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ADIC
Recorded: Aug. 23, 2025 Duration: 0:21:27Space Recording
Full Transcription
Hello everyone. I am going to get started since this is recorded. I won't be waiting for any particular audience to get going.
I am going to start by reviewing the white paper for AtticDAG, which is a new Layer 1 Distributed Ledger technology that I have invented with our collaborators here at the facility meaning the facility in canada physically where the team is working and
having the iso 9001 2015 audits for the organization and the other standardization occurring with the team and
operational backing behind the release of the new layer one uh notably the xi protocol protocol, XI token, and GEC, Desai meme coin
as well will be honored in
not as a liability swap or transfer, but having a
special place in the ecosystem with respect to an upcoming
snapshot and resulting
functionality thereof,
which will be further detailed.
But for now I'm focusing entirely
as a self-contained introduction to Attic
and the directed acyclic graph system
that Attic is as a L1.
I'm focusing on the description of the system and what the project is moving forward.
So we introduce AtticDAG, a feeless, reputation-weighted distributed ledger that organizes messages as a higher-dimensional directed acyclic hypergraph, a tangle of D-simplices.
The core novelty is a piatic ultrametric structure on message features enforcing multi-axis diversity at attachment time via D approvals.
Each new message forms a D simplex by approving D plus one parents across piatic neighborhoods.
This yields strong resistance to collision and symbols without transaction fees.
Finality is certified by one of two features one is a k-core coverage
test with access diversity thresholds and the other is stabilization in persistent homology
on the induced simplicial complex so that's a lot to perhaps process as a not a mathematician but essentially the tangle as originally invented
by the iota project um which i was a part of early on in 2017 and 2017 and then becoming
the cubic architect thereafter i was focusing on further generalizations of outsourced distributed
consensus which ended up leading to the innovations that caused what was depicted in XI protocol for the meta-oracle.
This system also is implementing the first arithmetic meta-oracles,
so there is a continuity of thought as well as architecture connecting the projects but xi as is is insufficient to be describing or utilizing
ethereum for this because this isn't a new layer one system entirely itself
in iota with the tangle which was the sort of original planar two dimensional version of this sort of system where you don't generate
a simple complex you're not generating simplices with higher dimensional features it's always
just a planar representation possible where if you post a tip meaning an attempted transaction
it is needing to verify two other transactions to be able to be considered as a having finality so
there were other problems with iota that ended up like for example there was a cryptographic
hash function called curl which mit dci ended up showing was exposed but that wasn't fundamental to the idea of a DAG. And there are higher dimensionalities
that are possible, or higher dimensional simplicial complex features. By simplicial
complex, I mean essentially a set of simplices that are in a certain arrangement. And a simplex
is a generalization of a triangle or a tetrahedron to higher dimensions. So if you have a planar tiling of triangles with a graph that, you know, the vertices are the points and the edges are the edges of the graph,
then that would construct a two-dimensional graph that is made of two simplices, namely triangles.
a two-dimensional graph that is made of two simplices, namely triangles.
If you have three simplices, namely three-dimensional simplices,
that's like a three-simplex is a tetrahedron.
So that's the smallest platonic solid that has four triangular faces constructing it.
And then there are higher simplices as well.
But for now, for the initial version of the
protocol instead of abstracting so far to like you know four five six seven eight dimensional simplices and doing all these other um more general parameter sets for p and d mainly like the prime
and the dimension that you're looking at the piatic numbers and as well as the dimension
of the simplicial complexes in. So by setting the d equals three, we're really specifying it to
something that's visualizable and understandable to people as a three-dimensional, you know,
generalization of the tangle to the hyper tangle. And then there would be essentially an entire tower of constructions
for higher dimensions and primes that could allow you to have
increasing sophistication to the consensus and finality of the transactions.
The persistent homology would get a lot more complicated
in the higher dimensional cases, as well as these coverage tests and access diversity.
So I'm going to go further.
We define the attic token as a native asset for sponsorship bounties, storage commitments and governance.
consensus remains fee-less and independent of token ownership refundable deposit anti-spam and
a non-transferable attic rep reputation score regulate participation we specify the genesis
procedure token allocation schedule diversity rules tip selection by multi-axis random walks
conflict resolution by in energy descent functional and the security controls
that make the system robust so i'm going to go in further to describing the attic dag system
so attic dag is a minimal mathematically principled ledger it has a feeless base layer there's no gas
participants escrow a refundable anti-spam deposit.
