Elaborated on tx-lifetime analysis (#628)

* Scripts for computing active slots
* Generated SVG figures
* Computed number of utxos spend when they are created
* Documented findings

Author: bwbush

docs/post-cip-findings.md

@@ -33,4 +33,18 @@ The `linleios` program executes the Markov model for EB production in Linear L
 
 The figure below shows example results for the probability distribution of the number of EBs generated per 100 RBs. This directly relates to Leios efficiency.
 
-![Example results](../analysis/markov/example-results.png)
+![Example results](../analysis/markov/example-results.png)
+
+## Analysis of UTxO set size and UTxO lifetime
+
+[Analysis of Cardano mainnet](../post-cip/tx-lifetime/tx-lifetime.ipynb) indicates that the number of active UTxOs has leveled off at approximately 11 million unspent transaction outputs. The data likely is not sufficient to build a statistical model to forecast the size of the UTxO set as a function of demand: a more speculative model would be needed.
+
+![Size of mainnet UTxO set as a function of slot number](../post-cip/tx-lifetime/utxo-set.png)
+In terms of lifetime, UTxOs have a trimodal distribution:
+- About 3% of UTxOs are spent in the same block that they are created.
+- About 65% of the UTxOs are active less than one day.
+- The remainder are active for multiple days, sometimes for months or years.
+
+|                                                                                                                 |                                                                                                                  |
+| --------------------------------------------------------------------------------------------------------------- | ---------------------------------------------------------------------------------------------------------------- |
+| ![Distribution of UTxO lifetime on mainnet (square-root scale)](../post-cip/tx-lifetime/utxo-lifetime-sqrt.svg) | ![Distribution of UTxO lifetime on mainnet (logarithmic scale)](../post-cip/tx-lifetime/utxo-lifetime-log10.svg) |

post-cip/active-slots/active-slots.sh

@@ -0,0 +1,5 @@
+#!/usr/bin/env bash
+
+psql -f active-slots.sql mainnet
+
+pigz -9fv active-slots.tsv

post-cip/active-slots/active-slots.sql

@@ -0,0 +1,20 @@
+
+drop table if exists active_slots;
+
+create table active_slots as
+select
+    slot_no
+  , cast(slot_no - lag(slot_no, 30, null) over (order by slot_no asc) as float)
+    / (block_no - lag(block_no, 30, null) over (order by block_no asc))
+    as slots_per_block
+  , (block_no - lag(block_no, 30, null) over (order by block_no asc))
+    / cast(slot_no - lag(slot_no, 30, null) over (order by slot_no asc) as float)
+    as blocks_per_slot
+  from block
+  where block_no is not null
+  order by block_no
+  desc
+;
+
+\copy active_slots to 'active-slots.tsv' csv header delimiter E'\t'
+