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ENE Schema Specification v1.0.0
Status: Formal specification for machine-checkable conformance
Date: 2026-04-18
Purpose: Type/schema contract separate from observed dataset
1. Type Hierarchy
BaseArchiveRecord -- Lossless preservation layer
↓ enhancement
EnhancedArchiveRecord -- Semantic enrichment layer
↓ attestation
AttestedArchiveRecord -- Provenance verification layer
2. BaseArchiveRecord (Lossless Layer)
Purpose: Complete, lossless preservation of original sources. No semantic processing required.
interface BaseArchiveRecord {
// Identity (§2.1)
archive_id: ArchiveID; // content-addressed per §2.1.1
source_type: SourceType; // §2.2
source_file: string; // absolute or relative path
// Content preservation (§2.3)
raw_content: JSONValue; // original structure, unchanged
extracted_text: string; // UTF-8, flattened for indexing
// Provenance (§2.4)
extracted_at: ISOTimestamp;
content_hash: SHA256Hex; // §2.5
extraction_version: string; // "ene_complete_extract_v1"
// Optional SQL metadata
row_number?: uint32; // SQL table row index
table_name?: string; // SQL table name
}
2.1.1 ArchiveID Derivation Rule
archive_id := source_prefix + "_" + content_truncated
where:
source_prefix := source_type + optional_table_or_filename
content_truncated := first 16 chars of content_hash
examples:
"sqlite_packages_0_755cad3f154c4dc7"
"chatgpt_aas_pi_computation_enhancement_b15d663e393283e4"
"json_event_catalog_42_a1b2c3d4e5f67890"
Invariant: content_hash is SHA256 over canonical raw_content JSON.
2.2 SourceType Enum
SourceType ::= "sqlite" | "sql_insert" | "json_catalog" | "chatgpt" | "legacy_lean"
2.3 Content Preservation Rules
raw_content: Original parsed structure, no transformationextracted_text: UTF-8 string, max 10,000 chars, for search/semantic processing- Bytes in source → hex string with
"_type": "bytes"marker in raw_content
2.4 Timestamp Format
ISOTimestamp := "YYYY-MM-DDTHH:MM:SS.ssssss" // ISO 8601 with microseconds
2.5 Hash Format
SHA256Hex := [0-9a-f]{64} // lowercase hex, no 0x prefix
3. EnhancedArchiveRecord (Semantic Layer)
Purpose: Multi-scale semantic representation for cross-linkage.
Extends: BaseArchiveRecord with required semantic fields.
interface EnhancedArchiveRecord extends BaseArchiveRecord {
// Multi-scale semantic representation (§3.1)
concept_vector: ConceptVector14; // required, 14-dim
phrase_vector: PhraseVector; // required, map<string, float>
entities: EntityList; // required, string[]
topic_clusters: TopicList; // required, string[]
// Connectivity (§3.2)
link_count: uint32; // number of semantic links
}
3.1 ConceptVector14 Specification
ConceptVector14 := [float; 14] // L2-normalized, each in [0.0, 1.0]
Axis ordering (fixed):
0: substrate -- universal computation, foam
1: compression -- soliton, encoding, entropy
2: topology -- graph, dag, manifold, node
3: hardware -- chip, verilog, hdl, fpga
4: time -- temporal, clock, tick
5: crypto -- hash, sha256, proof, verify
6: database -- sql, index, query, storage
7: semantic -- language, meaning, concept
8: physics -- thermo, quantum, entropy
9: security -- isolation, warden, boundary
10: os_vm -- kernel, vm, bytecode, runtime
11: research -- theorem, proof, discovery
12: omnitoken -- token, score, manifest, capsule
13: identity -- provenance, attestation, signature
Extraction version: "concept_vector_14_v1"
Normalization: L2 per-vector: sum(x^2) = 1.0
3.2 EntityList and TopicList
EntityList := string[] // extracted domain entities, max 50
TopicList := Topic[] // classified topics, max 10
Topic ::= "compression" | "topology" | "security" | "hardware" |
"physics" | "math_theorem" | "codon" | "neural_sae" |
"lean_semantics" | "geometry"
4. Provenance Layer
4.1 ProvenanceManifest
interface ProvenanceManifest {
pipeline_id: string; // e.g., "ene_complete_extract_v1"
manifest_hash: SHA256Hex; // §4.1.1 canonical hash
input_digest: SHA256Hex; // previous cumulative state
op_code: OpCode; // §4.1.2
signal_metadata: JSONValue; // operation parameters
output_digest: SHA256Hex; // record content hash
timestamp: ISOTimestamp;
sequence_num: uint32; // 0-indexed position in chain
prev_manifest_hash?: SHA256Hex; // previous manifest's manifest_hash
}
4.1.1 Canonical Manifest Hash
manifest_hash := SHA256(canonical_json)
where canonical_json is JSON serialization of:
{
"pipeline_id": string,
"input_digest": SHA256Hex,
"op_code": OpCode,
"signal_metadata": JSONValue,
"output_digest": SHA256Hex,
"timestamp": ISOTimestamp,
"sequence_num": uint32,
"prev_manifest_hash": SHA256Hex | null
}
with:
- sort_keys=True
- separators=(',', ':')
- ensure_ascii=False
- no manifest_hash field (self-reference excluded)
4.1.2 OpCode Enum
OpCode ::= "EXTRACT_SQLITE" | "EXTRACT_SQL_INSERT" | "EXTRACT_JSON_CATALOG" |
"EXTRACT_CHATGPT" | "EXTRACT_LEGACY_LEAN"
4.2 SentenceRecord
interface SentenceRecord {
data_hash: SHA256Hex; // content hash (hex, not base64)
prev_hash: SHA256Hex; // previous sentence hash
metadata_hash: SHA256Hex; // operation metadata hash
timestamp: UnixTimestamp; // seconds since epoch, float
cognitive_load: CognitiveLoadVector; // §4.2.1
features: FeatureVector9; // §4.2.2
}
UnixTimestamp := float // time.time() output
4.2.1 CognitiveLoadVector
CognitiveLoadVector := {
L_I: float, // Intrinsic: Shannon entropy / 8, bits per byte
L_E: float, // Extraneous: structural complexity
L_G: float, // Germane: semantic density
L_R: float, // Routing: decision cost
L_M: float, // Memory: storage cost
L_total: float, // sum of above
efficiency: float // L_G / L_total, or 0 if L_total = 0
}
All values in [0.0, ∞), typically L_total ∈ [0.5, 2.0]
4.2.2 FeatureVector9
FeatureVector9 := [float; 9]
Index semantics:
0: normalized_size -- len(text) / 10000
1: math_density -- 'theorem' count / 10
2: compression_domain -- 'compression' count / 10
3: security_domain -- 'security' count / 10
4: hardware_domain -- 'hardware' count / 10
5: code_density -- '```' count / 5
6: vocabulary_diversity -- unique_words / 1000
7: structure_density -- newline count / 100
8: capitalization_ratio -- uppercase / total chars
4.3 ArchiveAttestation
interface ArchiveAttestation {
attestation_id: string; // "attest_" + archive_id
archive_id: ArchiveID; // references EnhancedArchiveRecord
source_type: SourceType; // preserved from base record
content_hash: SHA256Hex;
provenance_key: SHA256Hex; // Merkle root of manifest chain
sentence_hash: SHA256Hex; // links to SentenceRecord
extracted_at: ISOTimestamp;
attested_at: ISOTimestamp;
verification_status: VerificationStatus; // §4.3.1
}
4.3.1 VerificationStatus Enum
VerificationStatus ::= "pending" | "verified" | "failed"
5. EnhancedGraph
interface EnhancedGraph {
meta: GraphMeta;
nodes: EnhancedNode[];
links: EnhancedLink[];
entity_index: Map<Entity, ArchiveID[]>;
}
interface GraphMeta {
total_records: uint32;
total_links: uint32;
links_per_record: float;
resolution: string; // "maximum" | "high" | "standard"
generated_at: ISOTimestamp;
}
interface EnhancedNode {
id: ArchiveID;
type: NodeType; // "chatgpt_conversation" | "sqlite_table_row" | ...
