Responsibility / Liability (monodromy of broken stance)
Responsibility, in the τ-framework, is the moral monodromy of a commitment-stance: a τ-categorical attribution of stance-failure to its source agent when transport of a Reg_C-section around a closed loop in the social base fails to return to identity. Liability is the readout of this monodromy in the institutional sphere — the side of Reg_C where the failure-charge is enforceable.
τ-Definition
Responsibility, in the τ-framework, is the moral monodromy of a commitment-stance: a τ-categorical attribution of stance-failure to its source agent when transport of a Reg_C-section around a closed loop in the social base fails to return to identity. Liability is the readout of this monodromy in the institutional sphere — the side of Reg_C where the failure-charge is enforceable.
Categorical invariant. Ρ = the monodromy class [γ] ∈ π₁(Soc, σ) of a Reg_C-section that fails to glue around a closed transport loop; equivalently, the holonomy of the commitment-connection along γ is non-identity, and the monodromy class assigns the failure to the agent whose typed-duty (VII.L11) is the loop's source.
Primary registry anchor:
VII.D68
τ-Derivation Chain
-
I.K0— Universe Postulate -
VII.D04— Commitment Register Reg_C with codomain Stance -
VII.D72— Commitment Register Admissibility — the typed gates whose failure is what monodromy detects -
VII.L11— Duty Typing Lemma — duties are typed by register and domain; cross-type comparison is ill-formed -
VII.D74— Earned/Unearned framework — responsibility attaches only to the earned summand -
VII.D68— Moral Monodromy — responsibility as non-trivial holonomy of broken Reg_C-section
Phenomenological Correlate
Responsibility is instantiated whenever a stance-failure traced around its causal loop returns blame to a specific agent. Examples: tort liability (negligence creates non-trivial monodromy); criminal mens rea (intent as monodromy charge); corporate accountability (institutional Reg_C with diffuse but non-zero monodromy); collective vs. individual responsibility disputes (which loop in π₁(Soc) carries the charge?).
Examples:
- Tort liability — negligence as non-trivial monodromy of a duty-of-care section
- Criminal mens rea — intent as the monodromy charge that distinguishes murder from accident
- Corporate accountability — institutional Reg_C with diffuse but non-zero monodromy (piercing-the-corporate-veil debates)
- Collective responsibility (war crimes, historical injustice) — disputes about which loop in π₁(Soc) carries the charge
- Strict liability — monodromy attributed without intent-witness (product safety, dangerous activities)
- Diminished capacity defense — typed-duty (VII.L11) under-applies when capacity-witness fails
Register codomain: Stance (Reg_C — responsibility is the monodromy class of a failed Reg_C-section in π₁ of the social base; lives in the earned summand of Reg_C per VII.D74)
Manuscript reference: manuscript-sources/book-07/part07/ch81.tex
Lean Coverage
Status: Planned