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2184 lines
69 KiB
Markdown
2184 lines
69 KiB
Markdown
# ENE Schema Specification v1.0.0
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**Status:** Formal specification for machine-checkable conformance
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**Date:** 2026-04-18
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**Purpose:** Type/schema contract separate from observed dataset
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---
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## 1. Type Hierarchy
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```
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BaseArchiveRecord -- Lossless preservation layer
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↓ enhancement
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EnhancedArchiveRecord -- Semantic enrichment layer
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↓ attestation
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AttestedArchiveRecord -- Provenance verification layer
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```
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---
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## 2. BaseArchiveRecord (Lossless Layer)
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**Purpose:** Complete, lossless preservation of original sources. No semantic processing required.
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```typescript
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interface BaseArchiveRecord {
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// Identity (§2.1)
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archive_id: ArchiveID; // content-addressed per §2.1.1
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source_type: SourceType; // §2.2
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source_file: string; // absolute or relative path
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// Content preservation (§2.3)
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raw_content: JSONValue; // original structure, unchanged
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extracted_text: string; // UTF-8, flattened for indexing
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// Provenance (§2.4)
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extracted_at: ISOTimestamp;
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content_hash: SHA256Hex; // §2.5
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extraction_version: string; // "ene_complete_extract_v1"
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// Optional SQL metadata
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row_number?: uint32; // SQL table row index
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table_name?: string; // SQL table name
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}
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```
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### 2.1.1 ArchiveID Derivation Rule
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```
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archive_id := source_prefix + "_" + content_truncated
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where:
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source_prefix := source_type + optional_table_or_filename
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content_truncated := first 16 chars of content_hash
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examples:
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"sqlite_packages_0_755cad3f154c4dc7"
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"chatgpt_aas_pi_computation_enhancement_b15d663e393283e4"
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"json_event_catalog_42_a1b2c3d4e5f67890"
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```
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**Invariant:** `content_hash` is SHA256 over canonical `raw_content` JSON.
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### 2.2 SourceType Enum
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```
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SourceType ::= "sqlite" | "sql_insert" | "json_catalog" | "chatgpt" | "legacy_lean"
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```
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### 2.3 Content Preservation Rules
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- `raw_content`: Original parsed structure, no transformation
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- `extracted_text`: UTF-8 string, max 10,000 chars, for search/semantic processing
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- Bytes in source → hex string with `"_type": "bytes"` marker in raw_content
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### 2.4 Timestamp Format
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```
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ISOTimestamp := "YYYY-MM-DDTHH:MM:SS.ssssss" // ISO 8601 with microseconds
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```
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### 2.5 Hash Format
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```
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SHA256Hex := [0-9a-f]{64} // lowercase hex, no 0x prefix
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```
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---
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## 3. EnhancedArchiveRecord (Semantic Layer)
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**Purpose:** Multi-scale semantic representation for cross-linkage.
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**Extends:** BaseArchiveRecord with required semantic fields.
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```typescript
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interface EnhancedArchiveRecord extends BaseArchiveRecord {
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// Multi-scale semantic representation (§3.1)
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concept_vector: ConceptVector14; // required, 14-dim
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phrase_vector: PhraseVector; // required, map<string, float>
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entities: EntityList; // required, string[]
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topic_clusters: TopicList; // required, string[]
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// Connectivity (§3.2)
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link_count: uint32; // number of semantic links
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}
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```
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### 3.1 ConceptVector14 Specification
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```typescript
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ConceptVector14 := [float; 14] // L2-normalized, each in [0.0, 1.0]
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Axis ordering (fixed):
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0: substrate -- universal computation, foam
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1: compression -- soliton, encoding, entropy
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2: topology -- graph, dag, manifold, node
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3: hardware -- chip, verilog, hdl, fpga
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4: time -- temporal, clock, tick
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5: crypto -- hash, sha256, proof, verify
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6: database -- sql, index, query, storage
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7: semantic -- language, meaning, concept
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8: physics -- thermo, quantum, entropy
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9: security -- isolation, warden, boundary
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10: os_vm -- kernel, vm, bytecode, runtime
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11: research -- theorem, proof, discovery
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12: omnitoken -- token, score, manifest, capsule
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13: identity -- provenance, attestation, signature
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Extraction version: "concept_vector_14_v1"
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Normalization: L2 per-vector: sum(x^2) = 1.0
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```
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### 3.2 EntityList and TopicList
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```typescript
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EntityList := string[] // extracted domain entities, max 50
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TopicList := Topic[] // classified topics, max 10
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Topic ::= "compression" | "topology" | "security" | "hardware" |
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"physics" | "math_theorem" | "codon" | "neural_sae" |
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"lean_semantics" | "geometry"
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```
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---
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## 4. Provenance Layer
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### 4.1 ProvenanceManifest
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```typescript
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interface ProvenanceManifest {
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pipeline_id: string; // e.g., "ene_complete_extract_v1"
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manifest_hash: SHA256Hex; // §4.1.1 canonical hash
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input_digest: SHA256Hex; // previous cumulative state
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op_code: OpCode; // §4.1.2
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signal_metadata: JSONValue; // operation parameters
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output_digest: SHA256Hex; // record content hash
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timestamp: ISOTimestamp;
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sequence_num: uint32; // 0-indexed position in chain
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prev_manifest_hash?: SHA256Hex; // previous manifest's manifest_hash
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}
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```
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#### 4.1.1 Canonical Manifest Hash
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```
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manifest_hash := SHA256(canonical_json)
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where canonical_json is JSON serialization of:
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{
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"pipeline_id": string,
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"input_digest": SHA256Hex,
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"op_code": OpCode,
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"signal_metadata": JSONValue,
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"output_digest": SHA256Hex,
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"timestamp": ISOTimestamp,
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"sequence_num": uint32,
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"prev_manifest_hash": SHA256Hex | null
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}
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with:
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- sort_keys=True
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- separators=(',', ':')
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- ensure_ascii=False
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- no manifest_hash field (self-reference excluded)
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```
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#### 4.1.2 OpCode Enum
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```
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OpCode ::= "EXTRACT_SQLITE" | "EXTRACT_SQL_INSERT" | "EXTRACT_JSON_CATALOG" |
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"EXTRACT_CHATGPT" | "EXTRACT_LEGACY_LEAN"
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```
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### 4.2 SentenceRecord
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```typescript
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interface SentenceRecord {
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data_hash: SHA256Hex; // content hash (hex, not base64)
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prev_hash: SHA256Hex; // previous sentence hash
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metadata_hash: SHA256Hex; // operation metadata hash
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timestamp: UnixTimestamp; // seconds since epoch, float
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cognitive_load: CognitiveLoadVector; // §4.2.1
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features: FeatureVector9; // §4.2.2
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}
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UnixTimestamp := float // time.time() output
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```
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#### 4.2.1 CognitiveLoadVector
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```typescript
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CognitiveLoadVector := {
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L_I: float, // Intrinsic: Shannon entropy / 8, bits per byte
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L_E: float, // Extraneous: structural complexity
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L_G: float, // Germane: semantic density
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L_R: float, // Routing: decision cost
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L_M: float, // Memory: storage cost
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L_total: float, // sum of above
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efficiency: float // L_G / L_total, or 0 if L_total = 0
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}
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All values in [0.0, ∞), typically L_total ∈ [0.5, 2.0]
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```
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#### 4.2.2 FeatureVector9
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```typescript
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FeatureVector9 := [float; 9]
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Index semantics:
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0: normalized_size -- len(text) / 10000
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1: math_density -- 'theorem' count / 10
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2: compression_domain -- 'compression' count / 10
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3: security_domain -- 'security' count / 10
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4: hardware_domain -- 'hardware' count / 10
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5: code_density -- '```' count / 5
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6: vocabulary_diversity -- unique_words / 1000
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7: structure_density -- newline count / 100
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8: capitalization_ratio -- uppercase / total chars
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```
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### 4.3 ArchiveAttestation
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```typescript
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interface ArchiveAttestation {
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attestation_id: string; // "attest_" + archive_id
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archive_id: ArchiveID; // references EnhancedArchiveRecord
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source_type: SourceType; // preserved from base record
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content_hash: SHA256Hex;
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provenance_key: SHA256Hex; // Merkle root of manifest chain
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sentence_hash: SHA256Hex; // links to SentenceRecord
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extracted_at: ISOTimestamp;
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attested_at: ISOTimestamp;
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verification_status: VerificationStatus; // §4.3.1
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}
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```
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#### 4.3.1 VerificationStatus Enum
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```
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VerificationStatus ::= "pending" | "verified" | "failed"
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```
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---
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## 5. EnhancedGraph
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```typescript
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interface EnhancedGraph {
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meta: GraphMeta;
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nodes: EnhancedNode[];
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links: EnhancedLink[];
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entity_index: Map<Entity, ArchiveID[]>;
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}
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interface GraphMeta {
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total_records: uint32;
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total_links: uint32;
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links_per_record: float;
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resolution: string; // "maximum" | "high" | "standard"
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generated_at: ISOTimestamp;
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}
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interface EnhancedNode {
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id: ArchiveID;
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type: NodeType; // "chatgpt_conversation" | "sqlite_table_row" | ...
