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e8823d9
Concurrent PSBT spec
nothingmuch Aug 4, 2026
eaeb023
Render math before mdbook-graphviz re-serializes the markdown
nothingmuch Oct 10, 2026
45d04a7
[WIP] Nest indented index entries as sub-chapters
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f71ae6b
Radix coinjoin denominations notebook
nothingmuch Aug 4, 2026
cd8717c
add a notebook derivation and a devshell for editing the notebook
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074f204
re-render notebook outputs with the notebook derivation
nothingmuch Oct 9, 2026
c694d0f
count combinations with replacement as multisets
nothingmuch Oct 9, 2026
8e5f763
clarify the notebook introduction
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3ab0a79
count combinations of up to k denominations, as the sumsets do
nothingmuch Oct 9, 2026
9c9b6c7
skip the median, not the 25th percentile, among the quantile dots
nothingmuch Oct 9, 2026
08ef6aa
clarify the sub-transaction counting argument
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34c8624
explain why sums are cut off above a multiple of max_denom
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adef927
explain subset sum density as an invariant of the mapping
nothingmuch Oct 9, 2026
92be6a9
Abstract cost function
nothingmuch Aug 4, 2026
b45805e
render jupyter notebook chapters as mdbook pages: hide code, paginate…
bc1cindy Aug 13, 2026
f7f60c5
[WIP] ████████████████████ Clarify abstract cost function
nothingmuch Aug 12, 2026
4c0c04b
assemble notebook chapters from docs/
nothingmuch Oct 22, 2026
c9657fb
fixup! Abstract cost function
nothingmuch Oct 22, 2026
46bd912
style plots: theme-neutral, colorblind-safe, re-rendered outputs
bc1cindy Aug 13, 2026
d8cc781
[WIP] ████████████████████ Record decision tree construction notes
nothingmuch Oct 22, 2026
fb7eaf4
point links to notebook chapters at their rendered pages
nothingmuch Oct 22, 2026
d2188cc
[WIP] ████████████████░░░░ Describe how the decision tree is built
nothingmuch Oct 22, 2026
12882cc
Skip separators and part titles when walking the book's chapters
nothingmuch Oct 22, 2026
f251904
[WIP] Add the cost function's words to the spelling dictionary
nothingmuch Oct 22, 2026
3090962
nb-table: print every row of paginated tables
bc1cindy Oct 12, 2026
3db8bc4
fixup! [WIP] ████████████████████ Clarify abstract cost function
nothingmuch Oct 22, 2026
7eb96cd
keep bar value labels black over the bar fills
bc1cindy Oct 12, 2026
f1e0775
fixup! Abstract cost function
nothingmuch Oct 22, 2026
3bbaca1
outline density series to read on dark pages
bc1cindy Oct 12, 2026
dfeb856
fixup! Abstract cost function
nothingmuch Oct 22, 2026
72b2b36
restore the density plot's legend frame
bc1cindy Oct 12, 2026
d2fd00e
fixup! Abstract cost function
nothingmuch Oct 22, 2026
f08d254
stop claiming six outputs close every gap above dust
nothingmuch Oct 9, 2026
ba2dc09
fixup! Abstract cost function
nothingmuch Oct 22, 2026
332eb9a
Keep the powers below the dust threshold until they are multiplied
nothingmuch Oct 23, 2026
1dc15c0
[WIP] Order inputs before outputs within a batch
nothingmuch Oct 22, 2026
ce1e6b3
Say that the gap plot's k=6 quantiles start at 2, not 1
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1a8d01c
[WIP] Model time dependence as piecewise linear offsets
nothingmuch Oct 22, 2026
8b3cd62
Bound the terms of a sum above the cutoff by its size alone
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64b6dd7
[WIP] Say what each end of the bracket means
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6048332
Say that a k:1 exchange changes the weight, not the fee
nothingmuch Oct 23, 2026
7cb54eb
[WIP] Distinguish the pure and mixed strategies
nothingmuch Oct 22, 2026
4e0549d
Qualify the density argument by the denominations that remain
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dca8177
[WIP] Describe commitment in multiparty protocols
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3d0b9d7
Define the on-chain privacy problems being addressed
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f466a31
Show the denomination generating code in the book
nothingmuch Oct 23, 2026
3abccd7
Merge the concurrent PSBT spec onto the book structure
nothingmuch Oct 23, 2026
c0d0ac8
[WIP] Rewrite the global privacy budget
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69cc036
Edits to Collaborative Transaction Privacy (#30)
deutschbitte Sep 9, 2026
c9cc193
Coalition formation
nothingmuch Aug 4, 2026
4f8b8cc
Show the sumset and gap computation code in the book
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d98dc69
Fix typos and a broken anchor in the concurrent PSBT spec
nothingmuch Oct 23, 2026
26f0b2c
[WIP] ████████████████░░░░ Penalize co-spend proposals that leak a co…
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5cb7688
Revise and clarify following editorial pass
nothingmuch Oct 9, 2026
e5cca89
Arrange the index into the parts proposed in #19
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1d16c3d
[WIP] ████████████████░░░░ Add input value constraints to proposal co…
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0b760af
