logos-blockchain/research
1
0
Fork 0
mirror of https://github.com/logos-blockchain/research.git synced 2026-08-11 05:33:32 +00:00
Code Issues Packages Projects Releases Wiki Activity

Correct §6.9's fork-depth figures to the post-fix measurement

Browse Source 
The depths quoted for the rival-coalition mechanism came from an exploratory run
made before the coalition-sizing fix, where beta=0.4 was realising 0.47. Measured
properly (median over 6 replicates, deepest fork off the canonical chain):

  K=1  865 blocks (784-964)    K=2  17    K=3  9    K=4  7

not the "~2000 and ~2" first written. The mechanism is unchanged and the contrast
is still stark. Also notes why the lead cap does not bound this: it caps the
LEAD, not the chain length, so a private chain can run long while the public
chain keeps pace beside it — the near-tie race that produces the deepest forks.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
This commit is contained in:
Marcin Pawlowski 2026-08-10 12:49:29 +02:00
parent 563db81b42
commit 6f28882510
No known key found for this signature in database
1 changed files with 1 additions and 1 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

2
reports/tsi/README.md
View File

@ -727,7 +727,7 @@ Everything above assumed a single coalition; this section asks what changes when
| 0.30 | 0.778 | 0.858 | 0.880 | 0.880 |
| 0.40 | 0.586 \* | 0.764 | 0.807 | 0.823 |
The mechanism is visible in the fork structure: a lone coalition holds one deep private chain (measured max fork depth ~2 000 blocks at `β` = 0.4), while rivals cut each other short (depth ~2 at `K` = 2). Rival coalitions spend their advantage orphaning *each other's* blocks instead of honest ones, so less honest work is displaced and the counted density recovers. **`D̂ ≈ 0.70` at `α` = 0.4 is therefore an upper bound on multi-coalition deflation after all**, not the under-estimate [§6.9](#s6-9) previously warned it might be. (\* the `β` = 0.4, `K` = 1 cell is boundary-affected — 66 % of its adversarial blocks were still private when the epoch ended even with the lead cap of [§9](#s9) — so read it as directional. The `β` = 0.2 and 0.3 rows have <1 % stranding and carry the result on their own.)
The mechanism is visible in the fork structure. At `β` = 0.4 the deepest fork off the canonical chain has median depth **865 blocks** with one coalition, **17** with two, and **7** with four: a lone coalition builds one long private chain, while rivals cut each other short. (The lead cap of [§9](#s9) bounds the *lead*, not the length — a private chain can run long while the public chain keeps pace beside it, which is exactly the near-tie race that produces the deepest forks.) Rival coalitions spend their advantage orphaning *each other's* blocks instead of honest ones, so less honest work is displaced and the counted density recovers. **`D̂ ≈ 0.70` at `α` = 0.4 is therefore an upper bound on multi-coalition deflation after all**, not the under-estimate [§6.9](#s6-9) previously warned it might be. (\* the `β` = 0.4, `K` = 1 cell is boundary-affected — 66 % of its adversarial blocks were still private when the epoch ended even with the lead cap of [§9](#s9) — so read it as directional. The `β` = 0.2 and 0.3 rows have <1 % stranding and carry the result on their own.)
**The threshold half is confirmed, and `⅓` does not hold at this load.** Per-coalition profitability — a coalition's share of the canonical chain against its own stake, `>1` meaning selfish mining pays: