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      "subject_id": "ttp.concept.divisibility"
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    {
      "confidence": "high",
      "evidence_locator": {
        "notes": "Preserve the label `thm:wilsons`.",
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    {
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      "evidence_locator": {
        "notes": "Preserve the label `thm:wilsons`.",
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        "notes": "Use in the supporting lemma; do not imply ordinary real reciprocals.",
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        "notes": "Used here through the divisibility of a subgroup order.",
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        "notes": "Written `\\left<a\\right>` in the authority.",
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        "notes": "Written `\\left<a\\right>` in the authority.",
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        "notes": "A translate `x\\left<a\\right>` of the cyclic subgroup.",
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        "notes": "Preserve `a^{\\phi(n)}\\equiv1\\pmod n` under the coprimality hypothesis.",
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      "evidence_locator": {
        "notes": "Use this established Indonesian word order consistently.",
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        "notes": "A monoalphabetic shift cipher; system name `kriptosistem Caesar`.",
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    {
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      "evidence_locator": {
        "notes": "Preserve the name and key-vector notation; the source uses a LaTeX accent macro.",
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        "notes": "Introduce the English term parenthetically once; use the Indonesian form thereafter.",
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      "evidence_locator": {
        "notes": "Introduce the English term parenthetically once; use the Indonesian form thereafter.",
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      "evidence_locator": {
        "notes": "Compare observed symbol frequencies with a reference-language distribution.",
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      "evidence_locator": {
        "notes": "Compare observed symbol frequencies with a reference-language distribution.",
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      "evidence_locator": {
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        "notes": "`n=pq` for distinct large primes `p,q`.",
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        "notes": "Product of two large primes of comparable size; do not generalize factoring hardness to arbitrary composites.",
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      "evidence_locator": {
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      "object_id": "ttp.concept.rsa_public_key",
      "predicate": "prerequisite_for",
      "relation_id": "ttp.r014.relation.3037",
      "subject_id": "ttp.concept.rsa_exponent"
    },
    {
      "confidence": "high",
      "evidence_locator": {
        "notes": "Pair `(n,d)` with `d=e^{-1}\\pmod{\\phi(n)}`.",
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      "native_object_sha256": "234f14148332ea116a7a0c0d83bd75b776ceb8a4bc4cd3089060864a057ed85a",
      "object_id": "ttp.concept.rsa_private_key",
      "predicate": "prerequisite_for",
      "relation_id": "ttp.r014.relation.3038",
      "subject_id": "ttp.concept.rsa_public_key"
    },
    {
      "confidence": "high",
      "evidence_locator": {
        "notes": "Pair `(n,d)` with `d=e^{-1}\\pmod{\\phi(n)}`.",
        "path": "qa/review-candidates/boundary28-r2/TERMINOLOGY.md",
        "sha256": "3e3fe31baa8565bbc54cd6d789570cac18ed469f68cf683f08dd639ef92d9bd1",
        "terminology_id": "crypto.rsa_private_key"
      },
      "native_object_sha256": "8ebbcabae0dcd200a224ffb0aeda46a0733e968f7c89302d9dc2b7a2c86c3270",
      "object_id": "ttp.concept.rsa_private_key",
      "predicate": "prerequisite_for",
      "relation_id": "ttp.r014.relation.3039",
      "subject_id": "ttp.concept.modular_inverse"
    },
    {
      "confidence": "high",
      "evidence_locator": {
        "notes": "Implemented by repeated squaring and binary expansion.",
        "path": "qa/review-candidates/boundary28-r2/TERMINOLOGY.md",
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        "terminology_id": "nt.fast_modular_exponentiation"
      },
      "native_object_sha256": "c1dfacfab3bfb84a1ba68bc8ee22af5f0062f3f5296dd92b981d782b79dab473",
