**Verdict.** Accept with conditions. Profile WM-ACT-030 as the only EM-STR-04 root. Business Case and Investment Decision do not need independent root identity: BC is an immutable contained release of WM-ACT-030; Investment Decision is a profile whose durable issued identity is WM-REC-010. Formalization alone mints WM-ACT-005 or WM-ACT-029 identity. Adjacent-draft gaps are profile conditions, not warrants for new roots.

**Strongest evidence.** The four tests are satisfiable without new roots. Two Alternatives can share one Initiative-contained expected-benefit fact while holding distinct WM-KNW-015 risk refs. As-of(D) is the bound BC release plus pinned knowledge and budget revisions plus the WM-REC-010 join, not live fields. A rejected WM-ACT-030 keeps identity, releases, appraisals and the rejecting record, and mints nothing. Ticket, approval and funding have no formalization side-effect onto WM-ACT-005 or WM-ACT-029. An extra BC or Investment Decision root would split mastership with the Initiative release stamp and with WM-REC-010.

**Strongest counterexample.** A portfolio-first capital decision that is not the appraisal of one Initiative. Contained-by-WM-ACT-030 cannot own that case; leave it on WM-ACT-029. Secondary fracture: unpinned live Assumption, Hypothesis, Risk/Opportunity or Budget pointers make as-of reconstruction fail and will tempt a fake Decision root. The fix is WM-REC-010 freeze plus version pins, not a fifth identity.

**Identity / mastership.** Initiative masters contained BC releases and Alternative appraisals. Assumption (WM-KNW-016) and Hypothesis (WM-KNW-009) remain knowledge-mastered; Initiative holds references only. Budget remains WM-ECO-012-mastered so shared pools are not captured. Mandate is an Initiative-scoped assertion, not a root and not shareable across Initiatives. Alternative-as-option is an Initiative-contained stable selector, not a root.

**Initiative transition.** Five facts stay distinct: Mandate (authority to pursue); Approval (accepted Alternative against a named BC release, as WM-ACT-024 plus WM-REC-010); Funding availability (WM-ECO-012 facts); Formalization (mint delivery identity); Realized benefit (post-delivery outcome). Rejection is a terminal appraisal state with history retained. Forecast supersession does not rewrite the bound decision graph.

**Business case.** An immutable contained release of the Initiative. Immutability applies to a release, not to the Initiative’s case slot; later releases may exist. Decision and Mandate bind a release identifier, never “current case.” Cross-Initiative reuse cites an immutable release; it does not create a shared mutable master.

**Alternative / assumption / hypothesis.** Option identity is Initiative-scoped and stable across releases so a later appraisal can say “same option, new scores.” Appraisal values live on the BC release. Do-nothing is mandatory inside the same pin set. Assumption and Hypothesis are external and distinct from each other, from Alternatives and from Mandates. Live-only pointers are forbidden; the release and Decision Record pin revisions or snapshot values. Forecasts are not Hypotheses; validated-learning claims are not Assumptions.

**Decision / mandate / funding.** Investment Decision binds WM-KNW-010 rationale, WM-ACT-024 occurrence, WM-REC-010 issued record and WM-ECO-012 funding facts. No fifth root. WM-REC-010 is the citeable issued act and must freeze the join. Mandate ≠ approval ≠ funding availability ≠ realized benefit. Mandate cannot mint delivery identity.

**Benefits / risks / costs.** No Benefit type is named among adjacent drafts; do not invent one. Expected benefit is an Initiative-contained appraisal fact, or an Opportunity ref if WM-KNW-015 already covers upside. Two Alternatives may share that one fact and must not inherit each other’s risks or costs. Cost estimate in the appraisal ≠ ECO-012 availability ≠ realized spend. Realized benefit stays off the appraisal and off the decision profile.

**Time / version / review.** A BC release is immutable once issued. New forecast = new release or a living projection that is not the bound case. Review creates a new release plus a new decision profile on the same Initiative identity; it does not rewrite prior WM-REC-010 graphs. Reconstruction at T uses pinned external versions, not current knowledge or budget state.

**Scenario.** Two Alternatives share one expected-benefit fact and distinct WM-KNW-015 risks under one pin set including do-nothing. After the Investment Decision, the forecast is revised as a new BC release; reproduce-as-of(D) returns the bound release, pinned Assumption/Hypothesis/Risk/Budget revisions, chosen and do-nothing Alternatives, and the original WM-REC-010/WM-ACT-024 join. The rejected Initiative remains addressable and mints no Project. A ticket, an approval and a funding-available fact each fail to create WM-ACT-005 or WM-ACT-029 identity.

**Invariants.**
1. WM-ACT-030 is the only EM-STR-04 root.
2. BC and Alternative have no independent root; option identity is Initiative-contained and stable across releases; appraisal values live on the release.
3. Investment Decision is a profile only; it binds WM-KNW-010, WM-ACT-024, WM-REC-010 and WM-ECO-012; WM-REC-010 is the issued durable identity.
4. Mandate is Initiative-scoped and non-shareable; Mandate ≠ approval ≠ funding availability ≠ realized benefit ≠ formalization.
5. Formalization is the sole mint of WM-ACT-005 / WM-ACT-029 identity.
6. Ticket, approval and funding availability never mint delivery identity.
7. A BC release is immutable after issue; a decision binds that release, never “current.”
8. Every compared release includes a do-nothing Alternative and one shared pin set (criteria, horizon, price base, metric revisions, method, uncertainty).
9. Two Alternatives may reference one expected-benefit fact and must not inherit each other’s risks or costs.
10. Cost estimate ≠ ECO-012 availability ≠ realized spend; realized benefit is post-delivery and off the appraisal/decision.
11. Post-decision forecast change issues a new release or living projection; the prior as-of graph does not mutate.
12. Rejected Initiative remains addressable with all releases, appraisals and the rejecting record; cascade delete and identity reuse are forbidden.

**Minimum model set.** Profiled root: WM-ACT-030. Mint-on-formalize only: WM-ACT-005, WM-ACT-029. External refs: WM-KNW-009, WM-KNW-016, WM-KNW-015. Decision profile members: WM-KNW-010, WM-ACT-024, WM-REC-010, WM-ECO-012. Contained non-roots (no new identifiers): Business Case release, Alternative option, Alternative appraisal, Mandate assertion, expected-benefit appraisal fact, fair-comparison pins.

**Blockers.** Unpinned Assumption, Hypothesis, Risk/Opportunity or Budget refs break as-of reproduction. Mutable profile members after issue if WM-REC-010 does not freeze the join. Shared expected benefit unspecified in named drafts; declare contained fact or Opportunity-ref rule, do not invent a Benefit identifier. Initiative ownership of funding facts leaks ECO mastership. Any auto-derivation ticket|approval|funding → Project fails the reject-auto-Project test. Portfolio-first capital with no single Initiative is out of this pack and must stay on WM-ACT-029. If WM-ACT-030 cannot contain immutable releases, the only-root claim is incomplete. Hypothesis/Assumption/forecast boundaries must remain distinct.