Show the analysis parameters in the book
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ae28f03
Move the concurrent PSBT spec into the book
nothingmuch Oct 23, 2026
50ab0fc
fixup! [WIP] ████████████████░░░░ Describe how the decision tree is b…
nothingmuch Oct 23, 2026
59ce690
fixup! [WIP] Say what each end of the bracket means
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ada4152
[WIP] ████████████████████ Describe the greedy decision loop
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a3a6ae2
[WIP] ████████████████████ Give the decision loop its own heading
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d8c739a
[WIP] ██████████████████░░ Move tree construction to the strategy cha…
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480d871
[WIP] ████████████████░░░░ Rename the chapter to Optimization framework
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424d28b
[WIP] ████████████████████ Introduce the strategy as generating and e…
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2e3c4c1
[WIP] ████████████████░░░░ Move the mixed strategy into its own chapter
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1241a68
[WIP] Add the Pure Strategy Evaluation chapter
nothingmuch Oct 24, 2026
66962a5
[WIP] ████████████████░░░░ Mark agent-generated text with 🤖
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746b8a2
[WIP] Add the Tactics chapter
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9db08a1
[WIP] Call the greedy loop a decision loop run as a greedy search
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d144f76
[WIP] Add the Privacy liability terms chapter
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3746f2e
Add an overview
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564eafe
[WIP] Specify peer and broadcast channels
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0f938de
[WIP] Move the cost function's structure into its own chapter
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8ae2f82
[WIP] Describe what each privacy liability term is for
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8080f86
Link the optimization framework chapter by its new file name
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12dfe89
[WIP] Compare candidate transports for the channels
nothingmuch Oct 25, 2026
59bd957
Move the problem definition into the mdbook
nothingmuch Oct 7, 2026
380b9bd
[WIP] Link the Tactics and Privacy liability terms chapters
nothingmuch Oct 24, 2026
ae24c1a
[WIP] Outline max flow based counterfactual path estimation
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4a94f1c
[WIP] Outline the consolidation penalty
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f410526
[WIP] Outline subset sum density, subset sum ambiguity and the siblin…
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89dfa42
[WIP] Add the randomized selection and Sybil resistance chapters
nothingmuch Oct 24, 2026
3e10b5d
[WIP] Add the Bottom-up construction chapter
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bc18c81
[WIP] Group the privacy metrics after the privacy liability terms
nothingmuch Oct 26, 2026
686efee
[WIP] Point the overview at the channel interfaces and asymmetric trust
nothingmuch Oct 23, 2026
d483a2e
[WIP] Specify the protocol messages
nothingmuch Oct 22, 2026
89a6e00
[WIP] Specify contacts and payment messaging
nothingmuch Oct 15, 2026
31f505e
[WIP] Move the BIP 322 gossip rules into peer to world broadcast
nothingmuch Oct 23, 2026
dd81be7
[WIP] Specify the abstract transport interfaces
nothingmuch Oct 22, 2026
330989b
Refer to the Radix CoinJoin Denominations chapter
nothingmuch Oct 23, 2026
915c548
README do-over
nothingmuch Oct 20, 2026
b846cd8
Merge the cost function term chapters
nothingmuch Oct 24, 2026
c7a5c9c
[WIP] Specify peer set reconciliation
nothingmuch Oct 14, 2026
b1b1e23
[WIP] Distinguish lists from sets, not DAG from non-DAG
nothingmuch Oct 23, 2026
8183885
[WIP] Specify the allocation registration validity proofs
nothingmuch Oct 17, 2026
786eefe
[WIP] Specify the recovery track
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eae73a6
[WIP] Specify the block DAG
nothingmuch Oct 23, 2026
2b8c84d
[WIP] Introduce transaction construction
nothingmuch Oct 23, 2026
950eca6
[WIP] Specify the optimistic track
nothingmuch Oct 14, 2026
41e5535
Integrate the protocol chapters
nothingmuch Oct 23, 2026
e6b5b0b
[WIP] Move the BIP 322 gossip rules to peer to world broadcast
nothingmuch Oct 23, 2026
0130924
Integrate the chapters under review
nothingmuch Oct 23, 2026
8e41ba2
[WIP] Serve the draft from /docs-draft/
nothingmuch Oct 23, 2026
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1 change: 1 addition & 0 deletions .gitignore
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book/
result
.ipynb_checkpoints/
11 changes: 11 additions & 0 deletions .typos.toml
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[default.extend-identifiers]
# Mermaid class for Alice's cluster in the intersection diagram.
aci = "aci"
# Author of The Byzantine Generals Problem.
Pease = "Pease"
# Author of Asymmetric Distributed Trust.
Cachin = "Cachin"

