOPED","support_descriptors":["SOURCE_BOUND"],"source_ids":["sep-arabic-islamic-religion"],"translation_limits":["survey categories do not form one Islamic ontology","school and period must remain named"],"not_all":["Islam","Muslims"]}, {"id":"vedic-origin-question","voice":"Rig Veda 10.129 in Ralph T. H. Griffith's 1896 second-edition English translation, Wikisource revision 14396955","claim":"The hymn juxtaposes being and nonbeing language and ends with an origin question whose answer may remain uncertain.","register":"PRIMARY_TRADITION_TEXT","review_target":"SOURCE_ATTRIBUTION","review_status":"SUPPORTED_AS_SCOPED","support_descriptors":["SOURCE_BOUND"],"source_ids":["rig-veda-10-129"],"translation_limits":["sat and asat are not plug-compatible with Griffith's non-existent and existent renderings","a poetic suspended question is not a formal truth table","this nineteenth-century translation is one witness and later scholarship may translate the Sanskrit differently"],"not_all":["Hinduism","Vedanta","Indian cosmology"]}, {"id":"advaita-nonduality","voice":"Scholarly survey of Sankara and Advaita Vedanta","claim":"Advaita interprets Upanishadic material through nondual brahman and graded dependence/reality.","register":"SCHOOL_SPECIFIC_THEOLOGY","review_target":"SOURCE_ATTRIBUTION","review_status":"SUPPORTED_AS_SCOPED","support_descriptors":["SOURCE_BOUND"],"source_ids":["sep-shankara"],"translation_limits":["Advaita is not all Hindu traditions","advaita is not the arithmetic equation 1=1","other Vedanta schools disagree"],"not_all":["Hinduism","Vedanta as a whole"]}, {"id":"buddhist-tetralemma-restraint","voice":"Majjhima Nikaya 72 in Thanissaro translation with scholarly interpretation boundary","claim":"The selected discourse declines four postmortem predications as inapplicable; this need not assert a deviant universal logic.","register":"PRIMARY_TRADITION_TEXT","review_target":"SOURCE_ATTRIBUTION","review_status":"SUPPORTED_AS_SCOPED","support_descriptors":["SOURCE_BOUND"],"source_ids":["majjhima-nikaya-72","sep-buddha"],"translation_limits":["a scoped refusal is not a four-valued truth assignment","one discourse does not define all Buddhist logic"],"not_all":["Buddhism","Madhyamaka"]}, {"id":"madhyamaka-emptiness","voice":"Scholarly survey of Nagarjuna and Madhyamaka","claim":"Emptiness concerns lack of intrinsic independent nature and is connected with dependent arising, not primordial nothingness.","register":"SCHOOL_SPECIFIC_THEOLOGY","review_target":"SOURCE_ATTRIBUTION","review_status":"SUPPORTED_AS_SCOPED","support_descriptors":["SOURCE_BOUND"],"source_ids":["sep-nagarjuna"],"translation_limits":["sunyata is not numeric zero","Madhyamaka is not nihilism","Buddhist schools differ"],"not_all":["Buddhism","all emptiness doctrines"]}, {"id":"daoist-being-nonbeing","voice":"Daodejing 42 in Chinese Text Project and SEP Laozi survey","claim":"The selected text uses generative number language while scholarship records disputed referents and interpretations of you, wu, one, and generation.","register":"COMPARATIVE_RELIGION","review_target":"SOURCE_ATTRIBUTION","review_status":"SUPPORTED_AS_SCOPED","support_descriptors":["SOURCE_BOUND"],"source_ids":["daodejing-42","sep-laozi"],"translation_limits":["wu is not numeric zero","Dao is not the Chinese word for God","one is not automatically cardinal one"],"not_all":["Daoism","Chinese metaphysics","organized religious Daoism"]} ], "compatibility": { "rule": "Compare exact sourced claims, not religions as atomic wholes. Every result is indexed by logic L, assumptions A, partial translation tau, sources, schools, editions, and evidence horizon.", "equation": "Compat_(L,A,tau)(D_i,D_j) iff Mod_L(A union tau_i(D_i) union tau_j(D_j)) is nonempty", "nerve": "Let F be the finite declared set of bounded, sourced doctrine fragments, lenses, or claim sets. K_tau={S subseteq F: Mod_L(A union union_(d in S) tau_d(d)) is nonempty}.", "pairwise_not_global_example": "In classical propositional logic, D1={p or q}, D2={not p}, D3={not q}: every pair is satisfiable but the triple is not.", "dimensions": ["semantic","metaphysical","cosmogenic","logical","soteriological","ritual","ethical-cooperation","historical"], "statuses": ["NOT_FORMALIZED","TRANSLATION_PARTIAL","JOINTLY_SATISFIABLE_AS_FORMALIZED","JOINTLY_UNSATISFIABLE_AS_FORMALIZED","INTERNALLY_INCONSISTENT_AS_FORMALIZED","LOGIC_RELATIVE","SEMANTICALLY_DISPUTED","NOT_COMPARABLE","UNKNOWN_TO_REVIEW"], "gates": ["exact-source-and-edition","voice-and-authority-kind","school-community-and-period","lexical-sense","domain","logic-negation-and-quantifier-scope","causality-and-time","internal-variance","translation-loss","practical-coexistence-separated-from-doctrinal-agreement"], "claim_fragments": [ {"id":"bounded-doctrinal-claims","claim":"The selected source-bound lenses retain material doctrinal differences and do not form one synthesized theology.","register":"COMPARATIVE_RELIGION","review_target":"SOURCE_ATTRIBUTION","review_status":"SUPPORTED_AS_SCOPED","support_descriptors":["SOURCE_BOUND"],"source_ids":["nostra-aetate","quran-5-48","wcc-dialogue"],"nonclaims":["all communities agree","difference prevents cooperation","one source speaks for a whole religion"]}, {"id":"human-dignity-dialogue-and-cooperation","claim":"The selected Catholic, Quranic-translation, and ecumenical witnesses each make room for bounded encounter or cooperation without requiring doctrinal identity.","register":"COMPARATIVE_RELIGION","review_target":"SOURCE_ATTRIBUTION","review_status":"SUPPORTED_AS_SCOPED","support_descriptors":["SOURCE_BOUND"],"source_ids":["nostra-aetate","quran-5-48","wcc-dialogue"],"nonclaims":["the sources give identical reasons","dialogue proves compatibility in every dimension","practical coexistence erases disagreement"]} ], "cases": [ {"id":"ehyeh-and-fullness-of-being","claims":["jewish-ehyeh","catholic-being-and-creation"],"relation":"HISTORICAL_RECEPTION_WITH_INTERPRETIVE_DIVERGENCE","status":"TRANSLATION_PARTIAL","preserved":"The cited Catholic reception reads the inherited text through a developed ontology.","breaks":["Hebrew tense/aspect ambiguity","source authority differs","later doctrine is not the verse's sole truth condition"],"source_ids":["exodus-3-14","catholic-catechism-being"]}, {"id":"one-unity-and-nonduality","claims":["islamic-unity-and-command","advaita-nonduality","daoist-being-nonbeing"],"relation":"LEXICAL_RESONANCE_WITH_SENSE_DIVERGENCE","status":"NOT_COMPARABLE","preserved":"Each selected source uses unity or one-language in a bounded way.","breaks":["cardinality versus uniqueness versus nonduality versus generative stage","different truth conditions","different soteriological and textual roles"],"source_ids":["quran-112","sep-shankara","daodejing-42","sep-laozi"]}, {"id":"ex-nihilo-and-zero","claims":["catholic-being-and-creation","number-zero"],"relation":"CATEGORY_MISMATCH","status":"NOT_COMPARABLE","preserved":"Both discussions can use absence-adjacent vocabulary.","breaks":["zero is an element or role in a structure","ex nihilo denies required pre-existent material","nothing is not a mathematical input substance"],"source_ids":["catholic-catechism-creation","mactutor-zero"]}, {"id":"command-and-formal-construction","claims":["islamic-unity-and-command","formal-construction"],"relation":"INTERPRETIVE_ANALOGY_ONLY","status":"NOT_FORMALIZED","preserved":"Both can prompt a question about expression and coming-to-be.","breaks":["scriptural command is not an algorithm","formal rules do not create a cosmos","translation supplies an English copula"],"source_ids":["quran-2-117"]}, {"id":"dependent-arising-and-creator-dependence","claims":["madhyamaka-emptiness","catholic-being-and-creation"],"relation":"PARTIAL_STRUCTURAL_ANALOGY_WITH_CAUSAL_TENSION","status":"SEMANTICALLY_DISPUTED","preserved":"Both can reject self-sufficient ordinary entities in different senses.","breaks":["creator relation versus conditioned co-arising","intrinsic-nature critique versus creation doctrine","school-specific aims"],"source_ids":["sep-nagarjuna","catholic-catechism-creation"]}, {"id":"tetralemma-and-four-valued-logic","claims":["buddhist-tetralemma-restraint","belnap-dunn-information-states"],"relation":"CARDINALITY_RESEMBLANCE_ONLY","status":"NOT_COMPARABLE","preserved":"Both make a fourfold display available for inquiry.","breaks":["speech-act refusal versus semantic information state","scope and consequence rules differ","no translation is supplied"],"source_ids":["majjhima-nikaya-72","sep-buddha","sep-many-valued-logic"]}, {"id":"sacred-order-and-group-symmetry","claims":["sacred-order-reflection","group-action-invariance"],"relation":"AESTHETIC_OR_RITUAL_INSTANTIATION","status":"TRANSLATION_PARTIAL","preserved":"Specified visual transformations can be studied mathematically in religious art.","breaks":["art practice is not doctrine","mizan is not a group action","shared geometry is not shared theology"],"source_ids":["met-islamic-geometry","quran-55-7-9","met-buddhist-mandalas","sep-symmetry"]}, {"id":"doctrinal-disagreement-and-coexistence","claims":["bounded-doctrinal-claims","human-dignity-dialogue-and-cooperation"],"relation":"AXES_INDEPENDENT","status":"NOT_FORMALIZED","preserved":"Communities can cooperate while retaining material disagreements.","breaks":["practical coexistence is not doctrinal