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title?: string;
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timestamp?: ISOTimestamp;
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// From EnhancedArchiveRecord
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concept_vector: ConceptVector14;
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entities: EntityList;
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topic_clusters?: TopicList;
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theorems?: string[];
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insights_count?: uint32;
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code_snippets_count?: uint32;
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link_count: uint32;
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text_preview?: string; // truncated extracted_text
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}
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interface EnhancedLink {
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source: ArchiveID;
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target: ArchiveID;
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score: float; // [0.0, 1.0]
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type: LinkType;
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}
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NodeType ::= "chatgpt_conversation" | "sqlite_table_row" | "sql_insert_row" |
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"json_catalog_entry" | "legacy_lean"
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LinkType ::= "concept_similar" | "entity_sha256" | "semantic_phrase" |
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"shared_topic" | "shared_substrate" | "ene_entity_bridge" |
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"weak_semantic"
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```
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---
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## 6. Integrity Invariants
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### 6.1 Archive Integrity
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```
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∀ record ∈ archive.records:
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record.content_hash = SHA256(canonical(record.raw_content))
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record.archive_id follows §2.1.1 format
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record.source_type ∈ SourceType enum
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record.extraction_version = "ene_complete_extract_v1"
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```
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### 6.2 Enhanced Graph Integrity
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```
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∀ node ∈ graph.nodes:
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node.id ∈ archive.records.keys()
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len(node.concept_vector) = 14
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∀ v ∈ node.concept_vector: 0.0 ≤ v ≤ 1.0
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node.link_count = count(link where link.source = node.id or link.target = node.id)
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∀ link ∈ graph.links:
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link.source ∈ graph.nodes.id
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link.target ∈ graph.nodes.id
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link.score ∈ [0.0, 1.0]
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link.type ∈ LinkType enum
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```
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### 6.3 Provenance Chain Integrity
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```
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∀ i ∈ [1, len(manifests)):
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manifests[i].prev_manifest_hash = manifests[i-1].manifest_hash
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manifests[0].prev_manifest_hash = null
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∀ manifest ∈ manifests:
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manifest.manifest_hash = compute_manifest_hash(manifest) per §4.1.1
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```
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### 6.4 Attestation Integrity
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```
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∀ attestation ∈ attestations:
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attestation.archive_id ∈ archive.records.keys()
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attestation.source_type = archive.records[attestation.archive_id].source_type
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attestation.verification_status ∈ VerificationStatus enum
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attestation.content_hash ≠ "" // never empty
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```
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### 6.5 Merkle Tree Integrity
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```
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merkle_leaves.length > 0
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∀ leaf ∈ merkle_leaves: leaf ≠ "" // no empty leaves
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merkle_root = compute_merkle_root(merkle_leaves)
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```
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---
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## 7. Conformance Checking (Lean Target)
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Future Lean verification should check:
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```lean
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-- Schema conformance
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def isValidArchiveRecord (r : ArchiveRecord) : Bool :=
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r.archive_id.length > 0 &&
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r.source_type ∈ SourceType.values &&
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r.content_hash.length = 64 &&
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isHex r.content_hash
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-- Enhanced conformance
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def isValidEnhancedRecord (r : EnhancedArchiveRecord) : Bool :=
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isValidArchiveRecord r &&
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r.concept_vector.length = 14 &&
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isL2Normalized r.concept_vector &&
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r.entities.length > 0
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-- Provenance chain validity
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def isValidManifestChain (manifests : List ProvenanceManifest) : Bool :=
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∀ i ∈ [1, manifests.length),
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manifests[i].prev_manifest_hash = manifests[i-1].manifest_hash
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-- Cross-reference integrity
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def isValidAttestation (a : ArchiveAttestation) (archive : Archive) : Bool :=
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a.archive_id ∈ archive.records &&
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a.source_type = archive.records[a.archive_id].source_type &&
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a.verification_status ∈ ["pending", "verified", "failed"]
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```
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---
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## 8. AVMR-Enhanced Vector Layer (Optional Physics-Rooted Indexing)
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**Purpose:** Alternative to HNSW indexing using AVMR (Algebraic Vector Mountain Range) spectral geometry from `Semantics/AVMR.lean`. Provides O(√N) shell-based search with field-coupled similarity.
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### 8.1 AVMR State Structure
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```typescript
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interface AVMRState {
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// Shell decomposition: n = k² + a = (k+1)² - b, where a+b = 2k+1
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shell: {
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n: uint32; // integer position in mountain range
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k: uint32; // floor(sqrt(n)) — shell number
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a: uint32; // forward offset from k²
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b: uint32; // backward offset to (k+1)²
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};
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// Tip coordinates: Tip(n) = (ab, a-b) ∈ ℝ²
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mass: int; // ab product
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polarity: int; // a - b
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// 8-bin spectral signature (from AVMR eventSpectrum)
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spectrum: [Q16_16; 8]; // quantized spectral bins
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// Field interaction state
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interaction: Q16_16; // computed interaction score
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phase: int; // -3 to 3 classification bucket
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// Aggregation metadata
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resonance_count: uint32; // degeneracy count from merges
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priority_bias: int; // 0 or 1 from parity check
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// Provenance
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derived_from: "concept_vector" | "text_embedding" | "direct";
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generation_timestamp: ISOTimestamp;
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}
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```
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### 8.2 Shell-Based Indexing
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```typescript
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interface ShellIndex {
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// Index by shell number k = floor(sqrt(n))
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shells: Map<uint32, {
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k: uint32;
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shell_range: [uint32, uint32]; // [k², (k+1)²)
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record_ids: ArchiveID[]; // records in this shell
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// Axial generators (A_k, G_k, C_k, T_k positions per AVMR)
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A_position: uint32; // k² — purine anchor
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G_position: uint32; // k² + k — purine mid-shell
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C_position: uint32; // k² + k + 1 — pyrimidine mid-shell
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T_position: uint32; // (k+1)² - 1 — pyrimidine anchor
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// Field aggregate for the shell (precomputed)
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aggregate_spectrum: [Q16_16; 8];
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total_mass: int;
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total_polarity: int;
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}>;
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// Search radius: how many adjacent shells to query
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default_search_radius: uint32; // typically 1 (3 shells total)
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}
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// Shell decomposition function (from AVMR.lean:67-71)
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function shellState(n: uint32): { k: uint32, a: uint32, b: uint32 } {
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const k = Math.floor(Math.sqrt(n));
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const a = n - k*k;
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const b = (k+1)*(k+1) - n;
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return { k, a, b };
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}
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```
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**Search Complexity:** O(√N) — search 2r+1 shells containing O(√N) records each, vs O(N) brute force.
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### 8.3 AVMR Similarity Scoring
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```typescript
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interface AVMRScoring {
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// Interaction score: J(n) = ab·F_m + (a-b)·F_p + ⟨χ(n), F_c(n)⟩
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computeInteractionScore(
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query: AVMRState,
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target_shell: { k: uint32, aggregate: LocalField },
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echo_depth: uint32 // 1, 2, or 3 for tailWeight decay
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): Q16_16;
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// Field construction with echo weights [1, ½, ¼]
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buildFieldAt(
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n: uint32,
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maxN: uint32,
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records: AVMRState[]
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): LocalField;
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// Resonance detection between siblings
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siblingResonance(left: AVMRState, right: AVMRState): uint32;
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// Final combined score
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computeAVMRScore(
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query: AVMRState,
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candidate: AVMRState,
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field: LocalField
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): float {
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const massTerm = query.mass * field.massField / Q16_16_SCALE;
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const polTerm = query.polarity * field.polarityField / Q16_16_SCALE;
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const specTerm = spectralOverlap(query.spectrum, field.spectrum) / Q16_16_SCALE;
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const resonance = siblingResonance(query, candidate) * 0.1;
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return massTerm + polTerm + specTerm + resonance;
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}
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}
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// Spectral overlap: Σᵢ(spectrum₁ᵢ · spectrum₂ᵢ)
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function spectralOverlap(a: [Q16_16; 8], b: [Q16_16; 8]): Q16_16 {
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|
return a.map((ai, i) => ai * b[i]).reduce((sum, x) => sum + x, 0);
|
|
}
|
|
```
|
|
|
|
### 8.4 Integration with Concept Vectors
|
|
|
|
```typescript
|
|
// Map 14-dim concept vectors to AVMR shell coordinates
|
|
function conceptVectorToAVMR(
|
|
concept_vector: [float; 14],
|
|
source_text_hash: SHA256Hex
|
|
): AVMRState {
|
|
// 1. Compute magnitude and map to shell position
|
|
const magnitude = Math.sqrt(concept_vector.reduce((a, b) => a + b*b, 0));
|
|
const n = Math.floor(magnitude * 1000); // scale factor tunable
|
|
|
|
// 2. Shell decomposition
|
|
const { k, a, b } = shellState(n);
|
|
|
|
// 3. Collapse 14 concept axes to 8 spectral bins
|
|
const spectrum = collapse14to8Bins(concept_vector);
|
|
|
|
// 4. Derive mass/polarity from dominant axes
|
|
// Axis 0: substrate, Axis 1: compression (example weighting)
|
|
const mass = Math.floor(concept_vector[0] * concept_vector[1] * 100);
|
|
const polarity = Math.floor((concept_vector[0] - concept_vector[1]) * 100);
|
|
|
|
// 5. Compute phase from interaction bucket
|
|
const phase = computePhaseFromPolarity(polarity, k);
|
|
|
|
return {
|
|
shell: { n, k, a, b },
|
|
mass, polarity, spectrum,
|
|
interaction: 0, // computed later via buildFieldAt
|
|
phase,
|
|
resonance_count: 0,
|
|
priority_bias: (polarity > 0) ? 1 : 0,
|
|
derived_from: "concept_vector",
|
|
generation_timestamp: now()
|
|
};
|
|
}
|
|
|
|
// Bin collapse: 14 axes → 8 spectral bins
|
|
function collapse14to8Bins(concept: [float; 14]): [Q16_16; 8] {
|
|
return [
|
|
quantize(concept[0] + concept[1]), // substrate + compression
|
|
quantize(concept[2] + concept[3]), // topology + hardware
|
|
quantize(concept[4] + concept[5]), // time + crypto
|
|
quantize(concept[6] + concept[7]), // database + semantic
|
|
quantize(concept[8] + concept[9]), // physics + security
|
|
quantize(concept[10] + concept[11]), // os_vm + research
|
|
quantize(concept[12] + concept[13]), // omnitoken + identity
|
|
Q16_16.zero // reserved
|
|
];
|
|
}
|
|
|
|
function quantize(f: float): Q16_16 {
|
|
return Math.floor(f * 65536); // Q16.16 fixed point
|
|
}
|
|
```
|
|
|
|
### 8.5 AVMR-Enhanced Merkle Aggregation
|
|
|
|
```typescript
|
|
// Replace standard Merkle with AVMR vector aggregation
|
|
interface AVMRMerkleNode {
|
|
// Standard Merkle
|
|
hash: SHA256Hex;
|
|
|
|
// AVMR enhancement: aggregate vector state
|
|
vec: AVMRState;
|
|
|
|
// Resonance tracking from merge
|
|
sibling_resonance: uint32;
|
|
|
|
// Queryable aggregate properties
|
|
aggregate_mass: int;
|
|
aggregate_polarity: int;
|
|
dominant_spectrum: [Q16_16; 8];
|
|
}
|
|
|
|
// AVMR merge: spectral superposition with resonance detection
|
|
function createAVMRParent(left: AVMRMerkleNode, right: AVMRMerkleNode): AVMRMerkleNode {
|
|
const resonance = siblingResonance(left.vec, right.vec);
|
|
|
|
return {
|
|
hash: SHA256(left.hash + right.hash),
|
|
vec: mergeAVMR(left.vec, right.vec, resonance),
|
|
sibling_resonance: resonance,
|
|
aggregate_mass: left.vec.mass + right.vec.mass,
|
|
aggregate_polarity: left.vec.polarity + right.vec.polarity,
|
|
dominant_spectrum: piecewiseMerge(left.vec.spectrum, right.vec.spectrum)
|
|
};
|
|
}
|
|
|
|
// Merge law from AVMR.lean:228-240
|
|
function mergeAVMR(l: AVMRState, r: AVMRState, resonance: uint32): AVMRState {
|
|
return {
|
|
shell: r.shell, // inherit from right (newer)
|
|
mass: l.mass + r.mass,
|
|
polarity: l.polarity + r.polarity,
|
|
spectrum: piecewiseMerge(l.spectrum, r.spectrum),
|
|
interaction: l.interaction + r.interaction,
|
|
phase: r.phase,
|
|
resonance_count: l.resonance_count + r.resonance_count + resonance,
|
|
priority_bias: l.priority_bias + r.priority_bias,
|
|
derived_from: "merged",
|
|
generation_timestamp: now()
|
|
};
|
|
}
|
|
|
|
// Piecewise spectral merge: bin-wise max or sum
|
|
function piecewiseMerge(a: [Q16_16; 8], b: [Q16_16; 8]): [Q16_16; 8] {
|
|
return a.map((ai, i) => Math.max(ai, b[i])); // or: ai + b[i]
|
|
}
|
|
```
|
|
|
|
**Benefit:** Merkle tree now carries **semantic aggregate state** — query "what's the spectral composition of subtree X?" without leaf traversal.
