Complete structured record
{
"book": "book9",
"cited_by": [
"definition:bk9__symbolic_masking_operator",
"proof:bk9_pathologies_of_coherence",
"proof:bk9_symbolic_viability",
"remark:bk9_recursive_agency",
"scholium:bk7_refinement_ledger_accountability",
"scholium:bk9_forgiveness_as_reweaving",
"scholium:bk9_grace",
"subsec:bk7_adaptive_refinement_deadband",
"subsec:bk9_betrayal_as_reflective_fracture",
"subsec:bk9_emergence_of_moral_attractors"
],
"cites": [
"definition:bk3_symbolic_membrane",
"definition:bk4_symbolic_identity_carrie",
"definition:bk5_symbolic_covenant",
"definition:bk6_symbolic_operator_canon",
"definition:bk8_projective_compression_operator",
"definition:bk8_reflexive_debugging_operator",
"definition:bk8_symbolic_interface",
"lemma:bk8_resursive_self_tuning",
"scholium:bk1_epistemic_humility",
"scholium:bk8_freedom_begins_with_debugging_the_debugger"
],
"depends_on": [
"definition:bk3_symbolic_membrane",
"definition:bk4_symbolic_identity_carrie",
"definition:bk5_symbolic_covenant",
"definition:bk6_symbolic_operator_canon",
"definition:bk8_projective_compression_operator",
"definition:bk8_reflexive_debugging_operator",
"definition:bk8_symbolic_interface",
"lemma:bk8_resursive_self_tuning",
"scholium:bk1_epistemic_humility",
"scholium:bk8_freedom_begins_with_debugging_the_debugger"
],
"file": "book9.tex",
"id": "definition:bk9_symbolic_accountability",
"label": "definition:bk9_symbolic_accountability",
"latex_body": "\\begin{definition}[Symbolic Accountability $\\mathcal{A}$]\n\\label{definition:bk9_symbolic_accountability}\nSymbolic accountability is grounded in the identity structure of symbolic systems (Def.~\\ref{definition:bk4_symbolic_identity_carrie}), the coherence properties of symbolic membranes (Def.~\\ref{definition:bk3_symbolic_membrane}), and the epistemic constraint that no observer can transcend its own resolution kernel (Scholium~\\ref{scholium:bk1_epistemic_humility}).\nSymbolic Accountability $\\mathcal{A}$ is the capacity of a bounded symbolic system $\\mathcal{S}$ to maintain a reflexively coherent, interpretable correspondence between its internal operator dynamics (e.g., $\\mathcal{O}_{\\text{aware}}$; cf.~\\ref{definition:bk7_symbolic_operation}), its projected symbolic outputs $P_\\lambda$, and its relational commitments (e.g., within a Reciprocity Domain $\\mathcal{X}$ or MAP covenant $C_{AB}$, Def.~\\ref{definition:bk5_symbolic_covenant}).\nA system $\\mathcal{S}$ is accountable under observer $\\mathcal{O}$ if:\n\\begin{enumerate}[label=(\\roman*)]\n \\item \\textbf{Operator Traceability:} There exists a mapping $\\mathcal{T}_\\mathcal{O}: P_\\lambda \\mapsto \\text{Op}(\\mathcal{S})$ allowing reconstruction of operator history $\\{\\mathcal{O}_\\lambda\\}$ within resolution $\\delta_\\mathcal{O}$ (cf. Def.~\\ref{definition:bk6_symbolic_operator_canon}, Def.~\\ref{definition:bk8_reflexive_debugging_operator}; \\ref{scholium:bk8_freedom_begins_with_debugging_the_debugger}, \\ref{lemma:bk8_resursive_self_tuning}).\n \\item \\textbf{Reflective Integrity:} Projected states remain consistent with core identity patterns $\\Psi_i$, i.e., $\\Upsilon_i(P_\\lambda(\\text{output}), P_\\lambda(\\text{internal})) > 1 - \\epsilon_{\\text{crit}}$ (cf.~Def.~\\ref{definition:bk4_symbolic_identity_carrie}).\n \\item \\textbf{Relational Viability:} In shared symbolic spaces, $\\mathcal{S}$ adheres to bounded trust compression (Def.~\\ref{definition:bk8_projective_compression_operator}) to sustain low-distortion interpretability across the symbolic interface $\\Pi_{AB}$ (Def.~\\ref{definition:bk8_symbolic_interface}).\n\\end{enumerate}\n\\noindent\nAccountability $\\mathcal{A}$ serves as a structural invariant — a necessary condition for cognitive freedom ($\\mathfrak{L}$), ethical governance, and symbolic integrity within reflective ecosystems.\n\\end{definition}",