title?: string;
timestamp?: ISOTimestamp;
// From EnhancedArchiveRecord
concept_vector: ConceptVector14;
entities: EntityList;
topic_clusters?: TopicList;
theorems?: string[];
insights_count?: uint32;
code_snippets_count?: uint32;
link_count: uint32;
text_preview?: string; // truncated extracted_text
}
interface EnhancedLink {
source: ArchiveID;
target: ArchiveID;
score: float; // [0.0, 1.0]
type: LinkType;
}
NodeType ::= "chatgpt_conversation" | "sqlite_table_row" | "sql_insert_row" |
"json_catalog_entry" | "legacy_lean"
LinkType ::= "concept_similar" | "entity_sha256" | "semantic_phrase" |
"shared_topic" | "shared_substrate" | "ene_entity_bridge" |
"weak_semantic"
6. Integrity Invariants
6.1 Archive Integrity
∀ record ∈ archive.records:
record.content_hash = SHA256(canonical(record.raw_content))
record.archive_id follows §2.1.1 format
record.source_type ∈ SourceType enum
record.extraction_version = "ene_complete_extract_v1"
6.2 Enhanced Graph Integrity
∀ node ∈ graph.nodes:
node.id ∈ archive.records.keys()
len(node.concept_vector) = 14
∀ v ∈ node.concept_vector: 0.0 ≤ v ≤ 1.0
node.link_count = count(link where link.source = node.id or link.target = node.id)
∀ link ∈ graph.links:
link.source ∈ graph.nodes.id
link.target ∈ graph.nodes.id
link.score ∈ [0.0, 1.0]
link.type ∈ LinkType enum
6.3 Provenance Chain Integrity
∀ i ∈ [1, len(manifests)):
manifests[i].prev_manifest_hash = manifests[i-1].manifest_hash
manifests[0].prev_manifest_hash = null
∀ manifest ∈ manifests:
manifest.manifest_hash = compute_manifest_hash(manifest) per §4.1.1
6.4 Attestation Integrity
∀ attestation ∈ attestations:
attestation.archive_id ∈ archive.records.keys()
attestation.source_type = archive.records[attestation.archive_id].source_type
attestation.verification_status ∈ VerificationStatus enum
attestation.content_hash ≠ "" // never empty
6.5 Merkle Tree Integrity
merkle_leaves.length > 0
∀ leaf ∈ merkle_leaves: leaf ≠ "" // no empty leaves
merkle_root = compute_merkle_root(merkle_leaves)
7. Conformance Checking (Lean Target)
Future Lean verification should check:
-- Schema conformance
def isValidArchiveRecord (r : ArchiveRecord) : Bool :=
r.archive_id.length > 0 &&
r.source_type ∈ SourceType.values &&
r.content_hash.length = 64 &&
isHex r.content_hash
-- Enhanced conformance
def isValidEnhancedRecord (r : EnhancedArchiveRecord) : Bool :=
isValidArchiveRecord r &&
r.concept_vector.length = 14 &&
isL2Normalized r.concept_vector &&
r.entities.length > 0
-- Provenance chain validity
def isValidManifestChain (manifests : List ProvenanceManifest) : Bool :=
∀ i ∈ [1, manifests.length),
manifests[i].prev_manifest_hash = manifests[i-1].manifest_hash
-- Cross-reference integrity
def isValidAttestation (a : ArchiveAttestation) (archive : Archive) : Bool :=
a.archive_id ∈ archive.records &&
a.source_type = archive.records[a.archive_id].source_type &&
a.verification_status ∈ ["pending", "verified", "failed"]
8. AVMR-Enhanced Vector Layer (Optional Physics-Rooted Indexing)
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.