      "object_id": "ttp.concept.fast_modular_exponentiation",
      "predicate": "prerequisite_for",
      "relation_id": "ttp.r014.relation.3040",
      "subject_id": "ttp.concept.binary_representation"
    },
    {
      "confidence": "high",
      "evidence_locator": {
        "notes": "Implemented by repeated squaring and binary expansion.",
        "path": "qa/review-candidates/boundary28-r2/TERMINOLOGY.md",
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        "terminology_id": "nt.fast_modular_exponentiation"
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      "object_id": "ttp.concept.fast_modular_exponentiation",
      "predicate": "prerequisite_for",
      "relation_id": "ttp.r014.relation.3041",
      "subject_id": "ttp.concept.congruence"
    },
    {
      "confidence": "high",
      "evidence_locator": {
        "notes": "Data attached to a document/message whose valid verification can support signer attribution only under the scheme's security assumptions, an uncompromised private key, and a trusted identity--key binding.",
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        "sha256": "3e3fe31baa8565bbc54cd6d789570cac18ed469f68cf683f08dd639ef92d9bd1",
        "terminology_id": "crypto.digital_signature"
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      "native_object_sha256": "5e899f450fdc2363e64fbaf83462e4595efa62aca3f3ce561ac5484d7176812a",
      "object_id": "ttp.concept.digital_signature",
      "predicate": "prerequisite_for",
      "relation_id": "ttp.r014.relation.3042",
      "subject_id": "ttp.concept.public_key_cryptosystem"
    },
    {
      "confidence": "high",
      "evidence_locator": {
        "notes": "Security property required before valid verification supports attributing a newly created signature to the private-key holder.",
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        "sha256": "3e3fe31baa8565bbc54cd6d789570cac18ed469f68cf683f08dd639ef92d9bd1",
        "terminology_id": "crypto.signature_unforgeability"
      },
      "native_object_sha256": "9bfa559fd244b4e86f7d6e74eb92143a3bb4f59fa2be1b730ef5e80dcbed248f",
      "object_id": "ttp.concept.signature_unforgeability",
      "predicate": "prerequisite_for",
      "relation_id": "ttp.r014.relation.3043",
      "subject_id": "ttp.concept.digital_signature"
    },
    {
      "confidence": "high",
      "evidence_locator": {
        "notes": "Maps arbitrary-length bit strings to fixed-length bit strings under three computational resistance requirements.",
        "path": "qa/review-candidates/boundary28-r2/TERMINOLOGY.md",
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        "terminology_id": "crypto.cryptographic_hash_function"
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      "native_object_sha256": "c55eeff37c7a06dd8377d838cd2c1ceb2d140b46e0e29738e85c7c11f106cff4",
      "object_id": "ttp.concept.cryptographic_hash_function",
      "predicate": "prerequisite_for",
      "relation_id": "ttp.r014.relation.3044",
      "subject_id": "ttp.concept.digital_signature"
    },
    {
      "confidence": "high",
      "evidence_locator": {
        "notes": "Trusted party that signs certificates under a stated verification policy.",
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        "sha256": "3e3fe31baa8565bbc54cd6d789570cac18ed469f68cf683f08dd639ef92d9bd1",
        "terminology_id": "pki.certificate_authority"
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      "native_object_sha256": "fc7f74531af6f656e8800d2bb177167d06a56e9775426a2914156fda6e549f42",
      "object_id": "ttp.concept.certificate_authority",
      "predicate": "prerequisite_for",
      "relation_id": "ttp.r014.relation.3045",
      "subject_id": "ttp.concept.digital_signature"
    },
    {
      "confidence": "high",
      "evidence_locator": {
        "notes": "Trusted party that signs certificates under a stated verification policy.",
        "path": "qa/review-candidates/boundary28-r2/TERMINOLOGY.md",
        "sha256": "3e3fe31baa8565bbc54cd6d789570cac18ed469f68cf683f08dd639ef92d9bd1",
        "terminology_id": "pki.certificate_authority"
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      "object_id": "ttp.concept.certificate_authority",
      "predicate": "prerequisite_for",
      "relation_id": "ttp.r014.relation.3046",
      "subject_id": "ttp.concept.identity_key_binding"
    },
    {
      "confidence": "high",
      "evidence_locator": {
        "notes": "Signed structured statement binding subject identity, public key, and necessary metadata.",
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        "terminology_id": "pki.digital_certificate"
