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ADIC Math and Applications
Recorded: Aug. 25, 2025 Duration: 0:35:10Space Recording
Full Transcription
Thank you. Thank you. Okay, everyone.
So I'm going to start now.
Welcome to the attic spaces today where I'm going to be now. Welcome to the attic spaces today
where I'm going to be going over the math
and applications further.
So I'll be finishing off the discussion
of the mathematical design improvements,
which are in the appendices of the math paper,
the third paper.
And then I'm going to be discussing the math paper, the third paper, and then I'm going to be discussing the applications paper
as well as just generally the system broadly for understandability outside of a mathematical
specialist. So to review, the Attic Dag math paper formalizes a reputation-weighted distributed ledger as a stochastic growth process on a directed simplicial complex embedded in D-dimensional QP space.
So that's P-Attic numbers in D dimensions.
So D products of Qp with each other.
In the case of the first version of the system, we're having p equals 3 and d equals 3,
which is the prime p and dimension 3, so we're over q3 cubed,
essentially where the directed simpletial complex is embedding in that describes this fee-less, reputation-weighted distributed ledger.
Each new vertex attaches to D plus 1 parents, so in this case 4, because 3 plus 1 is 4, under multi-axis,
P-adic diversity constraints forming a D-simplex.
constraints forming a D-simplex. So in our case, again, we would have that each new vertex attaches
to four parents under the multi-axis, three attic diversity constraints forming a three-simplex.
Tip selection is a multi-axis Gibbs-type random walk biased by ultrametric proximity and reputation.
Conflicts resolve via a super martingale potential with negative drift
while finality is certified by either a K-core diversity predicate or by topological stabilization.
So this means that the fundamental basis of the double spend problem is with conflict resolution,
and we'll describe that more. I also mentioned it prior, but this is in the case of essentially
what transactions are considered honest or valid
as part of the network
as opposed to have been considering bad approvals.
So I'm gonna go into the mathematical design improvements
now regarding the system described thus far.
So there's something called multiscale ultrametric diversity or MUD.
And so this is that for each axis, you fix these piatic radii and quotas and have a new condition for the term.
Enforcing that diversity has several nested piatic radii, blocks this thin fake diversity,
so there is a potential alleged attack of an attacker satisfying a single coarse-scale quota
while remaining tightly clustered at finer scales.
So sybil rings and parasite splits become much more expensive with the mud condition.
It doesn't hurt honest participants either because
decreasing quotas sufficiently mixing access and coners um that's all i'll mention on that one for
now the distribution transport diversity is another criterion that uh uses the definition of something called a Wasserstein cap. And using those
transport caps, you can complement the mud or the multi-scale ultrametric diversity by controlling
concentration across covered balls. So this covering of balls and using the piatic balls for defining radii that are staying close to a well-spread target to prevent this quota gaming where the MUDS ball counts are met, but the mass remains concentrated.
This raises the cost of coordinated symbols and censorship. So part of this is an upgrade to the anti-cibel measure-ness of the system.
This is an upgrade to the anti-cibel measure-ness of the system.
Another aspect for using MRW as a Gibbs sampler with mixing guarantees,
so there's rapid mixing that can upgrade the system further,
turning tip selection into a provably rapidly mixing Gibbs sampler, which enforces certain bounds
and prevents hurting or metastability to ensure that there's a explicit controllable latency
for the MRW. There is also a geometric ergodicity theorem for stability of conflict dynamics and that can strengthen the
negative drift and improve the bounds for conflicts resolution times so that these
long metastable ties can be eliminated. There's another topic of spectral topological finality
and this is involving spectral gaps. I'll not go too much
on this topic because it will be extensively delved into later. On sheaf-based spectral
finality, there is a notion of something called a sheaf, and that is going to be something that
I'm not going to talk about in depth because it's an algebraic geometry construction which requires a lot of further understandability. which sheaf you're on and essentially looking at
different properties of
restriction maps as well as
boundary conditions will allow you to analyze something called the stock
of the sheaf which is in a way a generalization of a kind of
an origin of a space or it's
like fiber running along it, if you think of it that way. And there is a additional criterion
called SSF to kind of cut to the chase on all that stuff to do with the sheaf called
sheaf spectral finality or SSF. And this is that for certain fixed thresholds and window lengths there is a restricted operator
which has a non-zero eigenvalue over those rounds so in the window length which is the rounds
there is this operator which has a non-zero eigenvalue so essentially it is saying that this gap exists so having that as
an additional criterion is one of the alternate finality criterions which we
would call the spectral finality predicate so using using, there's an ability for incremental sparse updates and complexity.