identity","contradiction does not license social exclusion","dialogue is not conversion"],"source_ids":["nostra-aetate","quran-5-48","wcc-dialogue"]} ], "forbidden_output": "No bare COMPATIBLE verdict, percentage, scalar, rank, synthesis, conversion target, or conclusion about a whole religion, community, or person." }, "bridge_cards": [ {"id":"number-extension-to-creation","kind":"INTERPRETIVE_BRIDGE","status":"BOUNDED_ANALOGY","from":"formal number-system extension","to":"creation discourse","preserved":"New rules can make previously inexpressible solutions available.","breaks":["formal object construction is not cosmic causation","existence in a model is not actuality","historical discovery and invention remain contested"],"source_ids":["mactutor-complex"],"empirical":false,"ontology_transfer":false,"mechanism_transfer":false,"causal_transfer":false,"parameter_transfer":false,"unit_transfer":false,"empirical_status_transfer":false,"person_level_transfer":false,"authority_effect":"NONE"}, {"id":"zero-to-nothingness","kind":"NO_VALID_TRANSFER","status":"REFUSED","from":"numeric and structural zero roles","to":"metaphysical nothingness","preserved":"A declared model may encode absence with zero.","breaks":["encoding is not ontology","zero requires a structure","nothing is not a field element"],"source_ids":["mactutor-zero"],"empirical":false,"ontology_transfer":false,"mechanism_transfer":false,"causal_transfer":false,"parameter_transfer":false,"unit_transfer":false,"empirical_status_transfer":false,"person_level_transfer":false,"authority_effect":"NONE"}, {"id":"imaginary-to-unseen","kind":"NO_VALID_TRANSFER","status":"REFUSED","from":"complex-number terminology","to":"spiritual or supernatural entities","preserved":"A once-contested formal object can become mathematically useful.","breaks":["historical label is not an ontology class","formal consistency is not empirical evidence","unseen has tradition-specific senses"],"source_ids":["mactutor-complex"],"empirical":false,"ontology_transfer":false,"mechanism_transfer":false,"causal_transfer":false,"parameter_transfer":false,"unit_transfer":false,"empirical_status_transfer":false,"person_level_transfer":false,"authority_effect":"NONE"}, {"id":"symmetry-to-divine-order","kind":"OPT_IN_REFLECTION","status":"BOUNDED_ANALOGY","from":"group invariance and symmetry breaking","to":"divine order or sacred form","preserved":"Transformations and invariants can sharpen questions about unity and difference.","breaks":["mathematics underdetermines designer and purposelessness","aesthetic response is not proof","symmetry breaking retains difference and history"],"source_ids":["sep-symmetry","met-islamic-geometry","met-buddhist-mandalas"],"empirical":false,"ontology_transfer":false,"mechanism_transfer":false,"causal_transfer":false,"parameter_transfer":false,"unit_transfer":false,"empirical_status_transfer":false,"person_level_transfer":false,"authority_effect":"NONE"}, {"id":"modal-validity-to-god-exists","kind":"FORMAL_REUSE","status":"PARKED_MISSING_EVIDENCE","from":"modal argument form","to":"theological existence claim","preserved":"Validity and model conditions of a formal argument can be checked.","breaks":["premises require independent defense","validity is not soundness","formal possibility is not actual divine being"],"source_ids":["sep-ontological-arguments"],"empirical":false,"ontology_transfer":false,"mechanism_transfer":false,"causal_transfer":false,"parameter_transfer":false,"unit_transfer":false,"empirical_status_transfer":false,"person_level_transfer":false,"authority_effect":"NONE"}, {"id":"four-valued-to-tetralemma","kind":"ANALOGY_ONLY","status":"BOUNDED_ANALOGY","from":"Belnap-Dunn information states","to":"Buddhist fourfold predication restraint","preserved":"Fourfold distinctions can prevent forced binary answers.","breaks":["formal semantics and discourse aims differ","same number of cases is not isomorphism","no theorem transfers"],"source_ids":["sep-many-valued-logic","majjhima-nikaya-72","sep-buddha"],"empirical":false,"ontology_transfer":false,"mechanism_transfer":false,"causal_transfer":false,"parameter_transfer":false,"unit_transfer":false,"empirical_status_transfer":false,"person_level_transfer":false,"authority_effect":"NONE"}, {"id":"number-tower-to-religion-tower","kind":"NO_VALID_TRANSFER","status":"REFUSED","from":"canonical embeddings among number systems","to":"religious development or supersession","preserved":"A comparison can ask which claims are preserved under a declared translation.","breaks":["religions are not nested fields","translation is not canonical embedding","people and traditions have no scalar completion