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      "native_object_sha256": "d2819ec20cf02599f1a4c198c03978f70ac730da2c109a942b13f09ef81f4a1f",
      "object_id": "ttp.concept.digital_certificate",
      "predicate": "prerequisite_for",
      "relation_id": "ttp.r014.relation.3047",
      "subject_id": "ttp.concept.certificate_authority"
    },
    {
      "confidence": "high",
      "evidence_locator": {
        "notes": "Signed structured statement binding subject identity, public key, and necessary metadata.",
        "path": "qa/review-candidates/boundary28-r2/TERMINOLOGY.md",
        "sha256": "3e3fe31baa8565bbc54cd6d789570cac18ed469f68cf683f08dd639ef92d9bd1",
        "terminology_id": "pki.digital_certificate"
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      "native_object_sha256": "508028714c07d226615bba81e51758760032835b48179f2362b7a0ed412b2b85",
      "object_id": "ttp.concept.digital_certificate",
      "predicate": "prerequisite_for",
      "relation_id": "ttp.r014.relation.3048",
      "subject_id": "ttp.concept.public_key"
    },
    {
      "confidence": "high",
      "evidence_locator": {
        "notes": "Validated certificate sequence ending at an independently trusted anchor.",
        "path": "qa/review-candidates/boundary28-r2/TERMINOLOGY.md",
        "sha256": "3e3fe31baa8565bbc54cd6d789570cac18ed469f68cf683f08dd639ef92d9bd1",
        "terminology_id": "pki.certification_path"
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      "native_object_sha256": "e8a25b6d8a004f5556511ca142cc2b68211424e4ec01fcbb25f828d72b56d2ff",
      "object_id": "ttp.concept.certification_path",
      "predicate": "prerequisite_for",
      "relation_id": "ttp.r014.relation.3049",
      "subject_id": "ttp.concept.digital_certificate"
    },
    {
      "confidence": "high",
      "evidence_locator": {
        "notes": "Validated certificate sequence ending at an independently trusted anchor.",
        "path": "qa/review-candidates/boundary28-r2/TERMINOLOGY.md",
        "sha256": "3e3fe31baa8565bbc54cd6d789570cac18ed469f68cf683f08dd639ef92d9bd1",
        "terminology_id": "pki.certification_path"
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      "native_object_sha256": "8c6bed74e606491929b7ba79bf056a26298b73128116760b9a443bd086b53513",
      "object_id": "ttp.concept.certification_path",
      "predicate": "prerequisite_for",
      "relation_id": "ttp.r014.relation.3050",
      "subject_id": "ttp.concept.trust_anchor"
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    {
      "confidence": "high",
      "evidence_locator": {
        "notes": "Certificates, CAs, trust anchors, distribution, and validation machinery.",
        "path": "qa/review-candidates/boundary28-r2/TERMINOLOGY.md",
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      "object_id": "ttp.concept.public_key_infrastructure",
      "predicate": "prerequisite_for",
      "relation_id": "ttp.r014.relation.3051",
      "subject_id": "ttp.concept.certification_path"
    },
    {
      "confidence": "high",
      "evidence_locator": {
        "notes": "`a^j\\equiv a^k\\pmod n` exactly when `j\\equiv k\\pmod{\\ord_n(a)}`.",
        "path": "qa/review-candidates/boundary28-r2/TERMINOLOGY.md",
        "sha256": "3e3fe31baa8565bbc54cd6d789570cac18ed469f68cf683f08dd639ef92d9bd1",
        "terminology_id": "nt.exponents_modulo_order"
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      "object_id": "ttp.concept.exponents_modulo_order",
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      "relation_id": "ttp.r014.relation.3052",
      "subject_id": "ttp.concept.multiplicative_order"
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    {
      "confidence": "high",
      "evidence_locator": {
        "notes": "`\\ord_n(a^k)=\\ord_n(a)/\\gcd(\\ord_n(a),k)`.",
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      "object_id": "ttp.concept.order_of_power",
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      "relation_id": "ttp.r014.relation.3053",
      "subject_id": "ttp.concept.multiplicative_order"
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    {
      "confidence": "high",
      "evidence_locator": {
        "notes": "`\\ord_n(a^k)=\\ord_n(a)/\\gcd(\\ord_n(a),k)`.",
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      "subject_id": "ttp.concept.greatest_common_divisor"
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    {
      "confidence": "high",
      "evidence_locator": {
        "notes": "`\\sum_{d\\mid n}\\phi(d)=n`.",
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      "subject_id": "ttp.concept.euler_phi_function"
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    {