|
|
|
|
### 8.6 Query Interface: AVMR-Enhanced Search
|
|
|
|
```typescript
|
|
interface AVMRSearchQuery {
|
|
// Input
|
|
query_text?: string;
|
|
query_concept_vector?: [float; 14];
|
|
query_avmr_state?: AVMRState;
|
|
|
|
// Constraints (same as FilteredConceptSearch)
|
|
filter_criteria?: {
|
|
source_type?: SourceType;
|
|
topic_cluster?: string[];
|
|
entity_presence?: string[];
|
|
shell_range?: [uint32, uint32]; // k_min to k_max
|
|
};
|
|
|
|
// AVMR-specific parameters
|
|
search_radius?: uint32; // shells to search (default: 1)
|
|
echo_depth?: uint32; // tailWeight depth (1-3, default: 2)
|
|
resonance_boost?: float; // weight for resonance bonus (default: 0.1)
|
|
|
|
// Output
|
|
top_k: uint32;
|
|
min_score?: float;
|
|
}
|
|
|
|
// Example: "Find records in shells adjacent to query, with field coupling"
|
|
function executeAVMRSearch(query: AVMRSearchQuery): SearchResult {
|
|
// 1. Get or compute AVMR state
|
|
const queryAVMR = query.query_avmr_state ??
|
|
conceptVectorToAVMR(query.query_concept_vector);
|
|
|
|
// 2. Determine shell search window
|
|
const centerK = queryAVMR.shell.k;
|
|
const radius = query.search_radius ?? 1;
|
|
const shellsToSearch = range(centerK - radius, centerK + radius + 1);
|
|
|
|
// 3. Collect candidates from shells
|
|
const candidates = shellsToSearch
|
|
.flatMap(k => shellIndex[k]?.record_ids ?? [])
|
|
.filter(id => matchesFilter(id, query.filter_criteria));
|
|
|
|
// 4. Build field at each candidate's position
|
|
const maxN = Math.max(...candidates.map(id => getAVMRState(id).shell.n));
|
|
|
|
// 5. Score with interaction + resonance
|
|
const scored = candidates.map(id => {
|
|
const candidate = getAVMRState(id);
|
|
const field = buildFieldAt(candidate.shell.n, maxN, candidates.map(getAVMRState));
|
|
const score = computeAVMRScore(queryAVMR, candidate, field);
|
|
return { id, score, shell: candidate.shell.k };
|
|
});
|
|
|
|
// 6. Return top-k
|
|
return scored
|
|
.filter(r => r.score >= (query.min_score ?? 0))
|
|
.sort((a, b) => b.score - a.score)
|
|
.slice(0, query.top_k);
|
|
}
|
|
```
|
|
|
|
### 8.7 AVMR Invariants
|
|
|
|
```
|
|
∀ record with avmr_state:
|
|
record.avmr_state.shell.n ≥ 0
|
|
record.avmr_state.shell.k = floor(sqrt(record.avmr_state.shell.n))
|
|
record.avmr_state.shell.a + record.avmr_state.shell.b = 2*k + 1
|
|
record.avmr_state.mass = record.avmr_state.shell.a * record.avmr_state.shell.b
|
|
record.avmr_state.polarity = record.avmr_state.shell.a - record.avmr_state.shell.b
|
|
len(record.avmr_state.spectrum) = 8
|
|
-3 ≤ record.avmr_state.phase ≤ 3
|
|
```
|
|
|
|
### 8.8 Comparison: Standard vs AVMR-Enhanced
|
|
|
|
| Feature | Standard (Cosine + HNSW) | AVMR-Enhanced |
|
|
|---------|---------------------------|---------------|
|
|
| **Indexing** | HNSW O(N) space | Shell index O(√N) space |
|
|
| **Search** | O(log N) ANN | O(√N) deterministic |
|
|
| **Similarity** | Cosine (angle only) | Interaction score (mass + polarity + spectrum) |
|
|
| **Aggregation** | None | mergeVec with resonance |
|
|
| **Theoretical basis** | Information theory | Spectral physics + braid topology |
|
|
| **Best for** | Large-scale ANN | Physics-rooted semantic clustering |
|
|
|
|
---
|
|
|
|
## 9. Bracketed/Witness Database Layer (Interval Semantics & Provenance Tracking)
|
|
|
|
**Purpose:** Apply bracket calculus (`BracketedDIAT`, `BraidBracket`) and witness structures to database operations for **interval queries**, **uncertainty bounds**, and **grounded provenance**. Derived from `Semantics/BracketedCalculus.lean` and `Semantics/Witness.lean`.
|
|
|
|
### 9.1 Bracketed Record Bounds
|
|
|
|
**Problem:** Standard databases store point values. Real-world semantic data has **uncertainty** — a record's concept activation is not a single float but a range with confidence bounds.
|
|
|
|
**Solution:** Store bracketed intervals for all scored fields:
|
|
|
|
```typescript
|
|
// Replace: concept_vector: [float; 14]
|
|
// With: bracketed concept bounds
|
|
interface BracketedConceptVector {
|
|
// Each axis stored as [lower, value, upper] with gap conservation
|
|
axes: {
|
|
lower: Q16_16; // conservative minimum
|
|
value: Q16_16; // measured/estimated value
|
|
upper: Q16_16; // conservative maximum
|
|
lowerGap: Q16_16; // value - lower
|
|
upperGap: Q16_16; // upper - value
|
|
prod: Q16_16; // lowerGap * upperGap (uncertainty metric)
|
|
scale: uint32; // precision/derivation level
|
|
}[14];
|
|
|
|
// Invariant: lowerGap + upperGap = width for each axis
|
|
gapConservation: bool[]; // checkGapConservation per axis
|
|
}
|
|
|
|
// Query using brackets: "find records where compression axis MAY exceed 0.8"
|
|
interface BracketedQuery {
|
|
axis: uint32; // which concept axis (0-13)
|
|
minLower?: Q16_16; // lower bound must exceed
|
|
minValue?: Q16_16; // value must exceed
|
|
minUpper?: Q16_16; // upper bound must exceed (weakest)
|
|
|
|
// Tolerance for approximate matches
|
|
tolerance: Q16_16; // max acceptable gap width
|
|
}
|
|
```
|
|
|
|
**Invariants from BracketedCalculus.lean:**
|
|
```
|
|
∀ axis in bracketed_vector.axes:
|
|
axis.lowerGap + axis.upperGap = axis.upper - axis.lower // gap conservation
|
|
axis.prod = axis.lowerGap * axis.upperGap // uncertainty product
|
|
|
|
∀ query match:
|
|
record.axes[query.axis].isInterior() || // value strictly inside bounds
|
|
record.checkGapConservation() // bounds are valid
|
|
```
|
|
|
|
### 9.2 Braid Bracket Provenance (Temporal Strands)
|
|
|
|
**Problem:** Linear provenance chains (manifest → manifest) lose the **braid structure** of real data evolution — multiple strands merging, crossing, diverging.
|
|
|
|
**Solution:** Track provenance as braid strands with bracket shells:
|
|
|
|
```typescript
|
|
interface BraidProvenance {
|
|
// Each record is a "strand" with accumulated phase state
|
|
strand_id: string; // unique strand identifier
|
|
slot: uint32; // position in braid (like AVMR slot)
|
|
|
|
// Phase accumulation from ancestor traversals
|
|
phase_accumulator: {
|
|
x: Q16_16; // accumulated x-component (from PhaseVec)
|
|
y: Q16_16; // accumulated y-component
|
|
};
|
|
|
|
// Bracket shell: admissibility bounds for this strand
|
|
bracket: {
|
|
lower: Q16_16; // minimum admissible phase magnitude
|
|
upper: Q16_16; // maximum admissible phase magnitude
|
|
gap: Q16_16; // upper - lower (admissibility window)
|
|
kappa: Q16_16; // norm approximation ||phase||
|
|
phi: Q16_16; // orientation/angle
|
|
admissible: bool; // lower ≤ upper (valid bracket)
|
|
};
|
|
|
|
// How this strand was formed
|
|
formation:
|
|
| { type: "leaf", source: SourceType } // initial extraction
|
|
| { type: "merge", parents: [strand_id, strand_id] } // two strands combined
|
|
| { type: "cross", parent: strand_id, crossing_id: string } // interaction event
|
|
| { type: "evolution", parent: strand_id, op: OpCode }; // transformed
|
|
}
|
|
|
|
// AVMR-style entry for audit trail
|
|
interface BraidAttestationEntry {
|
|
slot: uint32;
|
|
phase_accumulator: PhaseVec;
|
|
bracket: BraidBracket;
|
|
residual?: BraidBracket; // Some if from crossing/merge, None if leaf
|
|
timestamp: uint64;
|
|
archive_id: ArchiveID;
|
|
}
|
|
```
|
|
|
|
**Crossing Residual (from BraidBracket.lean:108-119):**
|
|
|
|
When two strands merge, compute their **interaction energy**:
|
|
|
|
```typescript
|
|
// R_ij = B_ij - (B_i + B_j)
|
|
// Measures semantic "tension" between merged records
|
|
function computeCrossingResidual(
|
|
merged: BraidBracket,
|
|
left: BraidBracket,
|
|
right: BraidBracket
|
|
): BraidBracket {
|
|
return {
|
|
lower: merged.lower - (left.lower + right.lower),
|
|
upper: merged.upper - (left.upper + right.upper),
|
|
gap: merged.gap - (left.gap + right.gap),
|
|
kappa: merged.kappa - (left.kappa + right.kappa),
|
|
phi: merged.phi - (left.phi + right.phi),
|
|
admissible: merged.admissible && left.admissible && right.admissible
|
|
};
|
|
}
|
|
|
|
// Use residual for anomaly detection:
|
|
// Large residual = unexpected interaction, possible data corruption
|
|
```
|
|
|
|
### 9.3 Witness Receipts for Grounded Retrieval
|
|
|
|
**Problem:** Retrieved records lack **epistemic status** — is this observation? inference? evolution? What was the cognitive load?
|
|
|
|
**Solution:** Attach witness receipts to query results:
|
|
|
|
```typescript
|
|
interface WitnessedRecord {
|
|
// Original record data
|
|
record: EnhancedArchiveRecord;
|
|
|
|
// Witness certification (from Witness.lean)
|
|
witness: {
|
|
witness_id: Nat;
|
|
provenance: WitnessProvenance; // observation | inference | evolution | ...