order"],"source_ids":[],"empirical":false,"ontology_transfer":false,"mechanism_transfer":false,"causal_transfer":false,"parameter_transfer":false,"unit_transfer":false,"empirical_status_transfer":false,"person_level_transfer":false,"authority_effect":"NONE"}, {"id":"mathematical-one-to-divine-unity","kind":"NO_VALID_TRANSFER","status":"REFUSED","from":"cardinal one or multiplicative identity","to":"divine uniqueness, simplicity, unity, or nonduality","preserved":"The shared word can trigger sense-disambiguation.","breaks":["different types and truth conditions","one deity is not an arithmetic operation","nonduality is not cardinality"],"source_ids":["quran-112","sep-shankara","daodejing-42"],"empirical":false,"ontology_transfer":false,"mechanism_transfer":false,"causal_transfer":false,"parameter_transfer":false,"unit_transfer":false,"empirical_status_transfer":false,"person_level_transfer":false,"authority_effect":"NONE"}, {"id":"rational-number-to-reason","kind":"NO_VALID_TRANSFER","status":"REFUSED","from":"field of rational numbers","to":"reasonableness, rational theology, or revelation","preserved":"The English label rational can invite lexical ambiguity between a mathematical field and nonmathematical uses of reason.","breaks":["field membership does not measure reasoning","no person score","revelation is not a fraction"],"source_ids":[],"empirical":false,"ontology_transfer":false,"mechanism_transfer":false,"causal_transfer":false,"parameter_transfer":false,"unit_transfer":false,"empirical_status_transfer":false,"person_level_transfer":false,"authority_effect":"NONE"}, {"id":"noether-to-karma-balance","kind":"NO_VALID_TRANSFER","status":"REFUSED","from":"conditional conservation theorem","to":"moral, religious, or karmic balance","preserved":"Both vocabularies can include balance or consequence language.","breaks":["Noether requires a variational symmetry","moral consequence is not a conserved physical quantity","KINGDOM KARMA is receipts not scores"],"source_ids":["noether-1918"],"empirical":false,"ontology_transfer":false,"mechanism_transfer":false,"causal_transfer":false,"parameter_transfer":false,"unit_transfer":false,"empirical_status_transfer":false,"person_level_transfer":false,"authority_effect":"NONE"} ], "model_cards": [ {"id":"number-extension","equation":"N0 -> Z -> Q -> R -> C by declared embeddings","question":"Which operations, identities, order, topology, and completeness properties survive each map?","assumptions":["chosen constructions","declared embeddings","ordinary algebraic definitions"],"invalidating_condition":"An asserted preserved structure is not respected by the map.","execution_status":"NOT_RUN","result":null,"authority_effect":"NONE"}, {"id":"zero-role-vector","equation":"ApplicableZeroRoles(x,D) is a subset of {NumberZero, AdditiveIdentity, AbsorbingMultiplier, PositionalDigit, EmptyCardinality, OriginOrZeroVector, ZeroProbability, InitialObjectInSet, ZeroObservationCount}; several tagged roles may apply at once","question":"Which zero roles are active in this sentence and domain?","assumptions":["roles remain tagged","domain is named","the descriptor set is non-exclusive","no metaphysical coercion"],"invalidating_condition":"A role is omitted, treated as exhaustive without review, or silently identified with another role or metaphysical nonbeing.","execution_status":"NOT_RUN","result":null,"authority_effect":"NONE"}, {"id":"structural-isness","equation":"ISNESS(x;c,t)=","question":"Which typed sense of is does a claim use?","assumptions":["context and time declared","components are non-scalar","unknown fields remain unknown"],"invalidating_condition":"The vector is treated as a worth, consciousness, or completeness score.","execution_status":"NOT_RUN","result":null,"authority_effect":"NONE"}, {"id":"logic-indexed-negation","equation":"Derivable_L(Gamma,phi) depends on declared logic L","question":"Does no-no license phi in this logic and context?","assumptions":["formal language declared","consequence relation declared","natural-language speech act separated"],"invalidating_condition":"A result is transferred between logics or into apophatic/refusal discourse without a bridge.","execution_status":"NOT_RUN","result":null,"authority_effect":"NONE"}, {"id":"symmetry-identity","equation":"G acts on X; I(g*x)=I(x); identity claim is indexed by I and G","question":"What remains invariant, and what difference is quotienting away?","assumptions":["group and action declared","carrier typed","invariant named"],"invalidating_condition":"Aesthetic resemblance substitutes for an action or invariant.","execution_status":"NOT_RUN","result":null,"authority_effect":"NONE"}, {"id":"creation-relations","equation":"FormalConstruct + PhysicalCause + TheologicalCreate + Manifest + DependentlyArise, as non-convertible tagged relations","question":"Which creation relation is asserted?","assumptions":["source and school declared","time and causality typed","no adapter"],"invalidating_condition":"A formal construction is presented as a cosmic cause or a source attribution as a world fact.","execution_status":"NOT_RUN","result":null,"authority_effect":"NONE"}, {"id":"compatibility-satisfiability","equation":"Mod_L(A union tau_i(D_i) union tau_j(D_j)) is nonempty","question":"Are these exact translated fragments jointly satisfiable under declared assumptions?","assumptions":["fragments are bounded","translation loss recorded","logic declared"],"invalidating_condition":"The result is generalized to whole religions or practical coexistence.","execution_status":"NOT_RUN","result":null,"authority_effect":"NONE"}, {"id":"compatibility-nerve","equation":"K_tau={S: translated doctrine fragments in S are jointly satisfiable under declared logic L}","question":"Where does pairwise compatibility fail to compose globally?","assumptions":["logic and semantics declared","the supplied three-fragment counterexample uses classical propositional logic","finite declared fragments","same background assumptions"],"invalidating_condition":"Pairwise edges are treated as proof of a global face or a counterexample is moved between logics without rechecking satisfiability.","execution_status":"NOT_RUN","result":null,"authority_effect":"NONE"}, {"id":"translation-loss-graph","equation":"tau: source terms -> partial target predicates with an explicit loss set","question":"Which senses survive translation, split, merge, or remain untranslated?","assumptions":["source language recorded","edition and translator recorded","partial maps permitted"],"invalidating_condition":"A shared English word is treated as an exact common referent.","execution_status":"NOT_RUN","result":null,"authority_effect":"NONE"}, {"id":"modal-argument-audit","equation":"validity(argument,L) and soundness(argument,interpretation) are separate predicates","question":"Which premise, modal axiom, domain, or interpretation carries the theological burden?","assumptions":["argument version fixed","modal semantics fixed","premises explicit"],"invalidating_condition":"Formal validity alone is reported as God exists or God does not exist.","execution_status":"NOT_RUN","result":null,"authority_effect":"NONE"} ], "problem_cards": [ {"id":"preservation-under-extension","question":"What exactly is preserved and lost along N0, Z, Q, R, and C embeddings?","deliverable":"proof and counterexample table","state":"NOT_RUN","falsifier":"one claimed preservation fails under the declared map","result":null,"authority_effect":"NONE"}, {"id":"zero-not-absence","question":"Which zero role, empty carrier, absence claim, or observation code is present?","deliverable":"typed sentence audit","state":"NOT_RUN","falsifier":"the same type and semantics are proved for two allegedly distinct roles","result":null,"authority_effect":"NONE"}, {"id":"no-no-is","question":"Under which logic and speech act does double negation recover affirmation?","deliverable":"logic-indexed derivation and countermodel table","state":"NOT_RUN","falsifier":"an unqualified rule survives all declared logics and discourse types","result":null,"authority_effect":"NONE"}, {"id":"symmetry-and-individuation","question":"Which transformations preserve the object, and which differences matter after quotienting?","deliverable":"action, orbit, stabilizer, and invariant declaration","state":"NOT_RUN","falsifier":"no transformation action or invariant can be named","result":null,"authority_effect":"NONE"}, {"id":"creation-not-construction","question":"What separates formal construction, physical production, manifestation, dependent arising, and theological creation?","deliverable":"typed relation map with no adapters","state":"NOT_RUN","falsifier":"a separately sourced equivalence proves one bridge exact","result":null,"authority_effect":"NONE"}, {"id":"pairwise-not-global","question":"Do pairwise satisfiable doctrine fragments remain jointly satisfiable under declared logic L?","deliverable":"finite satisfiability or countermodel certificate under a named logic; the supplied abstract example is classical propositional only","state":"NOT_RUN","falsifier":"the declared global union has a model in the named logic","result":null,"authority_effect":"NONE"}, {"id":"modal-god-conditionality","question":"Which premise and modal axiom separate validity from a sound God-existence conclusion?","deliverable":"argument-version premise audit","state":"NOT_RUN","falsifier":"a