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+=================
+Adaptive Slashing
+=================
+
+
+Overview
+========
+
+In Oxford2, each instance of a baker's misconduct results in the
+slashing of a fixed percentage of their staked funds. However, this
+approach does not distinguish between innocent mistakes and deliberate
+attacks. The rule conservatively punishes every misconduct with strong
+penalties. The rationale for this model is its simplicity and the
+observation that the cost of avoiding these mistakes is low anyway.
+Nonetheless, it overlooks the impact of double signing of attestations
+on the entire block committee, treating all cases uniformly and
+ignoring collusion among bakers.
+
+To better reflect this distinction, the Paris protocol
+adjusts the amount of slashing based on the fraction of
+double-attestation in a single block. A low fraction of misconduct
+incurs moderate penalties, while a high fraction of misconduct is
+deemed to be critical and faces more serious repercussions.
+
+This document presents the definition of an :ref:`adaptive slashing
+function<adaptive_slashing_fn>` implementing this idea, as well as a
+:ref:`new forbidden period<new_forbidden_period>`.
+
+.. _adaptive_slashing_fn:
+
+Adaptive Slashing Function
+==========================
+
+.. _adaptive_slashing_informal:
+
+Informal presentation
+---------------------
+
+For a given block, we call “fraction of double-attestations” the ratio
+between the total weight of attestations for which a valid
+denunciation has been included and the total weight of possible
+attestations in a block.
+
+The shape of the slashing function for double attestations is the
+following:
+
+.. figure:: adaptive-slashing-new.jpeg
+
+
++------------------------------------------+----------------------------------------+
+| f: fraction of double attestations       | S: slashing ratio                      |
++==========================================+========================================+
+| 1.00%                                    | 0.09%                                  |
++------------------------------------------+----------------------------------------+
+| 5.00%                                    | 2.25%                                  |
++------------------------------------------+----------------------------------------+
+| 10.00%                                   | 9.00%                                  |
++------------------------------------------+----------------------------------------+
+| 20.00%                                   | 36.00%                                 |
++------------------------------------------+----------------------------------------+
+| 23.57%                                   | 50.00%                                 |
++------------------------------------------+----------------------------------------+
+| 33.34%                                   | 100.00%                                |
++------------------------------------------+----------------------------------------+
+| 100.00%                                  |                                        |
++------------------------------------------+----------------------------------------+
+
+Instead of using a constant function as in Oxford2, we propose to use
+a convex function that saturates at 100% when a critical fraction of
+doubled attestations are issued. Accidental double attestations are
+unlikely to cause a large amount of slashing to be applied, but
+concerted attacks result in severe penalties.
+
+\ **Remark 1.** Even though the baker does not attest to a weight
+exactly equivalent to its staked funds at each block, the slashing
+function is applied to bakers’ total staked funds for simplicity.
+
+\ **Remark 2.** As in Oxford2, slashing happens at the end of each
+cycle. Since the denunciation period for a block ranges over its cycle
+and the next one, a baker can be punished for misbehaving during the
+previous cycle, not only the one that has just ended.
+
+\ **Remark 3.** If a baker wants to get back their at-stake funds, it
+takes more than 2 cycles to complete the unstaking process. This
+ensures that the baker can't decrease their at-stake funds after being
+denunciated and before facing penalties.
+
+.. _formal_adaptive_slashing:
+
+A formal definition of slashing function for double-attestations
+----------------------------------------------------------------
+
+* :math:`\mathcal{W}` denotes the maximal possible *weight* of
+  attestations in a block, that is, the fixed number of available
+  :ref:`slots<rights_paris>` in any block. It is also known as
+  :ref:`CONSENSUS_COMMITTEE_SIZE<tb_validator_paris>`.
+
+* :math:`f(B)` is the *fraction of double attestations* for block
+  :math:`B`, that is, the ratio of the total weight of double
+  attestations in :math:`B`, over :math:`\mathcal{W}`.
+
+* :math:`T` is the *threshold* for the fraction of double attestations
+  to be considered critical. A typical value for :math:`T` is
+  :math:`{1 \over 3} \mathcal{W}`, which is the difference between
+  :math:`\mathcal{W}` and the
+  :ref:`CONSENSUS_THRESHOLD<tb_validator_paris>` which is set to
+  :math:`{2 \over 3} \mathcal{W}`.
+
+We define :math:`S(B)` the percentage of slashed funds for all
+misbehaving bakers at the block :math:`B` as follows:
+
+:math:`S(B) = \text{min} (100\%, {1 \over T^2} \cdot f(B)^2 \cdot 100\%)`
+
+Then, the percentage of slashed funds :math:`S(b,C)` for a baker
+:math:`b` at the end of the cycle :math:`C` is defined as follows:
+
+:math:`S(b, C) = \text{min} (100\%, \sum_{(b, B) \in C} S(B))`
+
+where :math:`(b, B) \in C` means that:
+
+* the double attestation by baker :math:`b` of block :math:`B` has
+  been denounced before the end of cycle :math:`C`, and
+
+* :math:`C` is the last cycle of the denunciation period for
+  :math:`B`.
+
+.. _new_forbidden_period:
+
+A new definition for the forbidden period
+=========================================
+
+Given that slashing occurs with a delay, immediate action at
+denunciation time is necessary upon clear evidence of a baker's
+misbehavior to prevent further misconduct, or to protect the baker
+against their own faulty setup. Any double-signing denunciation
+immediately triggers the beginning of a forbidden period that lasts at
+least 2 cycles, to make sure the slashing occurs before accepting new
+attestations or blocks from the baker. Note that it is still possible
+for one baker to commit multiple double signings, but only if they all
+happen before any corresponding denunciation gets included in a block.
diff --git a/docs/paris/protocol.rst b/docs/paris/protocol.rst
index da493586f242f61eb909b15f040579e180c7a31e..080d9f0023d5b71856716283d123e7f7c491f65e 100644
--- a/docs/paris/protocol.rst
+++ b/docs/paris/protocol.rst
@@ -117,6 +117,11 @@ Sapling, etc), and some details about its implementation.
 
    adaptive_issuance
 
+.. toctree::
+   :maxdepth: 2
+
+   adaptive_slashing
+
 .. toctree::
    :maxdepth: 2