|
|
|
|
// Path from query to this record
|
|
path: {
|
|
steps: AtomicPath[]; // query → result traversal
|
|
isLawful: bool; // path obeys semantic constraints
|
|
};
|
|
|
|
// Cognitive cost of retrieval (from CognitiveLoad)
|
|
load: {
|
|
intrinsic: float; // L_I: entropy of path
|
|
extraneous: float; // L_E: overhead
|
|
germane: float; // L_G: useful computation
|
|
total: float;
|
|
efficiency: float; // L_G / L_total
|
|
};
|
|
|
|
timestamp: float;
|
|
};
|
|
|
|
// What was preserved vs lost in retrieval
|
|
atoms: {
|
|
preserved: Atom[]; // semantic atoms retained
|
|
lost: Atom[]; // atoms filtered/dropped
|
|
};
|
|
|
|
// Capability score: how well this result satisfies query
|
|
result_capability: float;
|
|
}
|
|
|
|
// Query now returns witnessed results
|
|
interface WitnessedQueryResult {
|
|
results: WitnessedRecord[];
|
|
|
|
// Aggregate witness statistics
|
|
summary: {
|
|
total_load: float;
|
|
average_efficiency: float;
|
|
provenance_breakdown: Map<WitnessProvenance, uint32>;
|
|
groundedness_checks: Groundedness[]; // §9.4
|
|
};
|
|
}
|
|
```
|
|
|
|
**Provenance Types (from Witness.lean:11-18):**
|
|
```
|
|
observation → Direct DB record retrieval
|
|
inference → Derived via semantic similarity/vector match
|
|
projection → Result of collapse/simplification (top-k truncation)
|
|
evolution → Retrieved from evolved/updated record
|
|
translation → Cross-source mapping (ChatGPT → SQLite schema alignment)
|
|
composed → Built from atomic path composition (multi-hop graph search)
|
|
```
|
|
|
|
### 9.4 Groundedness Checks for Query Validity
|
|
|
|
**Problem:** How to verify that a query result is **semantically valid** and not hallucinated/approximated into nonsense?
|
|
|
|
**Solution:** Apply `Groundedness` structure from Witness.lean:58-78:
|
|
|
|
```typescript
|
|
interface GroundednessCheck {
|
|
// 8 conditions for habitable semantic results
|
|
atomic_basis: bool; // Reducible to semantic atoms in our 14-axis space
|
|
lawful_reachability: bool; // Path from query obeys lawful atomic transitions
|
|
bounded_load: bool; // Cognitive load < threshold (not computationally absurd)
|
|
faithful_projection: bool; // Collapse (top-k truncation) preserves meaning
|
|
evolution_auditable: bool; // All changes from source are traceable
|
|
universal_dynamics: bool; // Result preserves universality class (not type confusion)
|
|
scaling_preserved: bool; // Scaling laws intact (small query → small result set)
|
|
class_membership_visible: bool; // Can inspect which dynamical class result belongs to
|
|
}
|
|
|
|
// Combined check
|
|
def Groundedness.habitable(g: GroundednessCheck): bool {
|
|
return g.atomic_basis &&
|
|
g.lawful_reachability &&
|
|
g.bounded_load &&
|
|
g.faithful_projection &&
|
|
g.evolution_auditable &&
|
|
g.universal_dynamics &&
|
|
g.scaling_preserved &&
|
|
g.class_membership_visible;
|
|
}
|
|
|
|
// Use in query pipeline:
|
|
function executeGroundedQuery(query: SearchQuery): WitnessedQueryResult {
|
|
const candidates = executeSearch(query);
|
|
|
|
// Filter for groundedness
|
|
const grounded = candidates.filter(r =>
|
|
Groundedness.habitable(computeGroundedness(r, query))
|
|
);
|
|
|
|
// If too few grounded results, warn about possible semantic drift
|
|
if (grounded.length < candidates.length * 0.5) {
|
|
return {
|
|
results: grounded,
|
|
warning: "High semantic drift detected — many candidates failed groundedness checks",
|
|
ungrounded_samples: candidates.filter(r => !Groundedness.habitable(...)).slice(0, 3)
|
|
};
|
|
}
|
|
|
|
return { results: grounded };
|
|
}
|
|
```
|
|
|
|
### 9.5 Interval Temporal Queries (Bracketed Time)
|
|
|
|
**Problem:** Temporal queries use point timestamps. Real data has **uncertainty** — "extracted sometime between 3pm and 5pm".
|
|
|
|
**Solution:** Bracketed temporal bounds:
|
|
|
|
```typescript
|
|
interface BracketedTimestamp {
|
|
earliest: ISOTimestamp; // conservative earliest
|
|
latest: ISOTimestamp; // conservative latest
|
|
nominal: ISOTimestamp; // best estimate (like value in BracketedDIAT)
|
|
|
|
// Uncertainty gaps
|
|
past_gap: Duration; // nominal - earliest
|
|
future_gap: Duration; // latest - nominal
|
|
|
|
// Source of uncertainty
|
|
precision: "exact" | "milliseconds" | "seconds" | "minutes" | "hours" | "derived";
|
|
}
|
|
|
|
// Temporal query with brackets
|
|
interface TemporalBracketQuery {
|
|
// "Find records that MAY overlap with [start, end]"
|
|
search_window: {
|
|
start: BracketedTimestamp;
|
|
end: BracketedTimestamp;
|
|
};
|
|
|
|
// Match criteria
|
|
match_type:
|
|
| "definite_overlap" // record.latest ≥ query.earliest AND record.earliest ≤ query.latest
|
|
| "possible_overlap" // record.latest ≥ query.earliest OR record.earliest ≤ query.latest
|
|
| "definitely_before" // record.latest < query.earliest (gap conservation check)
|
|
| "definitely_after"; // record.earliest > query.latest
|
|
}
|
|
```
|
|
|
|
### 9.6 Database Integration Summary
|
|
|
|
| Bracket/Witness Concept | Database Enhancement | Source File |
|
|
|------------------------|---------------------|-------------|
|
|
| `BracketedDIAT` | Interval-valued concept vectors | `BracketedCalculus.lean` |
|
|
| `BraidBracket` | Strand-based provenance with admissibility | `BraidBracket.lean` |
|
|
| `crossingResidual` | Merge anomaly detection | `BraidBracket.lean:108` |
|
|
| `AVMREntry` | Append-only audit with phase/bracket | `BraidBracket.lean:124` |
|
|
| `WitnessReceipt` | Epistemic status tracking | `Witness.lean:21` |
|
|
| `Groundedness` | Query result validity verification | `Witness.lean:58` |
|
|
| `PhaseVec` | 2D phase accumulation for traversal cost | `BraidBracket.lean:17` |
|
|
|
|
### 9.7 Example: Grounded Semantic Search
|
|
|
|
```typescript
|
|
// Execute search with full bracket/witness machinery
|
|
function groundedSemanticSearch(query: string): WitnessedQueryResult {
|
|
// 1. Extract bracketed concept vector (with uncertainty)
|
|
const queryConcept = extractBracketedConceptVector(query);
|
|
// → { axes: [{lower: 0.6, value: 0.85, upper: 0.9, ...}, ...] }
|
|
|
|
// 2. AVMR shell-based candidate retrieval
|
|
const candidates = executeAVMRSearch({
|
|
query_concept_vector: queryConcept.axes.map(a => a.value),
|
|
top_k: 50
|
|
});
|
|
|
|
// 3. Bracketed similarity: allow matches within uncertainty bounds
|
|
const bracketedMatches = candidates.filter(c =>
|
|
cosineSimilarity(queryConcept, c.bracketed_concept) > 0.7
|
|
);
|
|
|
|
// 4. Witness each result
|
|
const witnessed = bracketedMatches.map(c => ({
|
|
record: c,
|
|
witness: {
|
|
witness_id: generateWitnessId(),
|
|
provenance: "inference", // derived via vector similarity
|
|
path: computePath(query, c),
|
|
load: computeCognitiveLoad(query, c),
|
|
timestamp: now()
|
|
},
|
|
atoms: { preserved: c.entities, lost: [] },
|
|
result_capability: computeCapability(query, c)
|
|
}));
|
|
|
|
// 5. Groundedness filter
|
|
const grounded = witnessed.filter(w =>
|
|
Groundedness.habitable(computeGroundedness(w, query))
|
|
);
|
|
|
|
// 6. Braid attestation for audit trail
|
|
const attestation = createBraidAttestation({
|
|
slot: getNextSlot(),
|
|
phase_accumulator: accumulatePhase(witnessed.map(w => w.witness.path)),
|
|
bracket: computeBracketFromResults(grounded),
|
|
residual: computeCrossingResidualFromQuery(query, grounded)
|
|
});
|
|
|
|
return {
|
|
results: grounded,
|
|
summary: {
|
|
total_load: sum(grounded.map(w => w.witness.load.total)),
|
|
groundedness_rate: grounded.length / candidates.length,
|
|
attestation
|
|
}
|
|
};
|
|
}
|
|
```
|
|
|
|
---
|
|
|
|
## 10. PBACS/Compression Database Layer (Constraint-Based Storage)
|
|
|
|
**Purpose:** Apply PBACS (Physics-Based Addressable Compression System) and Unified Compression to database storage for **content-addressed encoding**, **thermodynamic cost tracking**, and **constraint-based retrieval**. Derived from `Semantics/Pbacs.lean` and `ExtensionScaffold/Compression/UnifiedCompression.lean`.
|
|
|
|
### 10.1 Content-Addressed Compression Encoding
|
|
|
|
**Problem:** Standard databases store raw bytes. PBACS provides **constraint-based encoding** where content determines its own storage address through thermodynamic-valid encoding steps.
