Encyclopedia Gravity Gravity Master Theorem Partial
ARTICLE 3 claims 3 theorems
Gravity Master Theorem Partial
A machine-checked theorem now proves a unified statement about quantum gravity, but only if three still-open physical conditions are supplied.
A conditional step
The gravity master theorem in Recognition Science is a single formal statement that would tie together the framework's account of quantum gravity. The theorem is conditional: it holds only if certain physical hypotheses are true. The module called gravity master theorem partial is the current state of that effort, a machine-checked theorem that reduces the number of unproved conditions from five to three.
In plain language, the theorem says: if three specific physical conditions hold, then the framework's full master statement about quantum gravity follows. The three remaining conditions concern the continuum limit of the Einstein equations with the Bianchi identity, the linearity of a forced amplitude, and the derivation of the Page curve. These are not small details; they are open research targets within the framework.
What the module itself establishes is narrower. It supplies two structural witnesses, one showing that a stochastic gravitational-wave background from pulsar timing arrays is distinct from an inflationary one, and another showing that strong-field tests are distinct from general relativity. These are not empirical confirmations. They are algebraic facts, proved in the machine-checked library, that the two phenomena are not the same thing. The witnesses are theorem-grade for the distinction itself, but hypothesis-grade for matching any specific dataset.
The theorem is honest about its limits. It does not claim discovery is complete. Three hypothesis inputs remain open, the master paper is not written, and the falsifier register is not fully populated. The module is a step, not the destination. It proves a conditional statement with fewer conditions, which is progress, but the conditions themselves are still the hard part.
THEOREM rs_quantum_gravity_master_partial_conditional · IndisputableMonolith/Gravity/MasterTheoremPartial.lean
theorem rs_quantum_gravity_master_partial_conditional
(H_d2 : RegEHContinuumAndBianchi)
(H_amp : AmplitudeLinearForcedUnconditional)
(H_page : PageCurveDerived) :
RSQuantumGravityMaster H_d2 H_amp H_page
ptaDistinctFromInflationWitness strongFieldDistinctFromGRWitness
```
The eight CLOSED clauses from Session 97 are still discharged inline
from existing theorems. The two NEWLY-FILLED clauses are discharged
from `ptaDistinctFromInflationWitness` and
`strongFieldDistinctFromGRWitness`. The three REMAINING hypothesis
inputs are the same as Session 97's `H_d2`, `H_amp`, `H_page`.
## Anti-retreat principle satisfied
The PTA and strong-field structural discriminators are theorem-grade
algebraically (`0 < log φ` and `0 < φ^{-44}`). They are
HYPOTHESIS-grade for empirical match against specific datasets
(NANOGrav, EPTA for PTA; EHT, GRAVITY, Cassini for strong-field) —
those dataset attachments remain separate falsifier-register
obligations in master plan §7.
The conditional theorem proves the master statement with **three**
remaining hypothesis inputs. No discovery claim, no master-statement
softening. Per §6 done-criteria, the discovery is complete only when:
1. The conditional theorem compiles with zero hypothesis inputs (all
three remaining tracks closed).
2. Master paper authored, peer-reviewed, posted to arXiv.
3. §7 falsifier register fully populated.
4. Six §8 done-criteria satisfied.
Zero `sorry`. Zero new RS-specific axioms.
-/
THEOREM rs_quantum_gravity_master_partial_conditional · IndisputableMonolith/Gravity/MasterTheoremPartial.lean
theorem rs_quantum_gravity_master_partial_conditional
(H_d2 : RegEHContinuumAndBianchi)
(H_amp : AmplitudeLinearForcedUnconditional)
(H_page : PageCurveDerived) :
RSQuantumGravityMaster H_d2 H_amp H_page
ptaDistinctFromInflationWitness strongFieldDistinctFromGRWitness
```
The eight CLOSED clauses from Session 97 are still discharged inline
from existing theorems. The two NEWLY-FILLED clauses are discharged
from `ptaDistinctFromInflationWitness` and
`strongFieldDistinctFromGRWitness`. The three REMAINING hypothesis
inputs are the same as Session 97's `H_d2`, `H_amp`, `H_page`.
## Anti-retreat principle satisfied
The PTA and strong-field structural discriminators are theorem-grade
algebraically (`0 < log φ` and `0 < φ^{-44}`). They are
HYPOTHESIS-grade for empirical match against specific datasets
(NANOGrav, EPTA for PTA; EHT, GRAVITY, Cassini for strong-field) —
those dataset attachments remain separate falsifier-register
obligations in master plan §7.
The conditional theorem proves the master statement with **three**
remaining hypothesis inputs. No discovery claim, no master-statement
softening. Per §6 done-criteria, the discovery is complete only when:
1. The conditional theorem compiles with zero hypothesis inputs (all
three remaining tracks closed).
2. Master paper authored, peer-reviewed, posted to arXiv.
3. §7 falsifier register fully populated.
4. Six §8 done-criteria satisfied.
Zero `sorry`. Zero new RS-specific axioms.
-/
THEOREM rs_quantum_gravity_master_partial_conditional · IndisputableMonolith/Gravity/MasterTheoremPartial.lean
theorem rs_quantum_gravity_master_partial_conditional
(H_d2 : RegEHContinuumAndBianchi)
(H_amp : AmplitudeLinearForcedUnconditional)
(H_page : PageCurveDerived) :
RSQuantumGravityMaster H_d2 H_amp H_page
ptaDistinctFromInflationWitness strongFieldDistinctFromGRWitness
```
The eight CLOSED clauses from Session 97 are still discharged inline
from existing theorems. The two NEWLY-FILLED clauses are discharged
from `ptaDistinctFromInflationWitness` and
`strongFieldDistinctFromGRWitness`. The three REMAINING hypothesis
inputs are the same as Session 97's `H_d2`, `H_amp`, `H_page`.
## Anti-retreat principle satisfied
The PTA and strong-field structural discriminators are theorem-grade
algebraically (`0 < log φ` and `0 < φ^{-44}`). They are
HYPOTHESIS-grade for empirical match against specific datasets
(NANOGrav, EPTA for PTA; EHT, GRAVITY, Cassini for strong-field) —
those dataset attachments remain separate falsifier-register
obligations in master plan §7.
The conditional theorem proves the master statement with **three**
remaining hypothesis inputs. No discovery claim, no master-statement
softening. Per §6 done-criteria, the discovery is complete only when:
1. The conditional theorem compiles with zero hypothesis inputs (all
three remaining tracks closed).
2. Master paper authored, peer-reviewed, posted to arXiv.
3. §7 falsifier register fully populated.
4. Six §8 done-criteria satisfied.
Zero `sorry`. Zero new RS-specific axioms.
-/
What this page does not claim
The module does not prove the master theorem unconditionally. The structural witnesses are not empirical confirmations against any specific dataset. The module does not claim discovery is complete.
Verify this page
Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:
$ lake env lean IndisputableMonolith/Gravity/MasterTheoremPartial.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)
A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.
Derived articles
This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red:
- What physical evidence would close the three remaining hypothesis inputs?
- How does the framework derive the Page curve from its own principles?
- What would it mean for the master theorem if one of the three conditions were false?
MACHINE LAYER · GROUNDED CLAIM TABLE · CLICK TO EXPAND
THEOREM rs_quantum_gravity_master_partial_conditional · IndisputableMonolith/Gravity/MasterTheoremPartial.lean
theorem rs_quantum_gravity_master_partial_conditional (H_d2 : RegEHContinuumAndBianchi) (H_amp : AmplitudeLinearForcedUnconditional) (H_page : PageCurveDerived) : RSQuantumGravityMaster H_d2 H_amp H_page ptaDistinctFromInflationWitness strongFieldDistinctFromGRWitness ``` The eight CLOSED clauses from Session 97 are still discharged inline from existing theorems. The two NEWLY-FILLED clauses are discharged from `ptaDistinctFromInflationWitness` and `strongFieldDistinctFromGRWitness`. The three REMAINING hypothesis inputs are the same as Session 97's `H_d2`, `H_amp`, `H_page`. ## Anti-retreat principle satisfied The PTA and strong-field structural discriminators are theorem-grade algebraically (`0 < log φ` and `0 < φ^{-44}`). They are HYPOTHESIS-grade for empirical match against specific datasets (NANOGrav, EPTA for PTA; EHT, GRAVITY, Cassini for strong-field) — those dataset attachments remain separate falsifier-register obligations in master plan §7. The conditional theorem proves the master statement with **three** remaining hypothesis inputs. No discovery claim, no master-statement softening. Per §6 done-criteria, the discovery is complete only when: 1. The conditional theorem compiles with zero hypothesis inputs (all three remaining tracks closed). 2. Master paper authored, peer-reviewed, posted to arXiv. 3. §7 falsifier register fully populated. 4. Six §8 done-criteria satisfied. Zero `sorry`. Zero new RS-specific axioms. -/The module proves a conditional theorem that reduces the number of unproved conditions from five to three. rs_quantum_gravity_master_partial_conditional · IndisputableMonolith/Gravity/MasterTheoremPartial.leanTHEOREM rs_quantum_gravity_master_partial_conditional · IndisputableMonolith/Gravity/MasterTheoremPartial.lean
theorem rs_quantum_gravity_master_partial_conditional (H_d2 : RegEHContinuumAndBianchi) (H_amp : AmplitudeLinearForcedUnconditional) (H_page : PageCurveDerived) : RSQuantumGravityMaster H_d2 H_amp H_page ptaDistinctFromInflationWitness strongFieldDistinctFromGRWitness ``` The eight CLOSED clauses from Session 97 are still discharged inline from existing theorems. The two NEWLY-FILLED clauses are discharged from `ptaDistinctFromInflationWitness` and `strongFieldDistinctFromGRWitness`. The three REMAINING hypothesis inputs are the same as Session 97's `H_d2`, `H_amp`, `H_page`. ## Anti-retreat principle satisfied The PTA and strong-field structural discriminators are theorem-grade algebraically (`0 < log φ` and `0 < φ^{-44}`). They are HYPOTHESIS-grade for empirical match against specific datasets (NANOGrav, EPTA for PTA; EHT, GRAVITY, Cassini for strong-field) — those dataset attachments remain separate falsifier-register obligations in master plan §7. The conditional theorem proves the master statement with **three** remaining hypothesis inputs. No discovery claim, no master-statement softening. Per §6 done-criteria, the discovery is complete only when: 1. The conditional theorem compiles with zero hypothesis inputs (all three remaining tracks closed). 2. Master paper authored, peer-reviewed, posted to arXiv. 3. §7 falsifier register fully populated. 4. Six §8 done-criteria satisfied. Zero `sorry`. Zero new RS-specific axioms. -/The theorem holds only if three specific physical conditions are supplied. rs_quantum_gravity_master_partial_conditional · IndisputableMonolith/Gravity/MasterTheoremPartial.leanTHEOREM rs_quantum_gravity_master_partial_conditional · IndisputableMonolith/Gravity/MasterTheoremPartial.lean
theorem rs_quantum_gravity_master_partial_conditional (H_d2 : RegEHContinuumAndBianchi) (H_amp : AmplitudeLinearForcedUnconditional) (H_page : PageCurveDerived) : RSQuantumGravityMaster H_d2 H_amp H_page ptaDistinctFromInflationWitness strongFieldDistinctFromGRWitness ``` The eight CLOSED clauses from Session 97 are still discharged inline from existing theorems. The two NEWLY-FILLED clauses are discharged from `ptaDistinctFromInflationWitness` and `strongFieldDistinctFromGRWitness`. The three REMAINING hypothesis inputs are the same as Session 97's `H_d2`, `H_amp`, `H_page`. ## Anti-retreat principle satisfied The PTA and strong-field structural discriminators are theorem-grade algebraically (`0 < log φ` and `0 < φ^{-44}`). They are HYPOTHESIS-grade for empirical match against specific datasets (NANOGrav, EPTA for PTA; EHT, GRAVITY, Cassini for strong-field) — those dataset attachments remain separate falsifier-register obligations in master plan §7. The conditional theorem proves the master statement with **three** remaining hypothesis inputs. No discovery claim, no master-statement softening. Per §6 done-criteria, the discovery is complete only when: 1. The conditional theorem compiles with zero hypothesis inputs (all three remaining tracks closed). 2. Master paper authored, peer-reviewed, posted to arXiv. 3. §7 falsifier register fully populated. 4. Six §8 done-criteria satisfied. Zero `sorry`. Zero new RS-specific axioms. -/The module supplies two structural witnesses, one showing that a stochastic gravitational-wave background from pulsar timing arrays is distinct from an inflationary one, and another showing that strong-field tests are distinct from general relativity. rs_quantum_gravity_master_partial_conditional · IndisputableMonolith/Gravity/MasterTheoremPartial.lean