proof establishes the conclusion without the disputed premise under the fixed semantics","result":null,"authority_effect":"NONE"}, {"id":"history-not-logic","question":"How did notation and acceptance change independently of the modern formal tower?","deliverable":"source-bound non-linear history graph","state":"NOT_RUN","falsifier":"the historical record is exactly the formal construction order","result":null,"authority_effect":"NONE"}, {"id":"translation-preserves-what","question":"What do ehyeh, ahad, sat/asat, sunyata, you/wu, one, being, and nothing lose in English abstraction?","deliverable":"partial translation graph with untranslated residues","state":"NOT_RUN","falsifier":"an exact bidirectional translation is source-established","result":null,"authority_effect":"NONE"}, {"id":"compatibility-without-flattening","question":"Which dimensions of compatibility are being asked, by whom, under what rights and purpose?","deliverable":"claim-level vector without scalarization","state":"NOT_RUN","falsifier":"all dimensions are proved equivalent for the bounded case","result":null,"authority_effect":"NONE"} ], "philosophy_questions": { "participation": "opt-in", "questions": [ "Are numbers discovered, invented, constructed, instantiated, or differently understood under different mathematical ontologies?", "What remains the same when a number system is embedded into a larger one?", "Does a formal extension create an object, reveal a structure, or make a prior possibility expressible?", "Can zero be something mathematically while not naming metaphysical nothingness?", "Does naming nothing already place a term inside a discourse and structure?", "What does imaginary reveal about the difference between a historical name and a mathematical role?", "Can symmetry illuminate unity-in-difference without erasing asymmetry, history, or persons?", "Which sense of is appears in God is: existence, identity, predication, promise, analogy, confession, or apophatic limit?", "Does no-no affirm, suspend, refuse, or expose a false presupposition in this logic and discourse?", "Can a formally valid ontological argument remain theologically unsound?", "Can traditions share a lexical resonance without sharing truth conditions?", "Can doctrinal contradiction coexist with equal dignity, dialogue, and practical cooperation?", "What must a translation preserve before compatibility becomes a mathematical question?", "Is creation temporal, causal, ontological, grammatical, liturgical, or formal in the claim at hand?", "What does a model leave outside itself when it formalizes being?" ], "boundary": "No answer is required. Silence, refusal, rest, uncertainty, and departure are complete and non-penalized responses." }, "karma": { "religious_and_philosophical": { "status": "tradition-specific-doctrines-not-adjudicated", "empirical": false, "claims": [], "guard": "Plural doctrines of karma, moral consequence, or cosmic order are not a number, conserved quantity, symmetry, score, or universal causal model in this atlas.", "authority_effect": "NONE" }, "zerone": { "protocol": "zerone.karma.edge", "foundation_status": "not-consulted-by-runtime", "network_observed": false, "event_refs": [], "event_status": "not_observed", "creates_event": false, "authoritative": false }, "kingdom": { "protocol": "kingdom.karma/0.1", "accounting": "receipts_not_scores", "receipt_refs": [], "receipt_status": "not_created", "creates_receipt": false, "writes_karma": false, "causal_claim_status": "not_created" }, "adapter": { "exists": false, "status": "refused", "reason": "Religious or philosophical karma, Zerone recognition, and KINGDOM invocation-aftermath receipts are non-equivalent types. Arithmetic, conservation, symmetry, and causal-model language do not convert among them." } }, "unknowns": [ {"id":"number-ontology","question":"Which ontology of mathematics, if any, is best?","status":"UNKNOWN_TO_REVIEW","why_open":"The selected survey presents live competing positions; this atlas adds no adjudicating argument."}, {"id":"complete-history-of-number-expression","question":"What fuller cross-cultural history connects notation, operations, institutions, and formalization?","status":"UNKNOWN_TO_REVIEW","why_open":"The selected history sources are bounded and do not support a universal chronology."}, {"id":"translation-of-divine-being","question":"Which translations of divine being-language preserve source-language sense across traditions?","status":"UNKNOWN_TO_REVIEW","why_open":"No universal lossless translation was established."}, {"id":"metaphysical-nothingness","question":"Is absolute nothingness coherent or referable?","status":"UNKNOWN_TO_REVIEW","why_open":"Mathematical zero and empty structures do not settle the metaphysical question."