|
|
|
|
**Solution:** Store records with their PBACS encoding trace:
|
|
|
|
```typescript
|
|
interface PBACSEncodedRecord {
|
|
// Original content (for retrieval)
|
|
raw_content: JSONValue;
|
|
|
|
// PBACS encoding trace (from Pbacs.lean)
|
|
encoding: {
|
|
// 8-step canonical loop execution
|
|
steps: PBACSStep[];
|
|
|
|
// Final encoded representation
|
|
encoded_bytes: UInt8[]; // Compressed form
|
|
|
|
// Content-addressed hash (address = encoding result)
|
|
content_address: SHA256Hex; // SHA256(encoded_bytes)
|
|
|
|
// Encoding cost (thermodynamic work required)
|
|
total_cost: Q16_16; // Σ binding costs per step
|
|
|
|
// Constraint satisfaction log
|
|
constraints_satisfied: {
|
|
arithmetic: bool; // Shell coordinates valid
|
|
geometric: bool; // 3-point contact detected
|
|
temporal: bool; // φ-accumulation valid
|
|
field: bool; // Standing-wave field built
|
|
contact: bool; // κ_A ∧ κ_B ∧ κ_C closure
|
|
};
|
|
};
|
|
}
|
|
|
|
// Single PBACS step (from Pbacs.lean:22-38)
|
|
interface PBACSStep {
|
|
t: uint32; // Step index
|
|
|
|
// Shell coordinates (from AVMR)
|
|
shell: { n: uint32; k: uint32; a: uint32; b: uint32 };
|
|
|
|
// Pulse generation (from UnifiedCompression.lean:44-54)
|
|
pulse: {
|
|
mode: "a" | "g" | "c" | "t" | "square"; // TriangleMode
|
|
mass: UInt32; // ab product
|
|
polarity: Int32; // a - b
|
|
width: uint32; // 2k+1
|
|
};
|
|
|
|
// Field interaction
|
|
field_interaction: {
|
|
support_values: [UInt32, UInt32, UInt32]; // [κ_A, κ_B, κ_C]
|
|
echo_weights: [Q16_16, Q16_16, Q16_16]; // [1, ½, ¼]
|
|
interaction_score: Int; // J(n) = ab·F_m + (a-b)·F_p + ⟨χ, F_c⟩
|
|
};
|
|
|
|
// Emission decision
|
|
emission: {
|
|
gate_closed: bool; // κ_A ∧ κ_C ∧ J>0
|
|
symbol_emitted: UInt8; // 4-bit nibble or 8-bit byte
|
|
binding_cost: Q16_16; // Cost to bind this symbol
|
|
};
|
|
|
|
// Control state (from Pbacs.lean:88-100)
|
|
control: {
|
|
state: "halt" | "hold" | "stable" | "transient";
|
|
score: Q16_16; // Weighted projection score
|
|
alpha_t: Q16_16; // Learning rate at step t
|
|
};
|
|
}
|
|
```
|
|
|
|
**Encoding Pipeline (UnifiedCompression.lean:16-22):**
|
|
|
|
```
|
|
X → G_θ{πᵢ} →contact→ {χᵢ} →g→ {eᵢ} →Λ→ {zᵢ} →bind→ L(X)
|
|
|
|
Where:
|
|
X: Input record content
|
|
G_θ: Generate structured pulses from shell coordinates
|
|
contact: Detect 3-point contact (κ_A, κ_B, κ_C)
|
|
g: Emission gate (κ_A ∧ κ_C ∧ J>0)
|
|
eᵢ: Emitted symbols
|
|
Λ: Constraint validation
|
|
zᵢ: Constrained codes
|
|
bind: Lawful binding (cost accumulation)
|
|
L(X): Final compressed representation
|
|
```
|
|
|
|
### 10.2 Thermodynamic Cost Tracking
|
|
|
|
**Problem:** Database operations consume resources. PBACS tracks **thermodynamic work** (Landauer-bound relevant) per operation.
|
|
|
|
**Solution:** Attach cost metrics to all storage and retrieval:
|
|
|
|
```typescript
|
|
interface ThermodynamicCost {
|
|
// Per-operation costs (Q16.16 fixed-point)
|
|
encoding_cost: Q16_16; // Cost to compress/store
|
|
retrieval_cost: Q16_16; // Cost to decompress/read
|
|
transmission_cost: Q16_16; // Cost to move over network
|
|
|
|
// Landauer-bound theoretical minimum
|
|
landauer_limit: Q16_16; // kT ln(2) per bit erased
|
|
|
|
// Efficiency ratio
|
|
efficiency: Q16_16; // landauer_limit / actual_cost
|
|
|
|
// Cost breakdown by component
|
|
breakdown: {
|
|
pulse_generation: Q16_16;
|
|
field_construction: Q16_16;
|
|
contact_detection: Q16_16;
|
|
emission_gating: Q16_16;
|
|
binding_accumulation: Q16_16;
|
|
};
|
|
}
|
|
|
|
// Attach to archive records
|
|
interface CostAwareArchiveRecord extends EnhancedArchiveRecord {
|
|
storage_cost: ThermodynamicCost;
|
|
|
|
// Cost-weighted retrieval priority
|
|
// Cheaper-to-retrieve records preferred when equivalent
|
|
retrieval_score: Q16_16; // semantic_score / storage_cost.encoding_cost
|
|
}
|
|
```
|
|
|
|
**Cost Invariant (from BracketedCalculus gap conservation):**
|
|
|
|
```
|
|
∀ encoding step:
|
|
step.emission.binding_cost > 0 // Positive cost to emit
|
|
step.field_interaction.interaction_score ≥ threshold // Gate threshold
|
|
|
|
∀ complete encoding:
|
|
encoding.total_cost = Σ steps[i].emission.binding_cost
|
|
encoding.total_cost ≥ encoding.landauer_limit // 2nd law respect
|
|
```
|
|
|
|
### 10.3 Constraint-Based Retrieval (PBACS Control)
|
|
|
|
**Problem:** Standard queries return all matches. PBACS provides **hysteretic control** — stateful filtering with entry/exit thresholds.
|
|
|
|
**Solution:** Apply PBACS control state machine to query processing:
|
|
|
|
```typescript
|
|
// PBACS Control State (from Pbacs.lean)
|
|
enum ControlState {
|
|
HALT, // Below entry threshold, not processing
|
|
HOLD, // Within hysteresis band, maintaining state
|
|
STABLE, // Confident match, proceed
|
|
TRANSIENT // Uncertain, require more samples
|
|
}
|
|
|
|
// Query with PBACS control
|
|
interface PBACSControlledQuery {
|
|
// Standard query parameters
|
|
filter: SearchFilter;
|
|
|
|
// PBACS control parameters (from Pbacs.lean:11-20)
|
|
control_config: {
|
|
entry_thresholds: {
|
|
halt_tau: Q16_16; // Start processing if score >
|
|
dmt_product: Q16_16; // Dual-mode threshold
|
|
hold_delta_dot: Q16_16; // Rate-of-change entry
|
|
hold_delta: Q16_16; // Absolute delta entry
|
|
};
|
|
exit_thresholds: {
|
|
halt_tau: Q16_16; // Stop processing if score <
|
|
dmt_product: Q16_16;
|
|
hold_delta_dot: Q16_16;
|
|
hold_delta: Q16_16;
|
|
};
|
|
// Hysteresis prevents oscillation
|
|
hysteresis_gap: Q16_16; // entry - exit > 0
|
|
|
|
// Adaptive learning rate
|
|
alpha0: Q16_16; // Base learning rate
|
|
beta: Q16_16; // Decay factor
|
|
};
|
|
|
|
// Current control state
|
|
control_state: ControlState;
|
|
|
|
// Accumulated score (hysteresis memory)
|
|
accumulated_score: Q16_16;
|
|
}
|
|
|
|
// PBACS query execution
|
|
function executePBACSQuery(query: PBACSControlledQuery): QueryResult {
|
|
const results = [];
|
|
let state = query.control_state;
|
|
let acc = query.accumulated_score;
|
|
|
|
for (const candidate of streamCandidates(query.filter)) {
|
|
// Compute projection scores (from Pbacs.lean:77-78)
|
|
const projections = computeProjections(candidate, query.filter);
|
|
const score = computeWeightedScore(projections, query.control_config);
|
|
|
|
// Update control state with hysteresis
|
|
const newState = nextControlState(
|
|
query.control_config,
|
|
state,
|
|
score,
|
|
acc
|
|
);
|
|
|
|
// Collect results based on state
|
|
if (newState === ControlState.STABLE) {
|
|
results.push({ candidate, score, confidence: "high" });
|
|
} else if (newState === ControlState.HOLD && state !== ControlState.HALT) {
|
|
results.push({ candidate, score, confidence: "medium" });
|
|
}
|
|
|
|
// Early termination if HALT and sufficient samples
|
|
if (newState === ControlState.HALT && results.length > 10) {
|
|
break;
|
|
}
|
|
|
|
state = newState;
|
|
acc = Q16_16.add(acc, Q16_16.mul(score, query.control_config.alpha0));
|
|
}
|
|
|
|
return {
|
|
results,
|
|
final_state: state,
|
|
accumulated_score: acc,
|
|
termination_reason: state === ControlState.HALT ? "threshold" : "exhausted"
|
|
};
|
|
}
|
|
```
|
|
|
|
**Hysteretic Entry/Exit (from Pbacs.lean:88-100):**
|
|
|
|
```
|
|
Entry condition (any must hold):
|
|
u_tau > entry.halt_tau
|
|
u_tau * u_chi > entry.dmt_product
|
|
|delta_dot| > entry.hold_delta_dot
|
|
|delta| > entry.hold_delta
|
|
|
|
Exit condition (any must hold):
|
|
u_tau < exit.halt_tau
|
|
u_tau * u_chi < exit.dmt_product
|
|
...
|
|
|
|
Invariant: entry.threshold > exit.threshold (hysteresis gap)
|
|
```
|
|
|
|
### 10.4 Addressable Compression Storage
|
|
|
|
**Problem:** Content-addressed storage (like a Merkle tree) doesn't track encoding costs or constraint satisfaction.
|
|
|
|
**Solution:** PBACS-enhanced content addressing with verification:
|
|
|
|
```typescript
|
|
// Addressable storage with PBACS verification
|
|
interface PBACSAddressableStorage {
|
|
// Content-derived address
|
|
address: SHA256Hex; // Hash of PBACS-encoded content
|
|
|
|
// Storage entry
|
|
entry: {
|
|
raw_content: JSONValue;
|
|
encoding_trace: PBACSStep[];
|
|
encoded_bytes: UInt8[];
|
|
|
|
// Verification that encoding is valid
|
|
verification: {
|
|
constraint_hash: SHA256Hex; // Hash of satisfied constraints
|
|
cost_verification: bool; // total_cost matches sum
|
|
landauer_compliance: bool; // total_cost ≥ landauer_limit
|
|
};
|
|
};
|
|
|
|
// Lookup index: content_hash → address
|
|
content_index: Map<SHA256Hex, SHA256Hex>;
|
|
|
|
// Deduplication: identical content → same address
|
|
deduplication_stats: {
|
|
unique_entries: uint32;
|
|
total_references: uint32;
|
|
compression_ratio: float; // raw_size / encoded_size
|
|
};
|
|
}
|
|
|
|
// Storage operation with cost tracking
|
|
function storeWithPBACS(content: JSONValue): StorageResult {
|
|
// 1. Encode with PBACS
|
|
const encoding = pbacsEncode(content);
|
|
|
|
// 2. Compute content address
|
|
const address = SHA256(encoding.encoded_bytes);
|
|
|
|
// 3. Verify constraints
|
|
const verification = {
|
|
constraint_hash: SHA256(encoding.constraints_satisfied),
|
|
cost_verification: verifyCostSum(encoding.steps, encoding.total_cost),
|
|
landauer_compliance: encoding.total_cost >= computeLandauerLimit(encoding.encoded_bytes.length)
|
|
};
|
|
|
|
// 4. Store if valid
|
|
if (verification.cost_verification && verification.landauer_compliance) {
|
|
storage[address] = { raw_content: content, encoding_trace: encoding.steps, ... };
|
|
return { success: true, address, cost: encoding.total_cost };
|
|
} else {
|
|
return { success: false, error: "constraint_violation", verification };
