Results are stated on declared carriers and metrics. A finite theorem retains its assumptions when it enters a larger programme.
Increasing-order orientation, unit Euclidean simplex basis, A = Bᵀ − B.
No physical frequency or time unit follows.
PI · §4.3 ↗Unique simplices on the specified two- and three-tetrahedron complexes.
Irrational active-frequency ratios prohibit a full-operator common period; special single-frequency states can still recur.
PI · §6.3 ↗The labeled 2↔3 move is compared in the 30-dimensional boundary of Δ⁴.
Changing the metric or jump contract defines a different branch.
PI · §6.5 ↗Signed action on the full graded filled-tetrahedron chain carrier.
Finite permutation symmetry is not a derivation of Standard Model gauge groups.
PIII · §2.3 ↗Valid normalized stocks, forest incidence receipts and one root reference per nonzero-support component.
Missing component references leave ambiguity; real-part currents alone do not supply all complex phases.
PII · §§3, 6 ↗Global unique-simplex chains, supplied closed skew dynamics, equal top-star sharing.
Open-system source terms and physical identification are separate.
PI · §5 ↗Supplied Hilbert spaces, Hamiltonians, initial resources, capture and matched renewal contracts.
No permanent autonomous memory, native preparation or fully renewed physical cycle is established.
PIV · §§3–9 ↗The filled-cell full-operator period is π in the declared internal parameter. K₋ and K₊ have incommensurate active frequencies; there is no finite common period for the full operator.
The attached v0.39 ledger and later portal v0.65 file are preserved as distinct objects. Browse the later ledger’s 448 rows with their original bins, status, and next gates. A label in a source ledger is not new independent verification.