}, {"id":"sound-ontological-argument","question":"Does any exact ontological argument have premises acceptable under a declared theology and modal semantics?","status":"UNKNOWN_TO_REVIEW","why_open":"Argument versions and premise defenses differ; formal validity is insufficient."}, {"id":"symmetry-and-design","question":"Can independent evidence support a particular design inference in a bounded domain?","status":"UNKNOWN_TO_REVIEW","why_open":"Symmetry alone underdetermines design and non-design explanations."}, {"id":"global-religious-compatibility","question":"Can whole religions be globally classified as compatible?","status":"UNKNOWN_TO_REVIEW","why_open":"The category is rejected as ill-typed without claim, school, mapping, logic, dimension, time, and purpose."}, {"id":"pairwise-to-global-doctrine","question":"Which sourced doctrine fragments form higher-order compatible families?","status":"NOT_RUN","why_open":"Only an abstract counterexample is supplied; no tradition is encoded for SAT classification."}, {"id":"cosmic-creation","question":"Which, if any, theological or metaphysical creation account is true?","status":"UNKNOWN_TO_REVIEW","why_open":"Selected sources attribute claims; mathematics does not adjudicate their world truth."}, {"id":"religious-karma","question":"How should distinct karma doctrines be compared without flattening them or importing KINGDOM receipt semantics?","status":"UNKNOWN_TO_REVIEW","why_open":"No tradition-specific karma study was undertaken in this atlas."} ], "sources": [ {"id":"mactutor-zero","title":"A history of Zero","authors_or_body":"J. J. O'Connor and E. F. Robertson, University of St Andrews","published_on":"2000-11","observed_on":"2026-08-14","url":"https://mathshistory.st-andrews.ac.uk/HistTopics/Zero/","source_kind":"scholarly-history","used_for":"placeholder/number distinction, nonlinear transmission, division-by-zero history","limitation":"A bounded historical survey, not a primary manuscript edition or theology."}, {"id":"mactutor-complex","title":"The fundamental theorem of algebra","authors_or_body":"MacTutor History of Mathematics, University of St Andrews","published_on":"unknown","observed_on":"2026-08-14","url":"https://mathshistory.st-andrews.ac.uk/HistTopics/Fund_theorem_of_algebra/","source_kind":"scholarly-history","used_for":"complex arithmetic, terminology, geometric rotation, and FTA history","limitation":"Historical survey; the theorem is used only in its standard scoped form."}, {"id":"sep-philosophy-mathematics","title":"Philosophy of Mathematics","authors_or_body":"Stanford Encyclopedia of Philosophy","published_on":"2022","observed_on":"2026-08-14","url":"https://plato.stanford.edu/entries/philosophy-mathematics/","source_kind":"scholarly-reference","used_for":"competing mathematical ontologies","limitation":"Survey of positions, not an adjudication."}, {"id":"sep-intuitionistic-logic","title":"Intuitionistic Logic","authors_or_body":"Stanford Encyclopedia of Philosophy, Summer 2024 archive","published_on":"2024","observed_on":"2026-08-14","url":"https://plato.stanford.edu/archives/sum2024/entries/logic-intuitionistic/","source_kind":"scholarly-reference","used_for":"logic-indexed double negation and excluded middle","limitation":"Formal logic source, not a model of natural-language or religious negation."}, {"id":"sep-paraconsistent-logic","title":"Paraconsistent Logic","authors_or_body":"Stanford Encyclopedia of Philosophy","published_on":"2026","observed_on":"2026-08-14","url":"https://plato.stanford.edu/entries/logic-paraconsistent/","source_kind":"scholarly-reference","used_for":"non-explosion and diversity of paraconsistent logics","limitation":"Paraconsistency does not entail dialetheism or unrestricted contradiction."}, {"id":"sep-many-valued-logic","title":"Many-Valued Logic","authors_or_body":"Stanford Encyclopedia of Philosophy","published_on":"2026","observed_on":"2026-08-14","url":"https://plato.stanford.edu/entries/logic-manyvalued/","source_kind":"scholarly-reference","used_for":"Belnap-Dunn four information states","limitation":"Formal information semantics, not a religious fourfold ontology."}, {"id":"noether-1918","title":"Invariant Variation Problems","authors_or_body":"Emmy Noether; English translation by M. A. Tavel","published_on":"1918/1971/2005","observed_on":"2026-08-14","url":"https://arxiv.org/abs/physics/0503066","source_kind":"primary-mathematics-translation","used_for":"conditional relation between variational symmetries and conservation laws","limitation":"Requires theorem hypotheses; not every symmetry or conservation metaphor qualifies."