So the SSF is something that will be enabled in future versions.
It's not for the initial test net, which just has the prior to these mathematical optimization upgrades details.
So there's just the F1 criterion for the test net.
There's further applications for improving
the mathematical nature of the system
that are found in the math paper in the appendix.
One of them that I'm gonna mention
is congestion aware deposits so this is
um essentially having the anti-spam deposit turn into a stabilizing feedback control and so it
allows for a system to not have um essentially congestion so there without that might have some
So without that might have some state of potential stuckness.
The time to finality tail bounds can also be improved,
which is analyzed in appendix K.
So those are some of the mathematical system improvements that are mentioned in the math paper.
I'm going to talk next about the applications paper and something called the OmniChain Commerce Intent Mempool, or OSIM, as well as JETCAS, or JETCAS, so just-in-time compiled agreements.
or JITCA's, so just-in-time compiled agreements.
So these are two applications on top of Attic
that for OSIM you can settle on Attic or externally.
And it's a fee-less broadcast layer on Attic
that has finalized intents submitted.
So it details the message types, state machine semantics, proof of finality, artifacts, and atomic settlement patterns.
We have as well a contact list tap to pay consumer card outside of the credit system,
which we have intended to be able to use with this system as a main application that is the attempted
consumer retail sort of killer app that is described with the system as well as
fiat connectivity being possible through mapping to ISO 20022 message fields as well as RTP ACH and SEPA handshakes so we'll outline further what's
possible there under further compliance guidance and potential partnerships with PSPs the NFC card
technology is not something requiring anything other than an Android device for the NFC tap, for example.
So the technology is not requiring its own card technology to be able to use an NFC.
So the OSIM is a finalized fee-less intent rail with minimal JSON schema, semantics, and SLAs.
JITCAs are compilation of intents into settlement native transactions on
ATTIC or external rails. So this means that the intents on OSIM can be settled on ATTIC or they
can be settled elsewhere with the intent to have settlement occur. The, an intent, I've been saying
this word, definition is a standard addict message whose payload encodes
a commercial desire, either buy, sell, pay, invoice, escrow, subscribe, redeem, but transfers
no token value at publication. It contains an optional DA pointed to a contract template for
compilation on a chosen settlement rail, which could be addict itself or an external rail.
There's a canonical JSON schema presented on page four of the applications paper
and the semantics for it. JITCAs are compiling finalized intent into settlement native transactions.
So the attic native ones would settle on attic. External DLTs like ETHSOL, BTC transactions,
or other L2s are constructed from the DA template. And fiat rails as well would be admitted by a licensed PSP
that is yet to be determined who in partnership with
or how that is possible to implement
in a legally compliant way.
So firstly, the attic native and external DLT aspects
will be addressed prior to the ability
for such potential fiat rails or to have to pay NFC cards.
There is also an aspect of atomic cross-ledger settlement patterns that we have designed with
hashed time locks as well as adapter signatures and proof of finality as a light client. So there is essentially a cross-ledger atomic swaps feature
that is using the intent to commit a hash
and then external payouts succeed only upon presenting the pre-image
before the deadline.
Otherwise, if it's not before the deadline,
that commish hash has a hash time lock expires
because the published reveal of the pre-image
only when finality holds yields the atomicity otherwise
you'd have to have a trusted bridge which we're not assuming an amazing an amazing feature that
is described in the offline flow as opposed to online flow which is of course still of interest
to have tap finality settle in receipt for this tap to pay NFC system. There's also an offline flow where you have a commit only
hash of intent at a POS with a later reveal on attic
and settlement occurs after finality.