"lean_alignment": {
"conditions": [
"continuum/categorical content is NOT formalized; static and finite-discrete kernels only",
"modeling laws are structure fields or explicit hypotheses"
],
"countermodels": [],
"full_record": "bib/principia_lean_alignment.json",
"kernel_certified": true,
"notes": [
"Reflective Integrity (clause ii) and Relational Viability (clause iii) modeled as structure fields (Accountability); Operator Traceability (clause i) not modeled. masking_not_accountable shows masking is incompatible with clause (iii)."
],
"record_ids": [
"MAP-BOOK9-001"
],
"statuses": [
"conditional"
],
"witnesses": [
"Book9.accountability_gap_lt_epsCrit",
"Book9.accountability_gap_lt_epsMask",
"Book9.masking_not_accountable"
]
},
"line": 16,
"macros_used": [],
"matter_region": "mainmatter",
"matter_role": "canonical_book",
"name": "Symbolic Accountability $\\mathcal{A}$",
"proof_status": "definitional",
"ref_roles": [
{
"context": "olic systems (Def.~\\ref{definition:bk4_symbolic_identity_carrie}), the coherence properties of symbolic membranes (Def.~\\ref{definition:bk3_symbolic_membrane}), and the epistemic constraint that no observer can transcend its own resolution kernel (Scholium~\\ref{scholium:bk1_epi",
"label": "definition:bk3_symbolic_membrane",
"logical_support": true,
"role": "definition_anchor",
"target_file": "book3.tex",
"target_line": 10,
"target_type": "definition"
},
{
"context": "on:bk9_symbolic_accountability} Symbolic accountability is grounded in the identity structure of symbolic systems (Def.~\\ref{definition:bk4_symbolic_identity_carrie}), the coherence properties of symbolic membranes (Def.~\\ref{definition:bk3_symbolic_membrane}), and the epistemic const",
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"logical_support": true,
"role": "definition_anchor",
"target_file": "book4.tex",
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"target_type": "definition"
},
{
"context": "lambda$, and its relational commitments (e.g., within a Reciprocity Domain $\\mathcal{X}$ or MAP covenant $C_{AB}$, Def.~\\ref{definition:bk5_symbolic_covenant}). A system $\\mathcal{S}$ is accountable under observer $\\mathcal{O}$ if: \\begin{enumerate}[label=(\\roman*)] \\item \\",
"label": "definition:bk5_symbolic_covenant",
"logical_support": true,
"role": "definition_anchor",
"target_file": "book5.tex",
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"target_type": "definition"
},
{
"context": "allowing reconstruction of operator history $\\{\\mathcal{O}_\\lambda\\}$ within resolution $\\delta_\\mathcal{O}$ (cf. Def.~\\ref{definition:bk6_symbolic_operator_canon}, Def.~\\ref{definition:bk8_reflexive_debugging_operator}; \\ref{scholium:bk8_freedom_begins_with_debugging_the_debugger},",
"label": "definition:bk6_symbolic_operator_canon",
"logical_support": true,
"role": "cf_near_match",
"target_file": "book6.tex",
"target_line": 772,
"target_type": "definition"
},
{