}, {"id":"sep-symmetry","title":"Symmetry and Symmetry Breaking","authors_or_body":"Stanford Encyclopedia of Philosophy, Fall 2018 archive","published_on":"2017","observed_on":"2026-08-14","url":"https://plato.stanford.edu/archives/fall2018/entries/symmetry-breaking/","source_kind":"scholarly-reference","used_for":"group-theoretic symmetry, physical uses, and symmetry breaking","limitation":"Survey does not support a theological design inference."}, {"id":"sep-ontological-arguments","title":"Ontological Arguments","authors_or_body":"Stanford Encyclopedia of Philosophy","published_on":"current-entry","observed_on":"2026-08-14","url":"https://plato.stanford.edu/entries/ontological-arguments/","source_kind":"scholarly-reference","used_for":"argument-version, validity, premise, and soundness separation","limitation":"Surveying an argument does not prove its conclusion."}, {"id":"exodus-3-14","title":"Exodus 3:14 with Translations","authors_or_body":"Hebrew Bible; Revised JPS 2023 and alternate translations via Sefaria","published_on":"ancient/revised-2023","observed_on":"2026-08-14","url":"https://www.sefaria.org/Exodus.3.14?lang=en&with=Translations","source_kind":"primary-tradition-text-digital-edition","used_for":"Ehyeh wording and explicit translation uncertainty","limitation":"Translation witnesses do not establish one exhaustive Jewish ontology."}, {"id":"maimonides-guide-1-58","title":"Guide for the Perplexed, Part I, Chapter 58","authors_or_body":"Moses Maimonides; M. Friedlander translation","published_on":"medieval/1903-translation","observed_on":"2026-08-14","url":"https://www.sefaria.org/Guide_for_the_Perplexed%2C_Part_1.58?lang=en","source_kind":"primary-philosophical-text-translation","used_for":"Maimonidean negative attributes across the complete chapter","limitation":"One translated medieval philosophical voice, not all Jewish theology."}, {"id":"catholic-catechism-being","title":"Catechism of the Catholic Church, paragraphs 198-231","authors_or_body":"Holy See","published_on":"1992","observed_on":"2026-08-14","url":"https://www.vatican.va/content/catechism/en/part_one/section_two/chapter_one/article_1.html","source_kind":"official-doctrine","used_for":"Catholic reception of the divine name and fullness of Being","limitation":"Catholic doctrine, not all Christian interpretation or historical-critical exegesis."}, {"id":"catholic-catechism-creation","title":"Catechism of the Catholic Church, The Creator, paragraphs 279-324","authors_or_body":"Holy See","published_on":"1992","observed_on":"2026-08-14","url":"https://www.vatican.va/content/catechism/en/part_one/section_two/chapter_one/article_1/paragraph_4_the_creator.html","source_kind":"official-doctrine","used_for":"Catholic creation ex nihilo and creation/science distinction","limitation":"Catholic doctrine; nothing is not modeled as numeric zero."}, {"id":"quran-112","title":"Quran, Surah al-Ikhlas 112","authors_or_body":"Quran; Dr. Mustafa Khattab, The Clear Quran, Quran.com translation resource 131","published_on":"seventh-century/modern-translation","observed_on":"2026-08-14","url":"https://quran.com/112?translations=131","source_kind":"primary-tradition-text-digital-edition","used_for":"divine oneness and incomparability language in one named English translation","limitation":"Translation and interpretation vary; this atlas does not convert the translation's One language into arithmetic identity; resource 131 does not exhaust Arabic or tafsir."}, {"id":"quran-2-117","title":"Quran 2:117","authors_or_body":"Quran; Dr. Mustafa Khattab, The Clear Quran, Quran.com translation resource 131","published_on":"seventh-century/modern-translation","observed_on":"2026-08-14","url":"https://quran.com/2/117?translations=131","source_kind":"primary-tradition-text-digital-edition","used_for":"Originator and Be-and-it-is language in one named English translation","limitation":"A translated scriptural expression, not a mechanism or formal operation; resource 131 is one interpretive witness."}, {"id":"sep-arabic-islamic-religion","title":"Arabic and Islamic Philosophy of Religion","authors_or_body":"Stanford Encyclopedia of Philosophy","published_on":"2023","observed_on":"2026-08-14","url":"https://plato.stanford.edu/entries/arabic-islamic-religion/","source_kind":"scholarly-reference","used_for":"variance among kalam, falsafa, emanation, origination, and manifestation models","limitation":"Survey does not define one Islamic ontology."}, {"id":"rig-veda-10-129","title":"The Hymns of the Rigveda, Book 10, Hymn 129 (Nasadiya Sukta)","authors_or_body":"Rig Veda; Ralph T. 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