So the proposal of a commit hash,
if it was a forged hash,
you're gonna be slashed of your anti-spam deposit. And if it was a forged hash, you're gonna be slashed of your anti-spam deposit.
And if it was a legitimate use,
then when it connects back online later,
it would reveal which it was.
So they would either get what you actually sent them
or because they didn't honestly spend,
you would end up getting their slashed deposits.
So the system has a way of really
equilibrating itself in a natural way as well as allowing for offline inputs to have
asynchronous timing. And that's one of the main benefits compared to this
sort of blockchain system of that there's a
timestamp starting the block and a timestamp ending the block and the block time happens
during that period where everybody then agrees on the consensus of what that block was and then it
moves on to the next block in this system there is there's always tips being posted and then there's
a finality region which is what actually got verified as having had happened and if someone is wanting to post a tip they have to verify
that the four other parent tips that they're confirming have finality in the system to
be able to post their tips. So you need to provide a mathematical proof of other potential
tips having finality to be able to post your tips which which then requires some other party or potentially yourself.
If you're doing honest approvals or if you're going to do a string of bad approvals, you're
eventually going to have a conflict resolution failure on, you know, an analysis to the actual So, further security notes, there's replay protection by nonces and expiries.
There's a planned lost card revocation via an attic attestation, as well as any of these NFC card reader aspects, having personally identifiable information remaining off-chain with a hash and a DA pointer.
So there's further details about potential fiat connectivity there as far as the message mapping.
And then beyond attic token transfers and value transfers on the network,
there is also the ability to have zero value applications
and the essentially value less transfers
or zero value transfers,
wherein because there's no gas fee,
you may wanna actually do that.
A lot of systems like Ether, Bitcoin,
or other distributed ledgers where you have to pay fees
are totally infeasible to be able to do systems
where you're even paying a cent or a guay
for doing some type of action,
especially if you're repeatedly spamming it multiple times
or trying to do micropayments.
If you're paying a fraction of a cent,
you don't want to pay a fraction of a cent
to send a fraction of a cent. There's sort of these epsilon values of machine to machine economy as well as IoT remittances and other ways of streaming value that are not feasible and unrealistic in standard DLT systems or blockchains generally with miners and fees and gas and so on. But with this system,
you're able to enable those applications. So there are various things that can be done with
valueless transactions,
because that's also part of the philosophy
behind the naming of them as messages,
because messages more broadly could just be
providing information, not necessarily value.
However, for that message to be posted,
it's going to need to be as a tip verifying these other
tips into having finality as part of the
growing simplicial complex or the Attic L1 hypertangle.
So that's essentially the presentation and talk for today.
If anybody wants to raise their hand
and come up and talk at all, we can do some Q&A,
but the rise, I'll probably end it off at here, but please
check out atticl1.com and follow atticl1tangle on X and yeah, get in touch with me if you're
interested in collaborating on the project or have more questions. I hope somebody is interested in coming up here.
So keep it going.
We've got two other people.
Hey guys, how's it going?
I approved two people to come up.
Hey there, how's it going? Did you want to speak or anybody interested in asking any questions before we wrapped
All right, well, I'll wrap up here with, you know,
if anybody manages to ask a question in the meantime,
I'll vet it, but essentially I'll wrap up here
with just saying that over the next 55 days here,
we're campaigning to have the Genesis mainnet
of the system.
We have the testnet compiling
and the first testnet node connectivity
having had occurred just hours ago
on the first node compiling
and that the progress on this project
is going faster than ever.
And the clean architecture of the system and design
has made it very amenable to fast implementation.
And we're getting ready to release more code and repos and papers soon
about the system and have increased adoption
and growth of the awareness of the community around this all.
So we are looking forward to collaborating
with everybody on it.
Hey, Seize, did you want to say anything?
Yeah, yeah.
I wanted to ask something.
Because it's all fee-less, this system,
I was wondering, because I don't understand
all the mathematical things you are telling us,
are telling us who's gonna pay for the computing power
who's going to pay for the computing power for this system?
for the system.