[default.extend-words]
# Groth16, the proof system named after Jens Groth.
Groth = "Groth"
51 changes: 31 additions & 20 deletions README.md
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# Fungi

This repository contains documents that describe a family collaborative Bitcoin transaction construction protocols. The protocols form a progression towards decentralized and market based privacy preserving transactions.
Fungi is a protocol for collaborative transactions designed to make using Bitcoin more private. Participants can also pay each other interactively in these transactions, which helps not just privacy but also blockspace efficiency.

A software development kit (SDK) is [in development](https://github.com/fungi-protocol/fungi). This repository contains the specifications and the analysis behind them.

> [!NOTE]
> **Work in progress**: most chapters are still under review. See the [open pull requests](https://github.com/fungi-protocol/docs/pulls) for material being drafted.
> **Work in progress**: most chapters are drafts under review. See the [open pull requests](https://github.com/fungi-protocol/docs/pulls) for material being drafted.
>
> Chapters, sections or paragraphs marked with 🤖 are LLM output. They have been partly verified but have not yet been edited or rewritten as necessary, and should be considered a working draft.

## Background

Censorship resistance and fungibility are among Bitcoin's foundational properties. Without privacy, both can be undermined largely outside the protocol's rules, whether by targeting specific individuals or through chilling effects.

Bitcoin transactions are public data, and they are connected in a graph structure. Chain analysis is the application of heuristics to this graph to infer which coins share an owner. While no heuristic is perfect, their effectiveness has been shown in numerous studies. Several heuristics can be combined for a more accurate analysis. Analysis might also draw on auxiliary information not recorded on the blockchain, such as which coins an exchange sent to which customer.

CoinJoin transactions seek to undermine some of the heuristics used to cluster coins across the transaction graph. They combine several users' inputs and outputs in one transaction in order to obscure ownership links within it. Several CoinJoin implementations exist with different approaches to their transaction structure.

## Fungi protocol suite
## Problem statement

### Honest setting
Unfortunately, CoinJoin privacy is often stated in terms of the number of indistinguishable outputs in a transaction. This tacitly ignores the fact that those coins will go on to be spent. The information revealed by the spending transactions, which are themselves related to other transactions, can dramatically affect privacy, in some cases making the CoinJoin inputs linkable to the outputs.

The *honest* setting assumes all participants can be trusted in two ways:
Recurring relationships give rise to patterns too. Transacting with the same employers, shops and friends leaves a structure in the transaction graph, even if techniques like PayJoin might hide the individual amounts and confound some of the clustering heuristics. Obscuring this structure necessitates transacting with unrelated users, chosen at random, so users who don't know or trust each other need a way to find each other and agree on a transaction. Random selection must additionally be Sybil resistant, so that the cost of an $n-1$ deanonymization attack, where the adversary controls all of the other (apparent) participants, is a sufficient deterrent.

