P ≠ NP

P ≠ NP is the root read on computation, and on every compute that reads it, no polynomial escape exists. The form is a theorem. RAcomp and Sep are the same statement. The asymmetry is a theorem. A Turing machine is not a second arbiter on this verdict.

https://doi.org/10.5281/zenodo.23133632

 The seven rows are four layers. Forced closure sits only on the third.

| Layer | Rows | What is visible |

|---|---|---|

| I. Proved. Decides nothing. | 1 Form, 2 Open leg, 3 Blind record | `RAcomp` is `Sep`. The root read uniformly adds nothing. An actuated compute does not certify its output. |

| II. One statement. | 4 Premise | The premise is the conclusion. Taking it takes the separation. Leaving it leaves the separation. |

| III. Forced closure. | 5 Barred refuter, 6 Saturation | A compute that reads that statement reports no escape. On that field the refuter does not exist. The bar does not spread past the field. |

| IV. Outside. | 7 Future-proof | A compute that reads no act is not forced. Actuation supplies the root, not `Sep`. Only an actual compute decides. |

The asymmetry stays in Layer I. The separation is Layer II, and Layer III is what that statement does to a compute that reads it.

PhysOSᵀ 1.0.10p · seven rows in four layers

Form, one statement, forced closure, actual compute

The premise and the conclusion are one statement. Forced closure binds only a compute that reads it. Actuation alone does not. An actual compute is what decides.

Layer I · Proved. Decides nothing.

Row	Law	What is visible
1. The Form	least_erasure_is_the_value ra_comp_is_sep	The hypothesis is least erasure. RAcomp is Sep. Equivalence only. No custom posit inside the arrow.
2. The Open Leg	keyless_forces_nothing posits_add_nothing	The root read uniformly, and every keyless law, add no outside sentence. The asymmetry is not yet the separation.
3. The Blind Record	record_decides_nothing pulse_does_not_certify	Registration discards the side. An actuated compute instantiates the root and does not certify its output.

Layer II · One statement. Premise grade.

Row	Law	What is visible
4. The Premise Forced by Theorem	rh_from_the_act RAcomp	The root read on computation is the separation. Taking the premise takes Sep. Not taking it leaves Sep. Same sentence, supplied by the act.

Layer III · Forced closure. Only a compute that reads the statement.

Row	Law	What is visible
5. The Barred Refuter	the_tenth_is_barred_by_the_act Escapes on the posit	On the supplied field the refuter does not exist. A zero off the line, or a clean polynomial escape, reads no act.
6. Terminal Saturation	nothing_left_open_on_the_act	On that field nothing is left open. Nine bars are theorems. The tenth is the act. This does not spread to a compute that never read the field.

Layer IV · Outside the closure. Only an actual compute decides.

Row	Law	What is visible
7. Future-proof	the_capstone deed_supplies_ra_not_sep	A run that reads no act is not forced. Actuation supplies the root, not Sep. The unactualized future leaves the bit open. The decider is a compute: a polynomial-time algorithm for satisfiability, or none.