Each node downloads and custodies a minimum of `CUSTODY_REQUIREMENT` subnets per slot. The particular subnets that the node is required to custody are selected pseudo-randomly (more on this below).
A node *may* choose to custody and serve more than the minimum honesty requirement. Such a node explicitly advertises a number greater than `CUSTODY_REQUIREMENT` via the peer discovery mechanism -- for example, in their ENR (e.g. `custody_subnet_count: 4` if the node custodies `4` subnets each slot) -- up to a `DATA_COLUMN_SIDECAR_SUBNET_COUNT` (i.e. a super-full node).
The particular columns that a node custodies are selected pseudo-randomly as a function (`get_custody_columns`) of the node-id and custody size -- importantly this function can be run by any party as the inputs are all public.
*Note*: increasing the `custody_size` parameter for a given `node_id` extends the returned list (rather than being an entirely new shuffle) such that if `custody_size` is unknown, the default `CUSTODY_REQUIREMENT` will be correct for a subset of the node's custody.
At each slot, a node advertising `custody_subnet_count` downloads a minimum of `subnet_sampling_size = max(SAMPLES_PER_SLOT, custody_subnet_count)` total subnets. The corresponding set of columns is selected by `get_custody_columns(node_id, subnet_sampling_size)`, so that in particular the subset of columns to custody is consistent with the output of `get_custody_columns(node_id, custody_subnet_count)`. Sampling is considered successful if the node manages to retrieve all selected columns.
In this construction, we extend the blobs using a one-dimensional erasure coding extension. The matrix comprises maximum `MAX_BLOBS_PER_BLOCK` rows and fixed `NUMBER_OF_COLUMNS` columns, with each row containing a `Blob` and its corresponding extension. `compute_extended_matrix` demonstrates the relationship between blobs and custom type `ExtendedMatrix`.
For each column -- use `data_column_sidecar_{subnet_id}` subnets, where `subnet_id` can be computed with the `compute_subnet_for_data_column_sidecar(column_index: ColumnIndex)` helper. The sidecars can be computed with the `get_data_column_sidecars(signed_block: SignedBeaconBlock, blobs: Sequence[Blob])` helper.
Verifiable samples from their respective column are distributed on the assigned subnet. To custody a particular column, a node joins the respective gossipsub subnet. If a node fails to get a column on the column subnet, a node can also utilize the Req/Resp protocol to query the missing column from other peers.
If the node obtains 50%+ of all the columns, it SHOULD reconstruct the full data matrix via `recover_matrix` helper. Nodes MAY delay this reconstruction allowing time for other columns to arrive over the network. If delaying reconstruction, nodes may use a random delay in order to desynchronize reconstruction among nodes, thus reducing overall CPU load.
Once the node obtains a column through reconstruction, the node MUST expose the new column as if it had received it over the network. If the node is subscribed to the subnet corresponding to the column, it MUST send the reconstructed DataColumnSidecar to its topic mesh neighbors. If instead the node is not subscribed to the corresponding subnet, it SHOULD still expose the availability of the DataColumnSidecar as part of the gossip emission process.
*Note*: A node always maintains a matrix view of the rows and columns they are following, able to cross-reference and cross-seed in either direction.
*Note*: There are timing considerations to analyze -- at what point does a node consider samples missing and choose to reconstruct and cross-seed.
*Note*: There may be anti-DoS and quality-of-service considerations around how to send samples and consider samples -- is each individual sample a message or are they sent in aggregate forms.
In the one-dimension construction, a node samples the peers by requesting the whole `DataColumnSidecar`. In reconstruction, a node can reconstruct all the blobs by 50% of the columns. Note that nodes can still download the row via `blob_sidecar_{subnet_id}` subnets.
The potential benefits of having row custody could include:
1. Allow for more "natural" distribution of data to consumers -- e.g., roll-ups -- but honestly, they won't know a priori which row their blob is going to be included in in the block, so they would either need to listen to all rows or download a particular row after seeing the block. The former looks just like listening to column [0, N) and the latter is req/resp instead of gossiping.
2. Help with some sort of distributed reconstruction. Those with full rows can compute extensions and seed missing samples to the network. This would either need to be able to send individual points on the gossip or would need some sort of req/resp faculty, potentially similar to an `IHAVEPOINTBITFIELD` and `IWANTSAMPLE`.
However, for simplicity, we don't assign row custody assignments to nodes in the current design.
To start with a simple, stable backbone, for now, we don't shuffle the subnet assignments via the deterministic custody selection helper `get_custody_columns`. However, staggered rotation likely needs to happen on the order of the pruning period to ensure subnets can be utilized for recovery. For example, introducing an `epoch` argument allows the function to maintain stability over many epochs.