So the user, when you try to post a transaction,
you have to verify other transactions
that are essentially pending in the system
to be able to post it.
So it essentially outsource distributes
in a very discreet asynchronous way way the computing tasks to anybody,
but it makes it in a very edge computable manner such that the laptop or phone that's computing that very lightweight computing requirement of verifying these math conditions on the graph so that they can then post their tip is not burdensome but so the entire
paradigm of this really computationally intensive miners using a ton of electricity to everybody's
trying to compute all these shaw 256 hashes to hope you get the pre-image of a zero being the
right answer and then boom that's the right one and everybody's brute forcing to try to find that with all these huge usage of electricity this system is a little more clean and discreet
mathematically with you know if a user wants to try to post into the system they need to help
reinforce the what pending ones were there confirm those to be able to have the right to post a pending one
themselves. So hope that explains a bit the kind of proof of useful work as well you can add to
outsourcing to the user posting the transactions. Yeah, thank you for the answer. It's all the
mathematical things are over my head. I don't understand that all so i think uh an explanation
for for people who are not mathematicians would be nice as well so more people understand
everything you are making another question i have is the contributors to the the wallet you you posted
that you posted, what's gonna happen with the deposits?
Yeah, so the deposits pro rata allow you
to inherit attic tokens on the L1,
which you can generate an address from that address
that's actually on the L1,
which allows you to claim your Genesis tokens essentially on the attic L1.
So imagine if you were Satoshi a little bit,
and so you can kind of claim your portion of your Satoshi coins
your portion of your Satoshi coins is like what's happening here with this
is what's happening here with this system.
system. So pro rata,
depending upon how much ends up being in the contributions is the
proportional right that those addresses would inherit as being able to claim
that proportion of the equivalent of the Satoshi coins of the attic
system. So, um, there, equivalent of the satoshi coins of the attic system so um there and as far as the use of
proceeds of it as well there will be centralized exchange liquidity pairing that will occur
with the tokens as well as other funding of the project
But the liquidity that it's going to provide does not make you any money, let's say like that.
Well, there's a possibility that I may pay myself or the team may pay itself partially out of some of the budget that ends up occurring for the project, but that would be a very reasonable,
sort of deserved to having a project,
allow the founder leader of it to have some compensation.
So it definitely is not all going to me
and it's mainly reserved for liquidity running
the project paying other people things like that but um you know it would be disingenuous to say
that i make zero dollars off the entire endeavor i do intend to as part of some sort of team tokens
have some sort of percent that would be reasonable and fair with respect to my role and effort and so on and that
would be approvable by a government's proposal attempt at some point in the future where uh you
know with a live mainnet existing uh such a proposal for some amount of team tokens doing
something would be proposed to the community
essentially so that's kind of how it would work logical and deserved of course uh and uh all the
other tokens will they have a place in this system or um so 50 of all of them go out to the original
contributing addresses so that is kind of like the sort of co-founders of the system in a way,
or the, you know, original portions.
And then there is the, those, yeah,
mentioned like kind of team founding type tokens.
And then there's a substantial portion reserved for liquidity,
as well as this community R&D grants comment that is like long-term reserve for being able to have
sustainable future of the ability to continue with
research and development and ecosystem scenarios.
So this is similar to the kind of IOTA ecosystem development
fund that happened and was incredibly useful for that
system growing over years.
But I mean like a toy or calc,
will they have a place in this system
or is that separate project?
