{
  "type": "exact cochain/derived-object diagram, with no sampled geometry",
  "supports": {
    "A": "complex diagonal Delta",
    "B": "p2^-1 H",
    "H": "Re t >= 0"
  },
  "input": "e=(c,f)",
  "kernel": "k=(a,b), degree N",
  "cup": "(ac,bc,(-1)^N af,(-1)^(N-1) bf)",
  "projection": "pi_A(x,x_A,x_B,z)=(x,x_A)",
  "homotopy": "S=pi_A H_rho; S(x,x_A,x_B,z)=(0,-rho_B z)",
  "identity": "pi_A-j_(A intersect B,A) Phi_rho=dS+Sd",
  "proper_traced_homotopy": "(-1)^N Q_N L_eta S F(k,-)",
  "domain_condition": "rho_B z is a coefficient on U_A; no extension across A",
  "collar_condition": "eta=1 near the whole diagonal; proper over the inner output",
  "derived_square": {
    "top_left": "K=R Gamma_H O",
    "top_right": "K=R Gamma_H O",
    "top_arrow": "a_H^Delta",
    "vertical_arrows": "j_H",
    "bottom_left": "O",
    "bottom_right": "O",
    "bottom_arrow": "T_+",
    "equation": "j_H a_H^Delta=T_+ j_H",
    "adjunction_conclusion": "a_H^Delta=R Gamma_H T_+",
    "category": "bounded-below derived category of complex-vector sheaves"
  },
  "proof_locators": [
    "AM.19d",
    "AM.19e",
    "AM.19f",
    "AM.19g",
    "AM.19h"
  ],
  "arbitrary_holonomic_comparison_asserted": false
}