- not to disrupt the execution of the protocol
- with privacy, which means not revealing to the adversary, ideally forgetting, any information that may be revealed by participants in the course of the protocol's execution
In general, deanonymizing a single user always makes it easier to deanonymize the other users. But sometimes the adversary might progress not just by process of elimination, but more like divide and conquer. This happens when deanonymizing that one user splits the problem of deanonymizing the rest into several smaller problems, as opposed to merely making it incrementally smaller.

In this as well as subsequent protocol, trust never means giving up control over one's funds. Input signatures in transactions enforce this safety by letting each party ensure its , requiring unanimous consent by all parties.
The [problem definition](docs/collaborative_txn_privacy.md) chapter discusses these on-chain privacy leaks in depth, and describes a particular transaction graph structure that resists deanonymization more robustly.

### Semi-honest setting
## How Fungi works

In the *semi-honest* setting, also known as *honest-but-curious*, we no longer assume peers have to be trusted to keep a secret. Instead this relies on privacy preserving transports for the communication, that allow a peer to broadcast its messages anonymously to the other participants. Because Bitcoin transactions are transparent, privacy further demands a more careful approach to transaction construction, or the actions of a peer may be revealing even if not directly attributable.
A user first tells their wallet which payments they intend to make, and the wallet keeps these in a queue. Intents can vary in their time, privacy or cost sensitivity. Making a payment quickly, cheaply and privately is a balancing act, and improving one usually means compromising on another. The wallet's job is to construct transactions that make the queued payments, balancing these goals in line with the user's preferences.

The semi-honest setting can provide some degree of confidentiality, especially against 3rd party observers, through the construction of net settlement transactions. But not anonymity. Transactions between peers that are somehow related have inherent privacy issues because such relationships constitute a social network, exhibiting community structure.
The wallet schedules and batches payments, negotiating with other participants to find terms that suit the user's priorities. The more flexible a payment's timing, the more cost-effective it can be, because there is more time for compatible proposals to be combined, so that its cost can be shared with more participants. The protocol and the strategy are designed together, and the SDK implements both.

### Byzantine fault tolerant setting
Avoiding links between coins is central to the strategy. The input and output amounts can imply such links if there aren't enough possibilities for how to group inputs and outputs so their totals match. But as mentioned above, a partition of a transaction's coins can also be evaluated based on the surrounding context in the transaction graph, not just the amounts associated with that transaction. So the strategy must consider not just whether the transaction's internal structure is sufficiently ambiguous, but also how a transaction sits in the wider transaction graph.

Overcoming the community analysis concern requires a Sybil resistant, permissionless protocol where peers with no meaningful economic relationship can find each other. This involves an additional *coalition formation* protocol that sets up transaction construction using a market based mechanism.
In Fungi, a *co-spend proposal* sets out the terms for spending a set of coins together. Proposals are made automatically according to the privacy optimization strategy. The transaction-wide terms of a co-spend proposal are public, constraining things like the range of acceptable feerates or whether or not non-SegWit inputs can be used. Proposals can also include fees, which are kept confidential. A proposal involving three or more parties additionally hides which of them made the proposal. Once accepted by all parties, co-spend proposals are publicly broadcast.

While it is beneficial for privacy, interacting with strangers in a permissionless protocol invites disruption or attempts at surveillance. For honest peers to be able to reliably transact, especially with the unanimity requirement, demands a byzantine fault tolerance from the transaction construction protocol.
Any participant can collect fully accepted co-spend proposals from multiple parties, and then make a *coalition formation proposal* which aggregates them together, so long as the terms are compatible. If everyone accepts the coalition formation proposal, then a coalition has been formed, and the parties can proceed with collaborative transaction construction. Privacy is brittle in small transactions. A critical mass of participants is therefore necessary for privacy to be robust and cost-effective, and coalition formation is designed to facilitate such a critical mass forming.

In the course of a BFT interaction with untrusted peers, a participant may still use the other variants of the protocol to coordinate activity with the subset of peers they do know or trust, for instance by performing net-settlement within a larger BFT CoinJoin.
During collaborative transaction construction, participants add their intended inputs and outputs anonymously. This preserves the unlinkability of inputs and outputs so long as it isn't undermined in some other way (for example by reusing an output address). Interactive payments additionally provide privacy against the payment counterparty. In addition to hiding the payment amount from third parties, the sender and receiver do not learn about each other's coins. Since many interactive payments can be settled in one collaborative transaction, this creates the opportunity for blockspace savings.