So we are looking at what, as far as, you know,
multi-asset like colored coins or other types of ideas
that are possible for like on Attic having
other assets at the moment we're focused on like the Attic token on Attic L1 as a system and
there you know we'll leave it for now to comment exactly on that I don't want to promise any
particular thing but as everybody knows I have invented various meme coins in the past, as well as there's the XI token for XI protocol, which is still continuing to be the utility token for the Geometric 2 mission and Doge 1 satellite to the moon with respect to the utility for the space displays and the SATCOM data reporting, meta oracle rewards and so on to come so those those
systems would continue to exist and be you know simultaneously a scenario that is the case ongoing
as far as other meme coins whether it be on solana or eth that had occurred as well i do not necessarily rebuke any particular
meme coin that may have happened or project other some of them were that i had had made
it as my idea other times it was where i am kind of the um like brought into someone else's idea more so um i'll provide further announcements and
commentary on any particular projects yeah i asked that because i was reading uh multiple times that
everything was connected so that's why i asked that yes we do intend to have and everything
is connected narrative for sure and to honor not rebuke necessarily any particular projects that existed but i just want
to make sure i'm not promising anything about like that you can you know convert your tokens or swap
them into another system or do anything like that indeed we're intending to have this overarching
narrative throughout all the projects and ensure that it all does make sense and is connected and there continues to be various plans to make sure that, you
know, what exists is honored further and so on to have, you know, cohesive corralling
of the community such that it is not with fractured discontent, but, you know, brought
together joint collaboration and cohesion towards more optimistic
community ecosystem so hope that's good enough comment for now yeah thank you very much for
your answers and uh i understand that you are very deep in the in the math but i would uh
like to also get more explanation in a more simple way because it's too hard to understand
what you are telling in the for me at least but thank you very much awesome well thanks for asking
some questions there and i'll make sure um you know we're kind of wrapping up this session but
in a future explanations as well i'll try to make make sure that I'm not speaking too overly technically.
I just wanted to make sure that as well,
at the outset for the first few conversations about it,
I really did speak to that, you know,
truly mathematically defined level such that if a mathematician or a computer
science professor was hearing the call,
they're going to click at that full level of what it is truly.
And then, you know,
I'll explain further in analogies and metaphors and understandable applications
and examples further about, you know, what that is and what that means and trying to
educate and teach towards those ideas. But I just wanted to make sure that it was
very much like, you know, actually just communicated technically correctly
firstly,
and then I'll go on a big education expose spree
about trying to have the explainability further of it all.
But yeah, I approved some two other speakers
to come up as well if you guys had some,
any other questions.
Yeah, thank you very much for the aim mate.
Yeah, thank you, Cease.
Did Chill Diver and Alien want to come up?
I approved both you guys.
Otherwise, I will wrap it up here.
Okay, well.
I think we'll just shut it down this time.
Thanks, everybody, for listening.
I'm going to do another Spaces tomorrow. So I'm trying to have a rather
regular thing here moving out this whole week of daily spaces for the project. So I hope that
I'm going to have one last speaker perhaps here. Did you join?
Did you join?
Oh, hey, thanks.
I was just wondering about the non-transferable reputation.
Does that have benefits like faster transaction time or anything like that?
Thanks.
Yeah, so one comment about that essentially to wrap up here would be that if your node has been doing honest approvals,
so they get verified as being part of the finality
of the main hyper tangle
that doesn't later get proven as being a bad approval
because it was a parasitic side tangle,
essentially, you'll have improving reputation
and improving reputation.
And then if it turns out, say,
you start doing some spamming, some false false transactions your reputation is going to start lowering ultimately
but maybe then you could stop spamming and and and then start doing honest approvals again
and then your reputation will will improve so you could kind of like recover a poor reputation
and then how the system really kind of like treats that in a way is that if you post a tip and you have very low reputation, you're sort of not prioritized really to check because the system mainly thinks you are kind of eaten through of what their tasks are.
And like maybe every once in a while, it might sample towards lower reputation stuff to try to compute.
But you'll essentially be, you know, less preferentially, less served up as more likely to get more possibly computed from an honest node more potentially.
So it's like this whole gradient phenomenon of really that, like, you know, the honest networks will run in packs.
And if you have a poor reputation node,
you still have like a chance of kind of recovery,
because if you just do a lot of honest approvals,
then you'll start having finality occur more and other people approving your
finality and your reputation will sort of like approve again.
Does that help explain the dynamic? That's sort of what's going on there.
That's a great answer. Thank you very much. That's awesome. Cool project.
Awesome. Thank you for your interest.
Okay, guys. Well, I think I'll wrap it up here unless there's any last questions.
Thanks for coming, everyone. And looking forward to talking about this again tomorrow.
