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ADIC Yellow Paper
Recorded: Aug. 24, 2025 Duration: 0:26:33Space Recording
Full Transcription
Thank you. Thank you. All right, I'm going to get started here as this is a recorded spaces.
So mainly for listening to anyone afterwards,
but anybody here is appreciated.
So the AtticDAG yellow paper is what's being reviewed today,
as well as the start of the math paper further.
I'm gonna sort of present both simultaneously
and not address the mathematical design improvements in the append paper and extends it with precise state machine semantics
admissibility invariance and mathematically stated conjectures together with partial results
and proof sketches those are generally improved upon or decisively finalized in architecture
further in the math paper that's the third paper as well as the fourth applications paper, which will be talked about on another.
Spaces tomorrow, around 24 hours from now.
The core ideas, a piatic ultrametric on message features, higher dimensional tangle attachments,
tangle attachments where each message approves d plus one parents and dual finality tests via k
core coverage and persistent homology are specified in a way intended to be machine checkable and
implementable we have begun the test net development in Rust, utilizing originally the Libatic C++ and Python bindings,
but are proceeding in a Rust library for rewriting Libatic
and then implementing in a self-contained Rust library
the initial Attic testnet,
which we hope to have in the coming days presentable on a GitHub publicly so to review further and introduce as well as explain the design goals for the system.
Attic DAG is a fee-less reputation-weighted distributed ledger where each message attaches to D plus one parents across distinct P-attic neighborhoods, which are axes, enforcing multi-axis diversity at the moment of attachment.
F1, which is a K-Core coverage criterion with access, diversity, and reputation thresholds.
And F2, which is a stabilization of weighted persistent homology in the future cone.
The ADDIC token funds utility, so storage, proof of useful work, bounties, and governance, but not consensus security.
Consensus weight derives from refundable deposits and a non-transferable reputation called the
attic rep
the simplicial dag and future cones there's a definition for a
simplicial hypergraph which is that the ledger state at any time is a directed
asynclic simplicial hypergraph where every vertex adds a simplex with directed approvals and with no
directed cycles the future cone of the vertex is the set that is transitively approving
that vertex the definition of admissibility and diversity, given P and Q, a candidate approval
set A of X is admissible if for each axis the three criteria C1, C2, and C3 are holding,
namely the periodic valuation distance between that vertex and a given ai is greater than or equal to the rho jth variable which is for c1 c2 is the
multi-set of peatic balls containing at least q distinct balls and then c3 is regarding a sum of
radii having a minimum radii bigger than or equal to R min, which is another parameter.
The node state machine description, each node maintains, firstly, a local view of tips.
Second, paraxis vector clocks to ensure a cyclicity on arrival.
Third, an escrow ledger of deposits and refunds. And then fourth, an estimator for finality with parameters.
The transition function validate and attach checks, signature format,
asyclicity, admissibility, escrows, and appends the simplex.
Periodic finalize runs on success, refund D or update attic rep.
success refund D or update attic rep the tip selection through multi-axis
random walk or mrw I'll say further is a complicated definition involving the
trust of an transitive vertex that's related to X as well as the
Prox P as well as the conflict so the difference of those
terms under a proportional variable is
essentially the
Probability that you are having
Proportional There's that you are having proportional.
There's further a notion of conflict energy and drift.
So this is sort of the approach to the double spend problem in this system,
where if you have mutually exclusive UTXO spends,
you have two, you can define the support over the conflict set and then analyze
descending for the negative drift of conflict energy.
So that gives you essentially, you know,
conjecture 4.1 in the yellow paper, which is addressed further later,
that you have the appropriate conflicts resolved with unique winner
with finite expected time as well as sub-exponential tails.
So that means it's the appropriate sort of algorithmic runtime.
For finality, which is K k core and persistent homology the definition of finality tests is the
notice final if either the future cone contains a k core with at least q distinct piatic balls per
axis the total reputation bigger than r star at a minimum depth greater than you're going to
the total reputation bigger than R star at a minimum depth greater than or equal to E star.
So that's F1.
F2 is a homology lineality constraint, which is that in the induced weighted simplicial complex,
HD stabilizes over a window of delta rounds,
and the bottleneck distance on HD minus 1 falls below epsilon.
There's a conjecture called the implication gap which is that there are these
thresholds where the attic model implies f1 and f2 as well as being able to present a proof of
that for economics and reputation there's definitions of the reputation update at the T plus one time. So
there are essentially ticks of time that are having reputation updates in terms of the variables
where you have a good or a bad approval that you're taking the difference of and then multiplying
that by a parameter. Well, it's really one minus that parameter, and then the prior reputation
time is added to that. So you end up having a reputation influence based on the essentially
diversity in depth weighting and bad penalties for overlapping the bad approvals happening essentially so there is if it's an
invalid signature or malformed approvals or have approvable civil civil overlap and that would
trigger the slashing of the deposits otherwise the every asset every message escrow is refunded on finality for it not being
considered a bad approval so that's sort of the system and there's parameters and safe operating
regions for these different parameters like p d rho q k d star delta these were for the initial version
picked as the first operating version that can be implemented essentially although there could be
essentially governance proposals for updating those parameters to more improved security versions or heightened anti-spam measures if there are further spam problems.