|
|
}
|
|
}
|
|
```
|
|
|
|
### 10.5 Temporal Buffer for Streaming Queries
|
|
|
|
**Problem:** Database queries are stateless. PBACS provides **temporal accumulation** for streaming/continuous queries.
|
|
|
|
**Solution:** Add temporal buffer state to long-running queries:
|
|
|
|
```typescript
|
|
// Temporal buffer (from Orchestrate.lean:23-91)
|
|
interface TemporalBuffer {
|
|
history: CanonicalState[]; // Recent query states
|
|
history_size: uint32; // Buffer capacity
|
|
|
|
// Temporal derivatives (from delta, delta_dot, gamma)
|
|
prev_delta: Option<Q16_16>; // Previous φ-difference
|
|
prev_phi: Option<Q16_16>; // Previous accumulated phase
|
|
prev_2phi: Option<Q16_16>; // φ at t-2
|
|
|
|
// Angular momentum (change in change)
|
|
angular_momentum: Q16_16; // |φ_t-1 · (δ_t - δ_t-1)|
|
|
|
|
// Step counter
|
|
step_count: uint32;
|
|
}
|
|
|
|
// Streaming query with temporal state
|
|
interface StreamingPBACSQuery {
|
|
// Static filter
|
|
filter: SearchFilter;
|
|
|
|
// Temporal state (accumulated across chunks)
|
|
temporal: TemporalBuffer;
|
|
|
|
// Trigger conditions for re-evaluation
|
|
triggers: {
|
|
on_angular_momentum: Q16_16; // Re-query if momentum > threshold
|
|
on_gamma_spike: Q16_16; // Re-query if acceleration > threshold
|
|
on_state_divergence: float; // Re-query if state drifts
|
|
};
|
|
}
|
|
|
|
// Update temporal buffer with new state
|
|
function updateTemporalBuffer(
|
|
buffer: TemporalBuffer,
|
|
new_state: CanonicalState
|
|
): TemporalBuffer {
|
|
// Compute delta = φ_t - φ_t-1
|
|
const delta = Q16_16.sub(new_state.phi, buffer.prev_phi);
|
|
|
|
// Compute delta_dot = delta_t - delta_t-1
|
|
const delta_dot = buffer.prev_delta
|
|
? Q16_16.sub(delta, buffer.prev_delta)
|
|
: Q16_16.zero;
|
|
|
|
// Compute gamma = |φ_t - 2·φ_t-1 + φ_t-2|
|
|
const gamma = (buffer.prev_phi && buffer.prev_2phi)
|
|
? Q16_16.abs(Q16_16.sub(
|
|
new_state.phi,
|
|
Q16_16.add(buffer.prev_phi, buffer.prev_phi) // 2·φ_t-1
|
|
), buffer.prev_2phi)
|
|
: Q16_16.zero;
|
|
|
|
// Compute angular momentum
|
|
const angular_momentum = buffer.history.length >= 2
|
|
? computeAngularMomentum(
|
|
buffer.history[1], // t-2
|
|
buffer.history[0], // t-1
|
|
new_state // t
|
|
)
|
|
: Q16_16.zero;
|
|
|
|
return {
|
|
history: [new_state, ...buffer.history].slice(0, buffer.history_size),
|
|
history_size: buffer.history_size,
|
|
prev_delta: some(delta),
|
|
prev_phi: some(new_state.phi),
|
|
prev_2phi: buffer.prev_phi,
|
|
angular_momentum,
|
|
step_count: buffer.step_count + 1
|
|
};
|
|
}
|
|
```
|
|
|
|
### 10.6 Integration Summary: PBACS + Database
|
|
|
|
| PBACS Concept | Database Enhancement | Source File |
|
|
|---------------------|----------------------|-------------|
|
|
| `Pbacs` control runtime | Hysteretic query processing | `Pbacs.lean` |
|
|
| `StepTrace` | Encoding trace with cost per step | `Pbacs.lean:22` |
|
|
| `UnifiedCompression` | Content-addressed encoding | `UnifiedCompression.lean` |
|
|
| `Pulse` | Shell-based pulse generation | `UnifiedCompression.lean:44` |
|
|
| `Contact` | 3-point constraint validation | `UnifiedCompression.lean:63` |
|
|
| `echoWeights` [1,½,¼] | Standing-wave field construction | `UnifiedCompression.lean:77` |
|
|
| `TemporalBuffer` | Streaming query state | `Orchestrate.lean:23` |
|
|
| `CanonicalState` | Accumulated query phase state | `Canon.lean` |
|
|
| `ControlState` | HALT/HOLD/STABLE/TRANSIENT gates | `Pbacs.lean:88` |
|
|
|
|
### 10.7 Complete Example: PBACS-Enhanced Storage
|
|
|
|
```typescript
|
|
// Store a research record with full PBACS encoding
|
|
async function storeResearchRecord(record: ResearchRecord): Promise<StorageReceipt> {
|
|
// 1. Extract concept vector for shell coordinates
|
|
const concept = extractConceptVector(record.text);
|
|
|
|
// 2. Map to AVMR shell (n, k, a, b)
|
|
const shell = conceptVectorToShell(concept);
|
|
|
|
// 3. PBACS encode with constraint tracking
|
|
const encoding = pbacsEncode(record, {
|
|
shell,
|
|
echo_depth: 2,
|
|
emission_threshold: 0x00008000 // 0.5 in Q16.16
|
|
});
|
|
|
|
// 4. Compute content address
|
|
const content_address = SHA256(encoding.encoded_bytes);
|
|
|
|
// 5. Verify thermodynamic compliance
|
|
const landauer = computeLandauerLimit(encoding.encoded_bytes.length);
|
|
if (encoding.total_cost < landauer) {
|
|
throw new Error("Landauer bound violated — encoding invalid");
|
|
}
|
|
|
|
// 6. Store with full trace
|
|
const entry: PBACSAddressableStorage = {
|
|
address: content_address,
|
|
entry: {
|
|
raw_content: record,
|
|
encoding_trace: encoding.steps,
|
|
encoded_bytes: encoding.encoded_bytes,
|
|
verification: {
|
|
constraint_hash: SHA256(encoding.constraints_satisfied),
|
|
cost_verification: true,
|
|
landauer_compliance: true
|
|
}
|
|
},
|
|
content_index: new Map([[record.content_hash, content_address]]),
|
|
deduplication_stats: {
|
|
unique_entries: 1,
|
|
total_references: 1,
|
|
compression_ratio: record.text.length / encoding.encoded_bytes.length
|
|
}
|
|
};
|
|
|
|
// 7. Return receipt with cost
|
|
return {
|
|
address: content_address,
|
|
storage_cost: encoding.total_cost,
|
|
landauer_limit: landauer,
|
|
efficiency: Q16_16.div(landauer, encoding.total_cost),
|
|
constraint_satisfaction: encoding.constraints_satisfied
|
|
};
|
|
}
|
|
```
|
|
|
|
---
|
|
|
|
## 11. Wormhole Throat Physics Layer (Topological Shortcuts)
|
|
|
|
**Purpose:** Model semantic graph traversals as **wormhole throat physics** — shortcuts through the manifold that bypass normal path distance. Derived from `ExtensionScaffold/Topology/Wormhole.lean` and `ExtensionScaffold/Thermodynamics/ThroatPhysics.lean`.
|
|
|
|
### 11.1 Core Throat Physics Model
|
|
|
|
**Physical Analogy:** In general relativity, a wormhole throat connects distant spacetime regions. In ENE, this represents **semantic shortcuts** — direct links between records that skip intermediate graph traversals.
|
|
|
|
```typescript
|
|
// Wormhole mouth: entry/exit point of the shortcut
|
|
interface WormholeMouth {
|
|
location: ManifoldPoint; // Position in semantic manifold
|
|
aperture: Q16_16; // Throat radius (Q16.16: minSafeAperture = 0.001)
|
|
tidalStress: Q16_16; // Gradient of potential (maxTidalStress = 10.0)
|
|
chronologyProtection: bool; // Prevents time-travel paradoxes
|
|
}
|
|
|
|
// Throat stability states (from Wormhole.lean:13-19)
|
|
enum ThroatStability {
|
|
COLLAPSED, // Singularity — non-traversable
|
|
FLUCTUATING, // Unstable — probabilistic traversal
|
|
STABLE, // Consistent bidirectional passage
|
|
CRYSTALLINE, // Perfectly preserved geodesic
|
|
RESONANT // Actively amplified by external field
|
|
}
|
|
|
|
// Complete wormhole throat structure
|
|
interface WormholeThroat {
|
|
// Mouths at each end
|
|
mouthA: WormholeMouth;
|
|
mouthB: WormholeMouth;
|
|
|
|
// Geometry
|
|
properLength: uint64; // Through-throat distance (often << manifold distance)
|
|
|
|
// Physics state
|
|
stability: ThroatStability;
|
|
exoticMatter: Q16_16; // Negative energy density required (0 = none needed)
|
|
|
|
// Information capacity
|
|
fluxCapacity: Q16_16; // Maximum information flux per unit time
|
|
resonanceFreq: Q16_16; // Natural oscillation frequency
|
|
bidirectional: bool; // True if traversable both ways equally
|
|
}
|
|
```
|
|
|
|
**Key Physical Constraints (from Wormhole.lean:47-61):**
|
|
|
|
```
|
|
Safe traversal requires:
|
|
aperture > minSafeAperture (0.001 in Q16.16)
|
|
tidalStress < maxTidalStress (10.0 in Q16.16)