## Motivation
In order to ensure funds are secure throughout, every participant retains control at all times and therefore signs their own inputs. Unfortunately, this means that as the number of participants grows, reliability will necessarily degrade. Even if the probability of any one participant causing a fault is low, that compounds when considering the probability that none of them will. Transaction construction is designed to be fault-tolerant, so that even when a valid transaction has not successfully been produced, participants have a basis to refine the coalition structure. Fault tolerance includes malicious disruption.

Wallet clustering is the broad term for a variety of techniques that can be used to deanonymize on chain activity. Clustering involves linking particular coins to one another, attributing their ownership to the same entity. Over the course of Bitcoin's existence many papers have been published on this subject, also about related privacy issues issues, such as Lightning network, or the transport layer.
## Compared to JoinMarket

This body of work has, time and again, shown that misconceptions about privacy invariably err on the side of optimism. Moreover, depending on individual users' threat models, their adversary may have access to comprehensive auxiliary information. Such auxiliary information doesn't even need to be about the target user, information about other users may be useful for deanonymization of the target user. In cryptography, rotating long lived keys or favoring ephemeral ones can limit the scope of a compromise, but an individual's identity is who they are.
Fungi could be described as a spiritual successor to JoinMarket (as implemented by [JoinMarket](https://github.com/JoinMarket-Org/joinmarket-clientserver) and [JoinMarket-NG](https://github.com/joinmarket-ng/joinmarket-ng)). Like JoinMarket, it is peer-to-peer and market-based, with no centralized coordinator, but differs substantially in how it approaches the order book mechanism as well as transaction construction.

The fungi protocol suite is designed to make arbitrary transactions possible between mutually consenting but distrusting peers. This means safety, liveness, and unlinkability of protocol messages. Within such a protocol peers are free to pursue whatever outcomes they desire.
JoinMarket distinguishes two roles: in each transaction, a user in the role of the taker selects several makers from the order book. Makers advertise their willingness to participate in CoinJoin transactions. Generally, the taker will pay the on-chain fees as well as any maker fees. The taker learns which coins belong to the makers it pays, so makers get no privacy from the taker. And because there is a single taker, a transaction can only include as many participants as one taker is willing to pay for.

Privacy does not simply emerge naturally from collaborative transactions. Peers must actively optimize for that. Optimization involves the use of a cost function, an extension or generalization of the kind used for coin selection. This repository makes specific recommendations with which the protocols are designed to be compatible. The recommended privacy related terms address Sybil resistance, the transaction structure (for example how output values are chosen in relation to others' input values) and the graph structure.
Fungi makes no distinction between the taker and maker roles. Instead, a participant can both send and accept proposals, and proposals involving multiple users can be aggregated, allowing a single transaction to be negotiated more as a group buy of blockspace. As the number of participants grows, the privacy benefits compound for everyone, which means each individual user needs to pay for proportionately less blockspace in order to meet their individual privacy requirements. Finally, the proposed transaction structure aims to address several deanonymization attacks that were not yet understood at the time JoinMarket's design was put in place.
10 changes: 9 additions & 1 deletion book.toml
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Expand Up @@ -6,6 +6,11 @@ src = "src"
[build]
create-missing = false

[preprocessor.jupyter]
command = "python3 contrib/jupyter_nb.py"
after = ["links"]
before = ["graphviz", "mermaid", "katex"]

[preprocessor.graphviz]
command = "mdbook-graphviz"
after = ["links"]
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[preprocessor.katex]
command = "mdbook-katex"
after = ["links"]
# mdbook-graphviz re-serializes the markdown, escaping the TeX source.
before = ["graphviz"]

[output.html]
additional-css = ["theme/diagrams.css"]
git-repository-url = "https://github.com/fungi-protocol/docs"
site-url = "/docs/"
site-url = "/docs-draft/"

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Not-found page base points to a path the Pages workflow does not deploy

On merge, the Pages workflow publishes the site at /docs/ (as docs/README.md documents), but site-url makes mdbook write <base href="/docs-draft/"> into the 404 page, so its CSS and JS resolve under a path the workflow does not deploy.

oak · automated · 8e41ba2

additional-js = ["theme/nb-table.js"]
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