Track3OperatorProcessEndpoint
plain-language theorem explainer
Packages the Track 3.C (Agent D) operator-process endpoint as a single Prop: inhabited bulk⊗radiation ledger and tick unitary, entropy readout with zero radiation entropy at start and end, and discrete unitary-tick evolution. Integration-lane authors cite it when wiring Fork D into the master handoff certificate. Pure definitional conjunction of interface facts, not a proved closure.
Claim. The Track 3 operator-process endpoint is the conjunction of: the bulk-radiation ledger on unit finite types is inhabited; a reversible page-tick unitary on those types exists; an operator page entropy readout exists; every operator page process satisfies $\mathrm{state}_{n+1}=U(\mathrm{state}_n)$ under its unitary tick; and every entropy readout has radiation entropy $0$ at tick $0$ and at the final tick count.
background
Module Track 7 records parallel fork handoffs without upgrading the discovery claim. Fork D is the Track 3.C discrete recognition-tick Page-capacity transfer: a Lean-facing bulk-radiation carrier, reversible linear tick, iterated evolution, and entropy readout tied to the ledger-tick Page curve.
Upstream, BulkRadiationLedger β ρ is the closed carrier BulkLedger β ⊗[ℂ] HawkingRadiationLedger ρ requested by Track 3.C. The fundamental RS time quantum is one tick ($\tau_0=1$); spatial dimension is forced to $D=3$ by the T8/T9 chain. Operator page processes carry a unitary tick and a state-at-tick map; entropy readouts expose radiation entropy along that discrete timeline.
The doc-comment stresses this remains a structural interface, not master-clause readiness: existence and boundary conditions only, on the minimal finite types Fin 1.
proof idea
Definitional packaging only: the declaration is a Prop abbreviation, a six-way conjunction of nonempty carriers, the unitary-tick evolution law for every OperatorPageProcess, and the two Page-curve boundary equalities (radiation entropy zero at tick 0 and at totalTicks). No tactics or lemmas are applied here. The companion theorem track3_operator_process_endpoint_holds discharges the Prop by invoking operator_page_process_interface_one_statement.
why it matters
Fork D's named receipt inside Track 7. Downstream, track3_operator_process_endpoint_holds proves the Prop; ForkHandoffIntegrationCert stores it as a field; and fork_A_B_C_D_E_F_handoffs_integrated_one_statement consumes it so Track 7 can cite "Fork D's tick-capacity Page layer" alongside Forks A–C, E, F and the structural master certificate.
In the RS gravity program this is the discrete recognition-tick Page-capacity handoff: bulk ledger tensored with Hawking radiation, evolved by reversible linear ticks, with entropy readout matching the Page-curve endpoints (vanishing radiation entropy at process start and end). It does not close the master theorem; the module doc keeps remaining Track 1 displacement-class leaves as the next dependency. Landmark contact is the eight-tick octave only indirectly via the tick quantum, not via a proved $2^3$ period here.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.