|
|
stability ∈ {stable, crystalline, resonant}
|
|
payloadSize ≤ fluxCapacity
|
|
```
|
|
|
|
### 11.2 Throat Regime Quantization
|
|
|
|
**Problem:** Continuous throat physics needs discrete states for database indexing.
|
|
|
|
**Solution:** Quantized throat regimes from `ThroatPhysics.lean`:
|
|
|
|
```typescript
|
|
// Input loads that determine throat state (from ThroatPhysics.lean:46-59)
|
|
interface QuantizedThroatInput {
|
|
// Physical loads
|
|
pinchLoad: Q16_16; // Pressure toward collapse
|
|
collapseLoad: Q16_16; // Critical destabilization force
|
|
boundaryLoad: Q16_16; // Boundary pressure
|
|
|
|
// Counts affecting stability
|
|
rejectCount: uint32; // Rejected traversals (weakens throat)
|
|
channelCount: uint32; // Active channels
|
|
branchCount: uint32; // Branching complexity
|
|
gateCount: uint32; // Control gates
|
|
|
|
// Regime classifications
|
|
mediumRegime: MediumRegime;
|
|
manifoldRegime: PlasmaManifoldRegime;
|
|
topologyRegime: PlasmaTopologyRegime;
|
|
invariantSurvivor: PlasmaTopologyInvariantSurvivor;
|
|
stabilityClass: StabilityClass;
|
|
}
|
|
|
|
// Discrete throat regimes (from ThroatPhysics.lean:61-66)
|
|
enum ThroatRegime {
|
|
OPEN_CHANNEL, // Unrestricted flow
|
|
PINCH, // Constricted but open
|
|
THROAT, // Minimal viable channel
|
|
COLLAPSE // Non-traversable
|
|
}
|
|
|
|
// Stability class bias factors (from ThroatPhysics.lean:73-79)
|
|
// Added to loads for regime determination
|
|
const STABILITY_BIAS: Record<StabilityClass, Q16_16> = {
|
|
stable: 0.25, // quarter
|
|
singular: 3.0, // three
|
|
throat: 1.0, // one
|
|
unstable: 0.5, // half
|
|
collapsed: 2.0 // two
|
|
};
|
|
|
|
// Regime quantization function (from ThroatPhysics.lean:90-96)
|
|
function quantizeThroat(input: QuantizedThroatInput): ThroatRegime {
|
|
const pinchIndex = input.pinchLoad + STABILITY_BIAS[input.stabilityClass];
|
|
const collapseGradient = input.collapseLoad + STABILITY_BIAS[input.stabilityClass];
|
|
const boundaryPressure = input.boundaryLoad + STABILITY_BIAS[input.stabilityClass];
|
|
|
|
// Thresholds in Q16.16
|
|
if (pinchIndex > 2.0) return ThroatRegime.PINCH; // 131072
|
|
if (collapseGradient > 1.0) return ThroatRegime.COLLAPSE; // 65536
|
|
if (boundaryPressure > 0.5) return ThroatRegime.THROAT; // 32768
|
|
return ThroatRegime.OPEN_CHANNEL;
|
|
}
|
|
```
|
|
|
|
### 11.3 Semantic Graph as Wormhole Network
|
|
|
|
**Database Application:** Model semantic links as traversable wormholes:
|
|
|
|
```typescript
|
|
// Semantic record positioned in manifold
|
|
interface ManifoldPoint {
|
|
coords: Q16_16[]; // Fixed-point coordinates (1-16 dimensions)
|
|
dimension: uint32; // Manifold dimension (1-16)
|
|
}
|
|
|
|
// Map archive record to manifold position
|
|
interface PositionedRecord extends EnhancedArchiveRecord {
|
|
manifold_position: ManifoldPoint;
|
|
|
|
// Shell coordinates from AVMR give natural manifold embedding
|
|
// n (shell position) → one manifold dimension
|
|
// k (shell index) → another dimension
|
|
// (a,b) tip coordinates → 2D submanifold
|
|
}
|
|
|
|
// Throat network: adjacency list of shortcuts
|
|
interface ThroatNetwork {
|
|
throats: WormholeThroat[];
|
|
|
|
// Index by mouth location for fast lookup
|
|
locationIndex: Map<ManifoldPoint, WormholeThroat[]>;
|
|
}
|
|
|
|
// Find traversable shortcuts from a record
|
|
function findSemanticShortcuts(
|
|
network: ThroatNetwork,
|
|
fromRecord: PositionedRecord,
|
|
payloadSize: Q16_16
|
|
): WormholeThroat[] {
|
|
return network.throats.filter(throat =>
|
|
(throat.mouthA.location == fromRecord.manifold_position ||
|
|
throat.mouthB.location == fromRecord.manifold_position) &&
|
|
throat.traversable(payloadSize)
|
|
);
|
|
}
|
|
```
|
|
|
|
### 11.4 Shortcut Efficiency Metrics
|
|
|
|
**Key insight:** Wormholes provide value when `properLength << manifoldDistance`.
|
|
|
|
```typescript
|
|
// Efficiency computation (from Wormhole.lean:68-73)
|
|
function computeThroatEfficiency(
|
|
throat: WormholeThroat,
|
|
manifoldDistance: uint64
|
|
): Q16_16 {
|
|
if (throat.properLength == 0) return 0; // Singular
|
|
|
|
// η = manifold_distance / throat_length (Q16.16 ratio)
|
|
return (manifoldDistance / throat.properLength) * 65536;
|
|
}
|
|
|
|
// Distance saved (from Wormhole.lean:64-65)
|
|
function computeShortcut(
|
|
throat: WormholeThroat,
|
|
manifoldDistance: uint64
|
|
): int64 {
|
|
return manifoldDistance - throat.properLength;
|
|
}
|
|
|
|
// Traversal cost (from Wormhole.lean:76-83)
|
|
function computeTraversalCost(throat: WormholeThroat): Q16_16 {
|
|
const stabilityPenalty: Record<ThroatStability, Q16_16> = {
|
|
collapsed: 65535.999, // 0xFFFFFFFF - effectively infinite
|
|
fluctuating: 8.0, // 0x00080000
|
|
stable: 1.0, // 0x00010000
|
|
crystalline: 0.5, // 0x00008000
|
|
resonant: 0.25 // 0x00004000 (externally supported)
|
|
};
|
|
|
|
return throat.exoticMatter + stabilityPenalty[throat.stability];
|
|
}
|
|
|
|
// Optimal path selection considering wormholes
|
|
interface PathSelection {
|
|
// Standard graph path (many hops)
|
|
graphPath: {
|
|
hops: uint32;
|
|
totalDistance: uint64;
|
|
cumulativeCost: Q16_16;
|
|
};
|
|
|
|
// Wormhole shortcut (if available)
|
|
wormholePath?: {
|
|
throat: WormholeThroat;
|
|
shortcutLength: uint64;
|
|
traversalCost: Q16_16;
|
|
efficiency: Q16_16;
|
|
};
|
|
|
|
// Optimal choice
|
|
optimal: 'graph' | 'wormhole' | 'hybrid';
|
|
savings: Q16_16; // Cost difference
|
|
}
|
|
```
|
|
|
|
### 11.5 Throat Dynamics for Streaming Queries
|
|
|
|
**Application:** As query state evolves, throat stability may change:
|
|
|
|
```typescript
|
|
// Throat state evolution (combines with TemporalBuffer from §10)
|
|
interface ThroatDynamics {
|
|
// Current state
|
|
currentRegime: ThroatRegime;
|
|
currentStability: ThroatStability;
|
|
|
|
// Historical loads (for trend analysis)
|
|
loadHistory: {
|
|
pinchLoad: Q16_16[];
|
|
collapseLoad: Q16_16[];
|
|
boundaryLoad: Q16_16[];
|
|
};
|
|
|
|
// Predictive thresholds
|
|
predictiveCollapse: bool; // Trending toward collapse
|
|
pinchImminent: bool; // Approaching pinch threshold
|
|
|
|
// Reactive control
|
|
stabilizeAction?: {
|
|
injectExoticMatter: Q16_16; // Add negative energy
|
|
reduceFlux: Q16_16; // Throttle throughput
|
|
reinforceGate: bool; // Add control gates
|
|
};
|
|
}
|
|
|
|
// Monitor throat health during long-running queries
|
|
function monitorThroatHealth(
|
|
throat: WormholeThroat,
|
|
dynamics: ThroatDynamics,
|
|
queryLoad: Q16_16
|
|
): ThroatHealth {
|
|
const regime = quantizeThroat({
|
|
pinchLoad: queryLoad,
|
|
collapseLoad: dynamics.loadHistory.collapseLoad[dynamics.loadHistory.collapseLoad.length - 1],
|
|
boundaryLoad: dynamics.loadHistory.boundaryLoad[dynamics.loadHistory.boundaryLoad.length - 1],
|
|
rejectCount: 0,
|
|
channelCount: 1,
|
|
branchCount: 1,
|
|
gateCount: 1,
|
|
// ... other fields
|
|
});
|
|
|
|
return {
|
|
traversable: regime != ThroatRegime.COLLAPSE,
|
|
regime,
|
|
recommendedAction: regime == ThroatRegime.PINCH
|
|
? 'reduce_flux'
|
|
: regime == ThroatRegime.THROAT
|
|
? 'stabilize'
|
|
: 'continue'
|
|
};
|
|
}
|
|
```
|
|
|
|
### 11.6 Integration with Other Layers
|
|
|
|
| Throat Concept | Integration | Source |
|
|
|-----------------|-------------|--------|
|
|
| `ManifoldPoint` | Embeds AVMR shell coordinates | `Wormhole.lean:22` |
|
|
| `ThroatStability` | Maps to PBACS `ControlState` | `Wormhole:13`, `Pbacs:88` |
|
|
| `fluxCapacity` | Thermodynamic cost constraint | `Wormhole:42`, `ThroatPhysics:47` |
|
|
| `exoticMatter` | Resource budget from `ThermodynamicCost` | `Wormhole:41`, `§10.2` |
|
|
| `resonanceFreq` | Connects to AVMR spectral overlap | `Wormhole:43`, `AVMR.lean:141` |
|
|
| `ThroatRegime` | Query routing decisions | `ThroatPhysics:61` |
|
|
|
|
### 11.7 Complete Example: Throat-Aware Graph Query
|
|
|
|
```typescript
|
|
// Execute query using wormhole shortcuts when available
|
|
async function executeThroatAwareQuery(
|
|
query: SearchQuery,
|
|
network: ThroatNetwork
|
|
): Promise<QueryResult> {
|
|
// 1. Position query in manifold (AVMR shell coordinates)
|
|
const queryPosition = conceptVectorToManifoldPoint(
|
|
extractConceptVector(query.text)
|
|
);
|
|
|
|
// 2. Find candidate records via standard graph search
|
|
const graphCandidates = await graphSearch(query, maxHops: 3);
|
|
|
|
// 3. Find wormhole shortcuts from query position
|
|
const shortcuts = findSemanticShortcuts(
|
|
network,
|
|
{ manifold_position: queryPosition } as PositionedRecord,
|
|
payloadSize: estimateQueryComplexity(query) // Q16_16
|
|
);
|
|
|
|
// 4. Evaluate each shortcut
|
|
const shortcutResults = shortcuts.map(throat => {
|
|
const destination = throat.mouthA.location == queryPosition
|
|
? throat.mouthB.location
|
|
: throat.mouthA.location;
|
|
|
|
// Records near destination mouth
|
|
const nearbyRecords = findRecordsNear(destination, radius: 0.1);
|
|
|
|
return {
|
|
throat,
|
|
records: nearbyRecords,
|
|