Although part of the entire point of the system is to have an anti-civil measures approach with respect to it.
with respect to it.
So some of the needed details further
are with respect to low distortion encoders,
minimal diversity thresholds,
as well as MRW mixing time,
fairness under heterogeneous reputations,
core threshold with diversity,
and separation between F1 and F2, which were the two
finality criterion, as well as reputation dynamics and the mechanism design and complexity bounds. So
I'm not going to go into those exactly further describing each of those, but those are the
sort of partial results and approaches presented in the yellow paper,
which later get detailed further in the math paper
and as well as in the applications papers
will be all evident in the testnet
that gets released ultimately.
So there is a general phase zero, phase one, phase two
plan for the implementation roadmap of the project where the first prototype, the phase one, phase two plan for the implementation roadmap
of the project where the first prototype phase zero
will have the message format encoders,
MRW admissibility, K-Core deposits,
refunds and an explorer.
The goal for that is to have the prototype.
Then what we were calling the beta for phase one
is the ability to have a streaming homology library,
adecrep, SBT, access, or gossip,
anti entropy checkpoints.
Phase two as a mainnet candidate
would be the proof of useful work hooks,
storage markets, governance, parameter sweeps,
and adversarial testing further.
So at the moment, we're focused on the test net creation,
I believe in Rust for having the ability to have the message format as well as tip selection.
And that's at the basis of the system,
such that there's the two finality tests for tip selection occurring in the system with messages posted um there's further
technicalities on problems mentioned in the page eight and nine of the yellow paper the problem
bank those go over the piatic geometry and axis encodings, the MRW on ultrametrics,
conflict energy, as well as finality, further details about hypergraph percolation, reputation
dynamics, and the deposit and mechanism design, as well as complexity. There's some pseudocode
throughout that paper, but to kind of conceptualize further
and bring to a level of understandability
for what we are building here
and the main ideas of the construction,
ignore thinking about block chains for a moment
and think instead of a growing set of triangles
and tetrahedra, which is a growing simplicial complex.
Each new event is a vertex
that must immediately attach to more earlier vertices, so together they form a new simplex,
and because attachments always point from newer to older vertices, the complex grows forward in
time without directed cycles. And sensing if there's a cycle or not is essentially part of the
consensus there as far as this part of the consensus there.
As far as this mention of persistent homology, that phrase is about if there is the cyclicity in the simplicial complex or not.
So to keep growth healthy and hard to game, we view every vertex through several independent coordinates
and have a course time bucket topic tag region tag service tier further
on each axis we equip the coordinates out with a metric that has hierarchies of neighborhoods
the most convenient choice is the piatic ultra metric so the numbers that agree in many leading
base p digits that are very close and the balls are nested like a tree this is essentially the
piatic number theory understanding
of like in bitcoin where you're trying to hash to get pre-images of zeros for knowing
if that's the one you want many leading base p digits for piatic numbers being very close is
the analogy of that and the piatic numbers is is a completion of Q or completion of rational numbers under peatic
absolute value so it's balls are clopin it's called which means that they're closed and open
at the same time and so that's a funny math word to become aware of clopin but normally you only
learn about that in topology so the the local geometry as well, I want to talk about the diversity rule.
So when a new vertex chooses its D plus one parents, it must pick them so that on each axis, these parents lie in several distinct balls.
So those are the distinct branches of the axis hierarchy.
And they must carry a minimum amount of reputation.
must carry a minimum amount of reputation.
So the weight summarizing past good behavior.
this enforced diversity prevents a colluding cluster
from proving only itself and forces the complex
to spread across the different axes.
So you, in trying to game the system,
have to actually create essentially an entire system
bigger than itself to be able to do that.
So if you're having a sort of
colluding approach towards clustering and approving only itself, you would have
to handle that from all of the perspectives in the system, which there
are many. So it is...
Yeah, so the...
How the parents are chosen as well as resolving disagreements is what I'm
going to mention next. So to find suitable parents, so this is existing prior tips that
had finality, and now you're posting a new tip, and then you're trying to find ones to
attach to that are essentially the real ones you
have a simple stochastic rule so a walk that prefers nearby on all axes reputable and non
conflicting candidates but still has randomness to explore you can think of it as a gibb sampler
on the set of recent vertices or tips it quickly mixes and finds a diverse set of parents without getting stuck.
Regarding resolving disagreements, so you have these potential drops.
This is part of this negative drift or energy descent type thinking.
So if you have two incompatible options ever appearing,
which is like a conflict in the hyper-tangle,
we measure the support of each option, and then there's descendants by an energy
or a potential function that later approvals contribute positive weight to what they descend
from and the key invariant is that under this diversity rule in the parent selection walk
the potential has a negative drift so on average it moves towards a unique winner
so ties don't persist over time the further asymptotically you go out,
the negative drift occurring between any disagreements that would occur. So if there was
some parasitic sub-hypertangle that is attempting to have an incompatible option with what's actually
real, it will eventually over time have a unique winner due to this descent which is ultimately
terminating on its drift so it eventually settles to finality that's
this scenario unless we have I do note the offline variant where you can have
like a pending forever type scenario I'll describe that a little more but
there is a very interesting application further which I'll talk about on the future spaces, as well as when I go over the mathematical design improvements.
With respect to that, you can have offline submissions of commits.
So you have a commit hash that's offline submitted into the system, which could get accepted for if the point of sale was able to understand that that hash is good commit it would
only when it reconnects online later potentially a very long time later it would only either slash
their deposit or actually refund their deposit because that was a hash that got committed which
was you know a real one so that's a way that there could be in the world essentially a nfc card tap to pay
system that's outside of the credit system which actually is offline and has the ability to if
your deposit have this anti-spam deposit that's sufficient for being able to have this payment
happen essentially through a commit hash that they only are able to check later
when they connect from being offline to being online whether it is essentially
legitimate or not and if it is legitimate then at that point you would get your
anti-spam deposit back because the finality will have actually happened whereas
um if the uh you know it know it's not then then the deposit
slashing would go to the other party for that they essentially were presented
with like a forged commit hash however the cost of having had presented the
forged commit hash from the person who had to actually have the hash originally to commit would be because they deposited the amount that's the anti-spam deposit, which they would then get slashed and lose if they were trying to have had game the system on the double spend.
So that's the whole point of this whole approach for the UTXO double spend as opposed to Bitcoin, where the double spend situation is something completely different. So I'm going to wrap it up here soon as I don't want to have these be too not self
contained and focused on particular topics, but I'll summarize with that the finality of knowing
when something is settled is that you certify that a vertex is done, namely it cannot be overturned, in two independent ways.
There's two different ways that you can have finality of the settlement.
One is the structural density graph view.
So the future of the vertex contains a large enough cake or made of approvals that are spread across many balls on every axis and reach sufficient depth and total weight.
That's one view of finality.
That's the graph view.
The other condition, this is like the F1
and the F2, this topological stabilization, which is the shape view. So you're looking at the
simplices formed by approvals, the holes and the voids in the relevant dimensions stop changing
over a short window. Intuitively, the complex has been filled in around the vertex, so there
are no bottlenecks left to flip the verdict of whether the vertex is done or not,
so if it can be overturned or not.
So the certificate is enough to declare the vertex final in either case.
And that's something that's really key about this distributed ledger technology,
because a lot of other systems, you have to have the one way that the consensus happens that the finality of the transactions are generally within a sort of global men pool within time-stamped windows of a block and stuff like
that there are no blocks here this isn't a blockchain if you were to think of it as a
block it would just be a block of one vertex each vertex is its own block in that case but it's not
a blockchain because there's no linear
order relation like it's a chain it's a graph that doesn't have a cyclicity so that is meaning that
it doesn't have cyclicity so it's meaning that it is acyclic so that means that you don't find
cycles in it and that's what the persistent homology tests and senses. It senses if there are these cycles in the graph, which is this DAG,
which is a similar sort of generalization of what the tangle was for iota in two dimensions, but
taking that from a planar case of a two-to-one approval system and looking at three dimensions with three parents for the P equals 3
D equals three initial case of attic and that's what's been presented here so
there are no fees a refundable deposit discourages spam a non transferable
reputation score summarizes past good attachments neither deposit nor
reputation changes the mathematics of the growth process. They only keep participation fair. So the diversity
rule forces wide multi-axis coverage and the parent selection walk steadily feeds honest mass
into well-connected regions. The potential function drifts towards unique choice in any conflict.
Once either the structural density
or the topological stabilization appears,
the decision's locked in.
Thus, honest additions almost surely become final
in finite time.
Other than this case of the offline pending forever
person having received a commit hash that was legitimate,
but then never online checked it.
That's the almost surely set of zero,
almost zero that is potentially,
you know, non-finite time settling because it never becomes final yet. It was legitimate.
And late perturbations cannot reorganize what the complex has already filled in.
So I'll wrap it up here for now. The next space is tomorrow. I'm going to go over the
mathematical design improvements in the appendices of the math paper to start off so that I'm able to speak of certain terms such as MUD,
which is the multi-scale ultrametric diversity, as well as the spectral topological finality,
so that it verges into the territory of this Hodge sheaf land
where we have more complicated mathematics going on
to get the sheaf spectral finality.
So that's the SSF, which is this certificate later
that is a sort of more algebraic geometry thing
that's more complicated to be able to understand
approaching motif where overlap penalties and other more complicated mathematics that are these
sort of mathematical design improvements that took the original system and specify axiomatically as
well as mathematically further about it to be able to have sort of the initial implementation
that the testnet happens off of with the best initial versions of things
that are adaptable to the mathematical design improvements most easily.
So stay tuned for the next spaces tomorrow,
and we will be providing
further updates such as paper releases and GitHub repos
as they exist. Thank you.