There's ultra metric security.
So PADC radii enforce multi-axis diversity on each attachment.
It's a higher dimensional tangle.
So every message creates a D simplex's approvals.
What people normally call transactions in blockchain systems
we're calling messages in the system
to make sure we have a distinguishing
of terminology uh deterministic finality tests so k core coverage and persistent homology
stabilization these phrases you become more of a mathematician or more of aware of the system
will make more sense and i recommend people ask ai about these things and just look up wikipedia
articles or wolfram math world or
whatever else is understandable um to you based on your level of technical understanding of math
and computer science and algorithms and blockchain and so on so two ledgers in one transferable
attic tokens for utility and a non-transferable attic reputation for consensus weighting. So that's a very key thing is a lot of systems try to
have both of those be in the same thing whereas it really is needing
bifurcating it appears. I'm not going to go over these
system parameters too much in depth but they're in the white paper.
To go over some further mathematical preliminaries as well
I will briefly describe.
So a piatic valuation is a function from the rationals to the power minus the valuation of x is how you describe the distance in
piatic ultrametric space so there's an ultrametric inequality that's similar to the triangle
inequality in regular euclidean space except in piatic space it's with respect to piatic
valuations and then the notion of a sphere or a piatic ball is also with respect to piatic valuations and then the notion of a sphere or a piatic ball is
also with respect to piatic valuations such that it's that difference between a radii just under
this norm rather than the regular euclidean norm that everybody's used to of like the x squared
plus y squared equals z squared giving you the you know standard pythagorean theorem type situation
which defines euclidean geometry metric distances.
This is defining a distance function that's different. It's using peatic numbers and peatic math as the peatic valuation. So if, yeah, you're having a very number theory perspective
where you're looking at a different completion of the rationals that's not the real numbers,
it's the peatic numbers. That's a different way of having a completion of the rationals that's not the real numbers it's the piatic numbers that's a different
way of having a completion of the rationals so you can have a completion of the rationals in various
ways one of them is the real numbers that's taking just standard koshy sequences completing q but
you can do other things to complete q into than metric space, an ultrametric space using
the PADC valuation. So doing everything
there with this PADC valuations and the PADC ultrametric
space is giving a completely different paradigm than these
Euclidean distance functions for regular
metrics.
So now we talked about simplices a bit,
but yeah, the AtticDAG is a directed acyclic simplicial hypergraph
where each new message adds a D-simplex to it.
And there's approvals respecting acyclicity.
So that means that there's no cycles in the graph, because that would be essentially a circular situation. And that's not what you want for time elapsing transactions that are occurring to have a consensus system. We leveraged persistent homology on the induced complex for finality checks.
So that's a mathematical method for finding if there are cycles in the simplicial complex.
And we use that for the finality checks in the system.
So what is the message in attic dag each message carries a payload
metadata approvals signature features and reputation there are axes that encode the
distinct orthogonal axis uh aspects of it and there's a canonical map into the piatic numbers
a canonical map into the periodic numbers um so given a bunch of periodic radii and in d dimensions
with a certain diversity a candidate approval set is admissible if these criterion these
equations hold c1 c2 and c3 on page three of the white paper um i'll not verbalize those saying out the math but
there's a tip selection algorithm which is a multi-axis random walk and if you have
current tips as a set then there's a proximity and trust you can define for a candidate parent relative
to the proposer. And that proxy metric of the description of the trust function is what
you look at conflict penalty and transition probabilities to then have certain candidates
that you end up sampling as what end up being parents that actually satisfy
those equations C1 to C3.
And those end up being how you can have the tip selection
in this system, which in a regular tangle
in a two dimensional graph works similarly,
just we're using piatic valuations
and piatic ultrametrics here.
So for each conflict set that would be like a utxo double spend there's a support for a node and we have a total energy
that we described correlating to that and with the multi-axis random walk and admissibility
the energy functional surely decreases with time so So that's called a negative drift. And this is ensuring a unique winner per conflict set.
So that means if you have a double spend,
then this is how you resolve that such that there's no double spend.
So the main situation with Bitcoin of why it was amazing as an innovation
in the first place was because it solved the double spending problem.
