update readme

Author: jianshu93

README.md

@@ -114,42 +114,42 @@ estimated weighted Jaccard: 0.004638671875
 
 Test for true weighted Jaccard from 0.005 to 0.98. Output for ERS:
 ```bash
-true weighted Jaccard: 0.9801980198019894
-estimated weighted Jaccard: 0.979248046875
-true weighted Jaccard: 0.923076923076927
-estimated weighted Jaccard: 0.916259765625
-true weighted Jaccard: 0.8691588785046818
-estimated weighted Jaccard: 0.870361328125
-true weighted Jaccard: 0.8181818181818254
-estimated weighted Jaccard: 0.815185546875
-true weighted Jaccard: 0.7391304347826214
-estimated weighted Jaccard: 0.728271484375
-true weighted Jaccard: 0.6666666666666645
-estimated weighted Jaccard: 0.661865234375
-true weighted Jaccard: 0.6000000000000002
-estimated weighted Jaccard: 0.602783203125
-true weighted Jaccard: 0.538461538461545
-estimated weighted Jaccard: 0.54296875
-true weighted Jaccard: 0.48148148148149517
-estimated weighted Jaccard: 0.4736328125
-true weighted Jaccard: 0.4285714285714275
-estimated weighted Jaccard: 0.42724609375
-true weighted Jaccard: 0.3793103448275884
-estimated weighted Jaccard: 0.373291015625
-true weighted Jaccard: 0.3333333333333343
-estimated weighted Jaccard: 0.320068359375
-true weighted Jaccard: 0.2500000000000003
-estimated weighted Jaccard: 0.241943359375
-true weighted Jaccard: 0.17647058823529319
-estimated weighted Jaccard: 0.187255859375
-true weighted Jaccard: 0.11111111111111192
-estimated weighted Jaccard: 0.110595703125
-true weighted Jaccard: 0.05263157894736851
-estimated weighted Jaccard: 0.04638671875
-true weighted Jaccard: 0.025641025641025394
-estimated weighted Jaccard: 0.026611328125
-true weighted Jaccard: 0.00502512562814068
-estimated weighted Jaccard: 0.00537109375
+true weighted Jaccard: 0.980198019801974
+estimated weighted Jaccard: 0.981689453125
+true weighted Jaccard: 0.9230769230769282
+estimated weighted Jaccard: 0.930419921875
+true weighted Jaccard: 0.869158878504667
+estimated weighted Jaccard: 0.873779296875
+true weighted Jaccard: 0.818181818181824
+estimated weighted Jaccard: 0.813232421875
+true weighted Jaccard: 0.7391304347826144
+estimated weighted Jaccard: 0.743408203125
+true weighted Jaccard: 0.6666666666666666
+estimated weighted Jaccard: 0.6650390625
+true weighted Jaccard: 0.6000000000000038
+estimated weighted Jaccard: 0.593994140625
+true weighted Jaccard: 0.5384615384615451
+estimated weighted Jaccard: 0.52978515625
+true weighted Jaccard: 0.4814814814814917
+estimated weighted Jaccard: 0.477783203125
+true weighted Jaccard: 0.42857142857142766
+estimated weighted Jaccard: 0.4443359375
+true weighted Jaccard: 0.3793103448275924
+estimated weighted Jaccard: 0.36767578125
+true weighted Jaccard: 0.33333333333333287
+estimated weighted Jaccard: 0.32275390625
+true weighted Jaccard: 0.24999999999999994
+estimated weighted Jaccard: 0.25390625
+true weighted Jaccard: 0.17647058823529382
+estimated weighted Jaccard: 0.1767578125
+true weighted Jaccard: 0.11111111111111145
+estimated weighted Jaccard: 0.112060546875
+true weighted Jaccard: 0.052631578947368515
+estimated weighted Jaccard: 0.05126953125
+true weighted Jaccard: 0.025641025641025373
+estimated weighted Jaccard: 0.030029296875
+true weighted Jaccard: 0.00502512562814075
+estimated weighted Jaccard: 0.005859375
 
 ```
 

src/rejsmp.rs

@@ -3,8 +3,10 @@
 //! Implements:
 //!   - RS (Shrivastava 2016): Algorithm 1/3 with constant-time ISGREEN via
 //!     integer-to-component and component-to-M maps.
-//!   - ERS (Li & Li 2021): single shared stream r_t, early stopping, and a safe
-//!     densification fallback using tabulation hashing.
+//!   - ERS (Li & Li 2021): K independent fixed-length sequences
+//!     r_{j,1..L} per hash position j; take the first green if any, otherwise mark
+//!     empty; then densify empties by uniformly picking from the non-empty positions.
+//!     All randomness is produced via tabulation hashing for consistency/speed.
 //!
 //! Inputs: sparse weighted vector `&[(u64, f64)]` where id ∈ [0, D) and weight ≥ 0.
 //! Randomness: purely via Tab32/Tab64 tabulation hashing (no stateful RNG required).
@@ -157,10 +159,11 @@ impl RsWmh {
     }
 }
 
-/// ERS MinHash (AAAI Algorithm 2): K independent fixed-length random sequences.
+/// ERS (AAAI Algorithm 2): K independent fixed-length random sequences.
 /// For each j in 0..K, scan r_{j,1},...,r_{j,L}; take first green. If none, mark E.
 /// Then densify: replace each E by a deterministic donor via rotation.
-/// ID is derived from the ACCEPTING COMPONENT INDEX i (and j), not from t.
+/// ID is derived from the ACCEPTED DRAW (j, t*) in the fixed sequence, not just the component.
+/// Using a per-draw identity ensures two sets collide iff they accept the same r_{j,t*}.
 pub struct ErsWmh {
     index: RedGreenIndex,
     d: usize,