8.2 KiB
Oracle Interrogation IDPC v0.1
Status
Claim state: BEAUTIFUL_PROVISIONAL
This spec records the IDPC operator — Inverse Delta Phi over Cosine — as part of the OTOM oracle-interrogation path.
Origin note
The operator began with the intuition chain:
Delphi
→ Delta Phi
→ Inverse Delta Phi over Cosine
This is not treated as a mystical claim. It is treated as a naming event that revealed the correct architectural placement: oracle interrogation.
Delphi matters here because an oracle is not just a database. An oracle is interrogated through a question, a perturbation, a response, and a reconciliation step.
The deeper point is that historical oracles were usually wrong at the literal-answer layer, but sometimes right enough to reveal a hidden pattern. OTOM should preserve that distinction.
Core thesis
Interrogation is inherently about change.
A question perturbs the oracle state. An answer is useful only if the resulting change remains coherent with the query context.
IDPC measures:
coherence per phase displacement
The stable operator is:
IDPC = cos(theta) / (DeltaPhi + epsilon)
For the integer/fixed-path scaffold:
IDPC_q = alignment * scale / (deltaPhi + epsilon)
Where:
alignment = encoder-supplied clipped/rescaled cosine alignment
DeltaPhi = phase / semantic displacement induced by interrogation
epsilon = stabilizer preventing division by zero
scale = integer precision multiplier
Fallible oracle reading
The oracle is not trusted because it is always right.
The oracle is useful because its answer can be wrong at the surface layer while still perturbing the interrogator toward a deeper invariant.
So the interrogation target is not:
Was the answer literally correct?
It is:
Did the wrong-or-partial answer expose a deeper pattern that survives later receipts?
This creates three layers:
literal answer layer
pattern-detection layer
receipt-validation layer
A fallible oracle may fail the first layer while still contributing signal at the second. It only earns stronger claim state at the third.
In short:
mostly wrong
→ sometimes right enough
→ deeper pattern detected
→ receipts decide whether the pattern was real
This is the Delphi-compatible interpretation. The oracle is a noisy phase-transition instrument, not an authority.
Why this belongs in oracle interrogation
Without change, there is no interrogation.
A static lookup asks:
What value is stored?
Oracle interrogation asks:
What changes when this question is applied?
Did the answer move the oracle state coherently?
Did the answer preserve the declared scope?
Did the answer create a new contradiction, adapter, or phase shift?
Did even a wrong answer reveal a pattern that can be receipted later?
So IDPC is not merely a stability score. It is a question-answer transition score and a deeper-pattern detection gate.
OTOM mapping
Question
→ perturb oracle state
→ answer emitted
→ literal correctness checked
→ phase displacement measured
→ alignment checked
→ deeper-pattern candidate extracted
→ IDPC computed
→ receipt / Warden gate
| Component | Meaning |
|---|---|
| Question | Controlled perturbation applied to oracle state |
| Oracle state before | Pre-query phase/coherence marker |
| Oracle state after | Post-answer phase/coherence marker |
| DeltaPhi | Magnitude of semantic/phase displacement |
| Cosine alignment | Directional agreement between query vector and answer vector |
| Literal correctness | Surface truth value of the answer |
| Pattern candidate | Possible deeper invariant exposed by the answer |
| IDPC | Coherence retained per unit change |
| Receipt | Evidence that the pattern survived later validation |
Change-centered reading
The phrase “changes are inherently about this” maps to the following rule:
Any meaningful oracle answer is a constrained state transition.
So the evaluation target is not just the answer text. It is:
before_state → after_state
IDPC asks whether that transition is coherent.
High IDPC means:
small DeltaPhi
high alignment
stable scope
low contradiction load
Low IDPC means:
large DeltaPhi
low alignment
scope drift
possible contradiction or hallucinated transition
But high IDPC does not mean the answer is literally true. It means the transition is coherent enough to nominate a pattern for receipt validation.
Deeper-pattern detector
IDPC should be paired with a pattern-survival gate:
surface answer may be wrong
pattern candidate may be useful
receipt determines promotion
Suggested result states:
literal_fail_pattern_fail
literal_fail_pattern_candidate
literal_pass_pattern_candidate
receipted_pattern
The critical state is:
literal_fail_pattern_candidate
This is the place where oracles historically mattered: not because they answered cleanly, but because they forced a productive reorientation.
Warden gates
Gate 1 — Not a mystical oracle claim
Blocked claim:
Delphi proves the operator.
Allowed claim:
The Delphi intuition supplied a useful name and architectural placement for an oracle-interrogation transition metric.
Gate 2 — Not answer-only scoring
Blocked claim:
IDPC scores the answer in isolation.
Allowed claim:
IDPC scores the query-answer state transition.
Gate 3 — Cosine is encoder-supplied
Blocked claim:
Lean computes semantic cosine similarity directly.
Allowed claim:
The encoder supplies a bounded alignment score; Lean checks the arithmetic and gates.
Gate 4 — DeltaPhi requires declared scope
Blocked claim:
Any phase change is bad.
Allowed claim:
A phase change is evaluated relative to declared scope; high change with low alignment is suspect, while high change with high alignment may indicate a useful discovery.
Gate 5 — Mostly wrong is not useless
Blocked claim:
If the oracle was wrong, discard the entire interrogation.
Allowed claim:
A wrong answer can still produce a pattern candidate if the induced transition is coherent and later receipts validate the deeper invariant.
Gate 6 — Pattern candidate is not reviewed truth
Blocked claim:
The oracle exposed a pattern, therefore the pattern is true.
Allowed claim:
The oracle exposed a pattern candidate; promotion requires receipts.
Lean artifact
Paired module:
0-Core-Formalism/lean/Semantics/Semantics/OracleInterrogation.lean
The module defines:
OracleState
OracleQuestion
OracleAnswer
OracleInterrogation
IDPCInput
OracleInterrogationResult
PatternSignal
PatternStatus
And the core operators:
idpcInputOfInterrogation
idpcScore
evaluateInterrogationStable
patternStatus
Key theorem shapes:
zero_alignment_idpc_zero
idpc_denominator_monotone_nonincreasing
deltaPhi_monotone_nonincreasing
valid_idpc_score_le_scaled_alignment
literal_failure_can_still_be_pattern_candidate
These encode the basic lawfulness guardrails:
no alignment -> no IDPC signal
more displacement weakly lowers score at fixed alignment
valid inputs remain bounded by scaled alignment
literal failure does not logically erase pattern candidacy
Relation to prior OTOM artifacts
Market filter:
behavioral match under changing market window
Alphabet reduction:
symbol deletion under biological composition change
Receipt core:
promotion change requires proof receipt
Oracle IDPC:
question-answer transition change requires coherence receipt
The shared invariant is:
change must pay for itself with preserved structure
The deeper oracle invariant is:
wrong surface answers can still reveal candidate structure, but only receipts can promote the structure.
Strongest formulation
IDPC is the oracle-interrogation operator that measures how much directional coherence survives a question-induced phase change, including cases where a mostly wrong answer is still right enough to expose a deeper pattern.
That is the clean form to carry forward.