efficiency: computeThroatEfficiency(
|
|
throat,
|
|
estimateManifoldDistance(queryPosition, destination)
|
|
),
|
|
cost: computeTraversalCost(throat),
|
|
traversable: throat.traversable(estimateQueryComplexity(query))
|
|
};
|
|
}).filter(s => s.traversable);
|
|
|
|
// 5. Merge results: graph path + wormhole shortcuts
|
|
const allCandidates = [
|
|
...graphCandidates.map(c => ({ source: 'graph', record: c, cost: c.hops * 65536 })),
|
|
...shortcutResults.flatMap(s =>
|
|
s.records.map(r => ({
|
|
source: 'wormhole',
|
|
record: r,
|
|
cost: s.cost,
|
|
efficiency: s.efficiency
|
|
}))
|
|
)
|
|
];
|
|
|
|
// 6. Score and rank
|
|
const scored = allCandidates.map(c => ({
|
|
...c,
|
|
score: semanticSimilarity(query, c.record) / c.cost
|
|
})).sort((a, b) => b.score - a.score);
|
|
|
|
return {
|
|
results: scored.slice(0, query.top_k),
|
|
pathAnalysis: {
|
|
graph_hits: graphCandidates.length,
|
|
wormhole_hits: shortcutResults.length,
|
|
average_wormhole_efficiency: average(shortcutResults.map(s => s.efficiency))
|
|
}
|
|
};
|
|
}
|
|
```
|
|
|
|
---
|
|
|
|
## 12. Version History
|
|
|
|
| Version | Date | Changes |
|
|
|---------|------|---------|
|
|
| 1.3.0 | 2026-04-18 | Added Wormhole Throat Physics Layer (§11) for topological shortcuts |
|
|
| 1.2.0 | 2026-04-18 | Added PBACS/Compression Database Layer (§10) |
|
|
| 1.1.0 | 2026-04-18 | Added AVMR-Enhanced Vector Layer (§8) and Bracketed/Witness Database Layer (§9) |
|
|
| 1.0.0 | 2026-04-18 | Initial formal specification |
|
|
|
|
---
|
|
|
|
## 13. Machine-Checkable Schema (JSON Schema Draft)
|
|
|
|
```json
|
|
{
|
|
"$schema": "http://json-schema.org/draft-07/schema#",
|
|
"$id": "ene_schema_v1.0.0",
|
|
|
|
"definitions": {
|
|
"SHA256Hex": {
|
|
"type": "string",
|
|
"pattern": "^[0-9a-f]{64}$"
|
|
},
|
|
"ConceptVector14": {
|
|
"type": "array",
|
|
"minItems": 14,
|
|
"maxItems": 14,
|
|
"items": { "type": "number", "minimum": 0.0, "maximum": 1.0 }
|
|
},
|
|
"VerificationStatus": {
|
|
"type": "string",
|
|
"enum": ["pending", "verified", "failed"]
|
|
},
|
|
"SourceType": {
|
|
"type": "string",
|
|
"enum": ["sqlite", "sql_insert", "json_catalog", "chatgpt", "legacy_lean"]
|
|
},
|
|
"Q16_16": {
|
|
"type": "integer",
|
|
"description": "Fixed-point Q16.16 representation (multiply by 65536)"
|
|
},
|
|
"AVMRShell": {
|
|
"type": "object",
|
|
"properties": {
|
|
"n": { "type": "integer", "minimum": 0 },
|
|
"k": { "type": "integer", "minimum": 0 },
|
|
"a": { "type": "integer", "minimum": 0 },
|
|
"b": { "type": "integer", "minimum": 0 }
|
|
},
|
|
"required": ["n", "k", "a", "b"]
|
|
},
|
|
"AVMRState": {
|
|
"type": "object",
|
|
"properties": {
|
|
"shell": { "$ref": "#/definitions/AVMRShell" },
|
|
"mass": { "type": "integer" },
|
|
"polarity": { "type": "integer" },
|
|
"spectrum": {
|
|
"type": "array",
|
|
"minItems": 8,
|
|
"maxItems": 8,
|
|
"items": { "$ref": "#/definitions/Q16_16" }
|
|
},
|
|
"interaction": { "$ref": "#/definitions/Q16_16" },
|
|
"phase": { "type": "integer", "minimum": -3, "maximum": 3 },
|
|
"resonance_count": { "type": "integer", "minimum": 0 },
|
|
"priority_bias": { "type": "integer" },
|
|
"derived_from": {
|
|
"type": "string",
|
|
"enum": ["concept_vector", "text_embedding", "direct"]
|
|
},
|
|
"generation_timestamp": { "type": "string" }
|
|
},
|
|
"required": ["shell", "mass", "polarity", "spectrum", "phase"]
|
|
},
|
|
"BracketedConceptAxis": {
|
|
"type": "object",
|
|
"properties": {
|
|
"lower": { "$ref": "#/definitions/Q16_16" },
|
|
"value": { "$ref": "#/definitions/Q16_16" },
|
|
"upper": { "$ref": "#/definitions/Q16_16" },
|
|
"lowerGap": { "$ref": "#/definitions/Q16_16" },
|
|
"upperGap": { "$ref": "#/definitions/Q16_16" },
|
|
"prod": { "$ref": "#/definitions/Q16_16" },
|
|
"scale": { "type": "integer", "minimum": 0 }
|
|
},
|
|
"required": ["lower", "value", "upper"]
|
|
},
|
|
"BracketedConceptVector": {
|
|
"type": "object",
|
|
"properties": {
|
|
"axes": {
|
|
"type": "array",
|
|
"minItems": 14,
|
|
"maxItems": 14,
|
|
"items": { "$ref": "#/definitions/BracketedConceptAxis" }
|
|
},
|
|
"gapConservation": {
|
|
"type": "array",
|
|
"minItems": 14,
|
|
"maxItems": 14,
|
|
"items": { "type": "boolean" }
|
|
}
|
|
},
|
|
"required": ["axes"]
|
|
},
|
|
"WitnessProvenance": {
|
|
"type": "string",
|
|
"enum": ["observation", "inference", "projection", "evolution", "translation", "composed"]
|
|
},
|
|
"CognitiveLoad": {
|
|
"type": "object",
|
|
"properties": {
|
|
"intrinsic": { "type": "number" },
|
|
"extraneous": { "type": "number" },
|
|
"germane": { "type": "number" },
|
|
"total": { "type": "number" },
|
|
"efficiency": { "type": "number" }
|
|
}
|
|
},
|
|
"WitnessReceipt": {
|
|
"type": "object",
|
|
"properties": {
|
|
"witness_id": { "type": "integer", "minimum": 0 },
|
|
"provenance": { "$ref": "#/definitions/WitnessProvenance" },
|
|
"timestamp": { "type": "number" },
|
|
"load": { "$ref": "#/definitions/CognitiveLoad" }
|
|
},
|
|
"required": ["witness_id", "provenance"]
|
|
},
|
|
"BraidBracket": {
|
|
"type": "object",
|
|
"properties": {
|
|
"lower": { "$ref": "#/definitions/Q16_16" },
|
|
"upper": { "$ref": "#/definitions/Q16_16" },
|
|
"gap": { "$ref": "#/definitions/Q16_16" },
|
|
"kappa": { "$ref": "#/definitions/Q16_16" },
|
|
"phi": { "$ref": "#/definitions/Q16_16" },
|
|
"admissible": { "type": "boolean" }
|
|
},
|
|
"required": ["lower", "upper", "gap", "kappa", "admissible"]
|
|
},
|
|
"PhaseVec": {
|
|
"type": "object",
|
|
"properties": {
|
|
"x": { "$ref": "#/definitions/Q16_16" },
|
|
"y": { "$ref": "#/definitions/Q16_16" }
|
|
},
|
|
"required": ["x", "y"]
|
|
},
|
|
"ControlState": {
|
|
"type": "string",
|
|
"enum": ["halt", "hold", "stable", "transient"]
|
|
},
|
|
"PBACSPulse": {
|
|
"type": "object",
|
|
"properties": {
|
|
"mode": { "type": "string", "enum": ["a", "g", "c", "t", "square"] },
|
|
"mass": { "type": "integer", "minimum": 0 },
|
|
"polarity": { "type": "integer" },
|
|
"width": { "type": "integer", "minimum": 0 }
|
|
},
|
|
"required": ["mode", "mass", "polarity", "width"]
|
|
},
|
|
"PBACSEmission": {
|
|
"type": "object",
|
|
"properties": {
|
|
"gate_closed": { "type": "boolean" },
|
|
"symbol_emitted": { "type": "integer", "minimum": 0, "maximum": 255 },
|
|
"binding_cost": { "$ref": "#/definitions/Q16_16" }
|
|
}
|
|
},
|
|
"PBACSStep": {
|
|
"type": "object",
|
|
"properties": {
|
|
"t": { "type": "integer", "minimum": 0 },
|
|
"shell": { "$ref": "#/definitions/AVMRShell" },
|
|
"pulse": { "$ref": "#/definitions/PBACSPulse" },
|
|
"emission": { "$ref": "#/definitions/PBACSEmission" },
|
|
"control": {
|
|
"type": "object",
|
|
"properties": {
|
|
"state": { "$ref": "#/definitions/ControlState" },
|
|
"score": { "$ref": "#/definitions/Q16_16" },
|
|
"alpha_t": { "$ref": "#/definitions/Q16_16" }
|
|
}
|
|
}
|
|
},
|
|
"required": ["t", "shell", "pulse"]
|
|
},
|
|
"ThermodynamicCost": {
|
|
"type": "object",
|
|
"properties": {
|
|
"encoding_cost": { "$ref": "#/definitions/Q16_16" },
|
|
"retrieval_cost": { "$ref": "#/definitions/Q16_16" },
|
|
"transmission_cost": { "$ref": "#/definitions/Q16_16" },
|
|
"landauer_limit": { "$ref": "#/definitions/Q16_16" },
|
|
"efficiency": { "$ref": "#/definitions/Q16_16" }
|
|
}
|
|
},
|
|
"TemporalBuffer": {
|
|
"type": "object",
|
|
"properties": {
|
|
"history_size": { "type": "integer", "minimum": 0 },
|
|
"angular_momentum": { "$ref": "#/definitions/Q16_16" },
|
|
"step_count": { "type": "integer", "minimum": 0 }
|
|
}
|
|
},
|
|
"ManifoldPoint": {
|
|
"type": "object",
|
|
"properties": {
|
|
"coords": {
|
|
"type": "array",
|
|
"items": { "$ref": "#/definitions/Q16_16" }
|
|
},
|
|
"dimension": { "type": "integer", "minimum": 1, "maximum": 16 }
|
|
},
|
|
"required": ["coords", "dimension"]
|
|
},
|
|
"ThroatStability": {
|
|
"type": "string",
|
|
"enum": ["collapsed", "fluctuating", "stable", "crystalline", "resonant"]
|
|
},
|
|
"WormholeMouth": {
|
|
"type": "object",
|
|
"properties": {
|
|
"location": { "$ref": "#/definitions/ManifoldPoint" },
|
|
"aperture": { "$ref": "#/definitions/Q16_16" },
|
|
"tidalStress": { "$ref": "#/definitions/Q16_16" },
|
|
"chronologyProtection": { "type": "boolean" }
|
|
},
|
|
"required": ["location", "aperture", "tidalStress"]
|
|
},
|
|
"WormholeThroat": {
|
|
"type": "object",
|
|
"properties": {
|
|
"mouthA": { "$ref": "#/definitions/WormholeMouth" },
|
|
"mouthB": { "$ref": "#/definitions/WormholeMouth" },
|
|
"properLength": { "type": "integer", "minimum": 0 },
|
|
"stability": { "$ref": "#/definitions/ThroatStability" },
|
|
"exoticMatter": { "$ref": "#/definitions/Q16_16" },
|
|
"fluxCapacity": { "$ref": "#/definitions/Q16_16" },
|
|
"resonanceFreq": { "$ref": "#/definitions/Q16_16" },
|
|
"bidirectional": { "type": "boolean" }
|
|
},
|
|
"required": ["mouthA", "mouthB", "properLength", "stability"]
|
|
},
|
|
"ThroatRegime": {
|
|
"type": "string",
|
|
"enum": ["open_channel", "pinch", "throat", "collapse"]
|
|
}
|
|
}
|
|
}
|
|
```
|
|
|
|
---
|
|
|
|
**End of Specification**
|