8.1 AVMR State Structure
interface AVMRState {
// Shell decomposition: n = k² + a = (k+1)² - b, where a+b = 2k+1
shell: {
n: uint32; // integer position in mountain range
k: uint32; // floor(sqrt(n)) — shell number
a: uint32; // forward offset from k²
b: uint32; // backward offset to (k+1)²
};
// Tip coordinates: Tip(n) = (ab, a-b) ∈ ℝ²
mass: int; // ab product
polarity: int; // a - b
// 8-bin spectral signature (from AVMR eventSpectrum)
spectrum: [Q16_16; 8]; // quantized spectral bins
// Field interaction state
interaction: Q16_16; // computed interaction score
phase: int; // -3 to 3 classification bucket
// Aggregation metadata
resonance_count: uint32; // degeneracy count from merges
priority_bias: int; // 0 or 1 from parity check
// Provenance
derived_from: "concept_vector" | "text_embedding" | "direct";
generation_timestamp: ISOTimestamp;
}
8.2 Shell-Based Indexing
interface ShellIndex {
// Index by shell number k = floor(sqrt(n))
shells: Map<uint32, {
k: uint32;
shell_range: [uint32, uint32]; // [k², (k+1)²)
record_ids: ArchiveID[]; // records in this shell
// Axial generators (A_k, G_k, C_k, T_k positions per AVMR)
A_position: uint32; // k² — purine anchor
G_position: uint32; // k² + k — purine mid-shell
C_position: uint32; // k² + k + 1 — pyrimidine mid-shell
T_position: uint32; // (k+1)² - 1 — pyrimidine anchor
// Field aggregate for the shell (precomputed)
aggregate_spectrum: [Q16_16; 8];
total_mass: int;
total_polarity: int;
}>;
// Search radius: how many adjacent shells to query
default_search_radius: uint32; // typically 1 (3 shells total)
}
// Shell decomposition function (from AVMR.lean:67-71)
function shellState(n: uint32): { k: uint32, a: uint32, b: uint32 } {
const k = Math.floor(Math.sqrt(n));
const a = n - k*k;
const b = (k+1)*(k+1) - n;
return { k, a, b };
}
Search Complexity: O(√N) — search 2r+1 shells containing O(√N) records each, vs O(N) brute force.
8.3 AVMR Similarity Scoring
interface AVMRScoring {
// Interaction score: J(n) = ab·F_m + (a-b)·F_p + ⟨χ(n), F_c(n)⟩
computeInteractionScore(
query: AVMRState,
target_shell: { k: uint32, aggregate: LocalField },
echo_depth: uint32 // 1, 2, or 3 for tailWeight decay
): Q16_16;
// Field construction with echo weights [1, ½, ¼]
buildFieldAt(
n: uint32,
maxN: uint32,
records: AVMRState[]
): LocalField;
// Resonance detection between siblings
siblingResonance(left: AVMRState, right: AVMRState): uint32;
// Final combined score
computeAVMRScore(
query: AVMRState,
candidate: AVMRState,
field: LocalField
): float {
const massTerm = query.mass * field.massField / Q16_16_SCALE;
const polTerm = query.polarity * field.polarityField / Q16_16_SCALE;
const specTerm = spectralOverlap(query.spectrum, field.spectrum) / Q16_16_SCALE;
const resonance = siblingResonance(query, candidate) * 0.1;
return massTerm + polTerm + specTerm + resonance;
}
}
// Spectral overlap: Σᵢ(spectrum₁ᵢ · spectrum₂ᵢ)
function spectralOverlap(a: [Q16_16; 8], b: [Q16_16; 8]): Q16_16 {
return a.map((ai, i) => ai * b[i]).reduce((sum, x) => sum + x, 0);
}
8.4 Integration with Concept Vectors
// 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
// 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
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:
// 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:
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:
// 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:
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:
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:
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
// 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:
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:
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:
// 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:
// 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:
// 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
// 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.
// 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:
// 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:
// 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.
// 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:
// 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
// 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)
{
"$schema": "http://json-schema.org/draft-07/schema#",
"$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