      "confidence": "high",
      "evidence_locator": {
        "notes": "`\\sum_{d\\mid n}\\phi(d)=n`.",
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      "subject_id": "ttp.concept.divisibility"
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    {
      "confidence": "high",
      "evidence_locator": {
        "notes": "If primitive roots modulo `n` exist, their count is `\\phi(\\phi(n))`; for prime `p`, it is `\\phi(p-1)`.",
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      "subject_id": "ttp.concept.primitive_root"
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    {
      "confidence": "high",
      "evidence_locator": {
        "notes": "If primitive roots modulo `n` exist, their count is `\\phi(\\phi(n))`; for prime `p`, it is `\\phi(p-1)`.",
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        "terminology_id": "nt.primitive_root_count"
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      "object_id": "ttp.concept.primitive_root_count",
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      "subject_id": "ttp.concept.euler_phi_function"
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    {
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      "evidence_locator": {
        "notes": "Polynomial congruence over `\\ZZ/p\\ZZ`; a nonzero degree-`n` polynomial has at most `n` roots when `p` is prime.",
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      "object_id": "ttp.concept.polynomial_mod_p",
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      "subject_id": "ttp.concept.congruence"
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    {
      "confidence": "high",
      "evidence_locator": {
        "notes": "Polynomial congruence over `\\ZZ/p\\ZZ`; a nonzero degree-`n` polynomial has at most `n` roots when `p` is prime.",
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        "terminology_id": "algebra.polynomial_mod_p"
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      "relation_id": "ttp.r014.relation.3060",
      "subject_id": "ttp.concept.prime"
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    {
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      "evidence_locator": {
        "notes": "Residue class making the polynomial congruent to zero.",
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      "subject_id": "ttp.concept.polynomial_mod_p"
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    {
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      "evidence_locator": {
        "notes": "In `\\ZZ/p\\ZZ` for prime `p`, a product is zero only if one factor is zero.",
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        "terminology_id": "algebra.zero_product_property"
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      "subject_id": "ttp.concept.polynomial_mod_p"
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    {
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      "evidence_locator": {
        "notes": "Ring with no nonzero zero divisors; the source uses the shorter word `domain`.",
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      "subject_id": "ttp.concept.zero_product_property"
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    {
      "confidence": "high",
      "evidence_locator": {
        "notes": "For prime `p` and positive `d\\mid p-1`, exactly `\\phi(d)` residue classes have order `d`.",
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        "terminology_id": "nt.order_class_count"
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      "subject_id": "ttp.concept.primitive_root"
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    {
      "confidence": "high",
      "evidence_locator": {
        "notes": "For prime `p` and positive `d\\mid p-1`, exactly `\\phi(d)` residue classes have order `d`.",
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    {
      "confidence": "high",
      "evidence_locator": {
        "notes": "Least positive `k` satisfying `b\\equiv a^k\\pmod n` when `a` is a primitive root modulo `n`.",
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        "sha256": "3e3fe31baa8565bbc54cd6d789570cac18ed469f68cf683f08dd639ef92d9bd1",
        "terminology_id": "nt.index_relative"
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      "object_id": "ttp.concept.index_relative",
      "predicate": "prerequisite_for",
      "relation_id": "ttp.r014.relation.3066",
      "subject_id": "ttp.concept.primitive_root"
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    {
      "confidence": "high",
      "evidence_locator": {
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