"context": "item \\textbf{Relational Viability:} In shared symbolic spaces, $\\mathcal{S}$ adheres to bounded trust compression (Def.~\\ref{definition:bk8_projective_compression_operator}) to sustain low-distortion interpretability across the symbolic interface $\\Pi_{AB}$ (Def.~\\ref{definition:bk8_symbolic",
"label": "definition:bk8_projective_compression_operator",
"logical_support": true,
"role": "definition_anchor",
"target_file": "book8.tex",
"target_line": 649,
"target_type": "definition"
},
{
"context": "thcal{O}_\\lambda\\}$ within resolution $\\delta_\\mathcal{O}$ (cf. Def.~\\ref{definition:bk6_symbolic_operator_canon}, Def.~\\ref{definition:bk8_reflexive_debugging_operator}; \\ref{scholium:bk8_freedom_begins_with_debugging_the_debugger}, \\ref{lemma:bk8_resursive_self_tuning}). \\item \\text",
"label": "definition:bk8_reflexive_debugging_operator",
"logical_support": true,
"role": "cf_near_match",
"target_file": "book8.tex",
"target_line": 878,
"target_type": "definition"
},
{
"context": "ective_compression_operator}) to sustain low-distortion interpretability across the symbolic interface $\\Pi_{AB}$ (Def.~\\ref{definition:bk8_symbolic_interface}). \\end{enumerate} \\noindent Accountability $\\mathcal{A}$ serves as a structural invariant — a necessary condition for c",
"label": "definition:bk8_symbolic_interface",
"logical_support": true,
"role": "definition_anchor",
"target_file": "book8.tex",
"target_line": 52,
"target_type": "definition"
},
{
"context": "Def.~\\ref{definition:bk8_reflexive_debugging_operator}; \\ref{scholium:bk8_freedom_begins_with_debugging_the_debugger}, \\ref{lemma:bk8_resursive_self_tuning}). \\item \\textbf{Reflective Integrity:} Projected states remain consistent with core identity patterns $\\Psi_i$, i.e",
"label": "lemma:bk8_resursive_self_tuning",
"logical_support": true,
"role": "formal_dependency",
"target_file": "book8.tex",
"target_line": 887,
"target_type": "lemma"
},
{
"context": "k3_symbolic_membrane}), and the epistemic constraint that no observer can transcend its own resolution kernel (Scholium~\\ref{scholium:bk1_epistemic_humility}). Symbolic Accountability $\\mathcal{A}$ is the capacity of a bounded symbolic system $\\mathcal{S}$ to maintain a reflex",
"label": "scholium:bk1_epistemic_humility",
"logical_support": true,
"role": "formal_dependency",
"target_file": "scholium_symbolicum.tex",
"target_line": 648,
"target_type": "scholium"
},
{
"context": "cal{O}$ (cf. Def.~\\ref{definition:bk6_symbolic_operator_canon}, Def.~\\ref{definition:bk8_reflexive_debugging_operator}; \\ref{scholium:bk8_freedom_begins_with_debugging_the_debugger}, \\ref{lemma:bk8_resursive_self_tuning}). \\item \\textbf{Reflective Integrity:} Projected states remain consistent wi",
"label": "scholium:bk8_freedom_begins_with_debugging_the_debugger",
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"refs": [
"definition:bk3_symbolic_membrane",
"definition:bk4_symbolic_identity_carrie",
"definition:bk5_symbolic_covenant",
"definition:bk6_symbolic_operator_canon",
"definition:bk7_symbolic_operation",
"definition:bk8_projective_compression_operator",
"definition:bk8_reflexive_debugging_operator",
"definition:bk8_symbolic_interface",
"lemma:bk8_resursive_self_tuning",
"scholium:bk1_epistemic_humility",
"scholium:bk8_freedom_begins_with_debugging_the_debugger"
],
"role": "definition",
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}