Data Model¶

Records are stored in the LelielStore in-memory columnar store backed by DuckDB for write-through durability. There is no graph database. The factor graph is built in memory from the ingested records and updated on every ingest event.

Record¶

The canonical unit of data in Leliel. Every record is one node in the factor graph.

Field	Type	Required	Description
`record_id`	string	Yes	Unique identifier; primary key within the store
`source_id`	string	Yes	Producer identifier; used to scope list and query results
`signal_value`	float	Yes	Normalised quality signal in `[0.0, declared_upper_bound]`
`declared_upper_bound`	float	No	Upper bound for `signal_value`; defaults to `1.0`
`timestamp`	string	No	ISO 8601 timestamp; used for recency fallback ordering
`extra_data`	JSON object	No	Arbitrary metadata; field-value pairs drive the IDF semantic index

Re-ingesting an existing record_id updates the columnar metadata in-place without resetting the accumulated mass. Mass is preserved across upserts.

Factor graph¶

The factor graph is the in-memory graph over which the quantum walk evolves.

Nodes: one node per record. Node index i aligns exactly with the columnar metadata vectors so all field reads are O(1) index accesses with no hash lookup.

Co-occurrence edges: within each source, a sliding window of width K=5 connects each record to its K nearest neighbours by ingest order. Edges represent temporal proximity in the ingested signal stream.

Cross-source co-failure edges: when a record is ingested with a negative signal (signal_value low relative to declared_upper_bound), up to 3 edges are drawn to the nearest-mass records from other sources. These edges capture cross-source failure correlation.

Wormhole edges (structural): after each ingest, the Fiedler eigenvector of the graph Laplacian is cached. Any two high-mass nodes whose Fiedler components differ by less than WORMHOLE_ALPHA * std(v2) receive a wormhole edge. Wormhole edges are injected into the walk snapshot at query time. They represent structural proximity in the ER=EPR sense: nodes that are topologically equivalent in the Laplacian embedding may exhibit correlated behaviour even when not directly connected.

Mass field¶

Every node carries a scalar utility mass value. Mass accumulates from REINFORCE feedback and decays via Hawking radiation. Three sources contribute to the effective mass used by the walk Hamiltonian:

Component	Source	Description
Utility mass	REINFORCE feedback	Accumulates on negative signal; decays on positive signal and over time
Structural mass	Fiedler proximity	Wormhole edges encode structural co-location (ER=EPR)
Semantic mass	IDF feature similarity	Cold-start bias toward semantically similar records via `extra_data` IDF vectors

Utility mass is the primary component at query time. Structural and semantic components operate via edge injection and walk seed bias respectively rather than as additive mass terms.

Hawking decay: mass decays continuously with a half-life of 86400 seconds (one day). The decay is time-proportional and applied lazily on each write; the decay constant is derived from the one-day half-life via alpha_H = ln(2) / 86400.

Schwarzschild threshold: M_s = lambda_2(L) * log(1/epsilon) / (G * K). Derived from the Fiedler eigenvalue of the live graph; not a configurable constant. Nodes above M_s are black holes: the walk's Born-rule amplitude suppresses them without explicit exclusion logic.

DuckDB schema¶

DuckDB provides write-through durability. The hot query path reads exclusively from the in-memory columnar store; no SQL is issued during query execution.

records¶

Durable record store. One row per record.

Column	Type	Description
`record_id`	text	Primary key; matches the in-memory node identifier
`source_id`	text	Producer identifier
`signal_value`	double	Quality signal
`declared_upper_bound`	double	Declared amplitude upper bound
`timestamp`	text	ISO 8601 timestamp string, nullable
`extra_data`	text	JSON-serialised extra metadata, nullable
`ingested_at`	timestamp	UTC time this record was written to DuckDB

record_masses¶

Durable mass index. One row per record. Updated on REINFORCE writes.

Column	Type	Description
`record_id`	text	Foreign key to records
`mass`	double	Current utility mass value
`last_updated`	timestamp	UTC time of most recent mass write

analysis_summaries¶

Source-level analysis summaries computed by the background analysis worker.

Column	Type	Description
`source_id`	text	Source identifier
`record_count`	integer	Number of records in this source
`mean_signal`	double	Mean signal_value across records
`mean_mass`	double	Mean mass across records
`black_hole_count`	integer	Records above M_s at time of summary
`computed_at`	timestamp	UTC time this summary was computed

mesh_snapshots¶

Append-only SLEM trend log written by the analysis worker each cycle.

Column	Type	Description
`slem`	double	Second Largest Eigenvalue Modulus of the walk weight matrix
`spectral_gap`	double	`1 - slem`
`node_count`	integer	Graph size at snapshot time
`computed_at`	timestamp	UTC time of this snapshot