So this is the context under which the AtticDAG solves the double spending problem. So this is the context under which the attic dag
solves the double spending problem.
It's with conflict sets and energy descent.
Then the finality tests use finality
by either K-core finality or homology finality.
We call these F1 and F2.
So a node is final if the induced future cone
contains a K-core exceeding threshold on number one, distinct balls per axis number two, and has a total reputation that's big enough as well as the depth big enough.
These are star and D star terms we can refer to in the documentation.
Homology finality is if you have a simple complex formed by approvals in the future cone of the node,
if the weighted persistent homology stabilizes over a window,
and the d-1 dimensional homology bottleneck distance falls below a certain epsilon,
then you mark the node as final,
so there is essentially a smaller dimensional distance that you are bottlenecking
the lower dimensional homology, and so you look at the
d-dimensional weighted persistent homology, in this case it would be for the
first version of the attic dag with d equals 3
it would be h3 stabilizing over an h2 bottleneck distance
so you're looking at the two-dimensional bottleneck distance over a window that is,
with respect to the weighted persistent, while GH3 stabilizing.
So this just means you're tracking the tetrahedron and those over the triangles.
So there'd be higher-dimensional versions of this where you're looking at like a four-simplex, for example,
but we're not looking at that at the moment so um consensus is fee-less each proposal
escrows a deposit and that's right refunded at finality objective false um incur slashing
the attic token is a transferable utility slash governance token that is not used for consensus security.
So a lot of DLTs try to have the token be also what is the consensus security.
Our system is not doing that.
There is the other way that we've described the situation here with respect to ADDIC having the ability to sponsor compute and storage bounties.
So this is proof of useful work hooks and data availability of payments,
long-term storage commitments and archival incentives, as well as governance,
such as parameter updates or grants as well as subject to quadratic voting caps. So parameter
updates would be, for example, taking P equals 3 and upgrading it to
P equals 5, or D equals 3 and upgrading it to D equals 4. These would only be steps that would
be sort of necessary to take when we've got essentially a dimensionality of the hypertangle
is rather full and used up to a point that the P equals 3d equals 3 case is is essentially you know needing some further
higher dimensional scenarios to you know address on top of it we may have some type of like l2 l3
on top of it type scenarios happening for those higher parameters and that those sorts of proposals or grants for R&D or governance aspects of choosing what to do with the future of the system further
are intended to be very driven by the original co-founders of the system, which is contributing to the Genesis period creation.
the system, which is contributing to the genesis period creation.
The adder crap, which is a reputation, is a
non-transferable reputation that's soulbound. It's a soulbound score for a public
key, and that takes the differences of the good
and bad, namely finalized approval weights minus overlap penalty and
multiplies it by this factor, 1 minus gamma. You add
that to gamma times RT of P, and that gives you RT plus 1
of P. So doing that over these parameters, gamma
show you where the
reputation at T plus 1 as opposed to the reputation at T
is for consensus weighting.
Now, the
genesis of
the system will
create a genesis hyper
edge with D plus one system
identities, and they will have preloaded
the attic rep score, the lock deposit
pool, as well as the initial
set of access anchors. This will
essentially be the equivalent of the genesis
block of Bitcoin, and the genesis block of bitcoin and
the genesis manifest with which has hash the hash parameters anchors multi-party signatures will be
published as as well further as we approach which is not yet published the white paper
yellow paper and further third math paper are distinct with respect to that.
Now, there's going to be further implementation, and I'm not going to recite protocols or algorithms,
but there's an admissibility scoring and a selection pseudocode that's provided in the white paper,
as well as description of validation and finality.
There's a security analysis presented and an implementation plan so
this all is going to lead to an l1 with a token and there's a contribution phase occurring up until october 20th you can visit atticl1.com to see more information and read the various
papers and access the telegram community as well as follow the twitter at attic l1 tangle
we'll be releasing further details and information as well as repos of code publicly and having testnet forming soon.
So I wanted to see if anybody had any questions, but this was the initial white paper review
attic spaces.
I'll be holding a second attic spaces tomorrow to go over the first yellow
paper and another one on monday to go over the math paper i'm intentionally keeping these
somewhat self-contained and short enough to be listenable to a recorded uh on a recorded call. So if there's any questions, please, you know, let me know or speak up or comment in the
chat or otherwise we'll end it here for the first recorded Twitter spaces with respect
to Attic.
