OMEGA Computing · paper release r1577
Chambers vote on which
candidates are worth checking.
OMEGA compute is candidate biasing by patch consensus. A federation of optical chambers reaches agreement about which candidate answers to a hard problem look plausible. An ordinary exact verifier makes the final call. The chamber never decides correctness — it changes the distribution of candidates the verifier has to look at.
The verifier stays in the loop, no complexity class is broken, no photon becomes an answer by itself. That is the whole shape of the claim.
§01 · Framing
This is not another optical accelerator.
Conventional optical compute tries to do arithmetic in light. OMEGA does not. It uses light to run a consensus loop over local constraints, and it leaves the exact answer to the verifier the problem already came with.
conventional optical
Compute the answer in light.
Photonic MACs, mesh interferometers, coherent Ising machines. The optical field is meant to be the arithmetic. Any error in the field is an error in the result.
You have to trust the field. Calibration, drift and readout noise all become correctness bugs.
OMEGA
Bias the candidate stream. Verify exactly.
Chambers propose candidate answers under local agreement constraints (patches and collars). A cheap, exact verifier — the one the problem already ships with — checks each candidate.
The field never has to be exact. It only has to make good candidates more likely than bad ones.
That split is what makes the construction auditable. Every claim reduces to two questions the verifier can answer on its own: did this candidate check out, and did the chamber propose it faster than a fair baseline.
§02 · Mechanism
Patches, collars, one global witness.
A hard search problem is rewritten as a small set of local relations between wires — patches. Adjacent patches share variables on thin overlaps — collars. When every patch is happy locally and every collar agrees pairwise, the local stories glue to one global answer.
Figure · chambers bias the candidate distribution; collar agreement funnels survivors to an exact verifier
01
Patches
Each patch is a bag of local relations: this bit is a rotation of that bit, this carry is the majority of three inputs. Zero local energy means every wire inside the patch is consistent.
02
Collars
Patches share a few variables at their edges. Bad candidates die at collars, not at the verifier. Most of the pruning happens in the physical field before the verifier is ever called.
03
Consensus → verifier
When all local energies are zero and all collars agree, one global candidate emerges. The exact verifier accepts or rejects. Nothing about that step trusts the optics.
This is the Patch Equalizer Theorem doing the load-bearing work: local agreement plus collar agreement equals one global witness. The chambers are how you make that agreement play out in physical time, cheaply and in parallel.
§03 · Worked example
SHA-256d proof of work.
A concrete instance of the general pattern. SHA-256d is the hash Bitcoin miners run, and it factors cleanly into four constraint patches. It is the example we have hardware for; the mechanism above is not specific to it.
the four patches
Source · schedule · compression · target.
Source varies the nonce. Schedule expands the message. Compression runs the 64 rounds. Target checks the digest against the difficulty. Adjacent patches share their edge variables on collars; a candidate nonce survives only if all four agree.
what OMEGA changes
The verifier still hashes. Fewer candidates get to it.
A real SHA-256 ASIC still decides acceptance. The chamber only shapes which nonces are proposed. The bet is that a nonce that survives collar agreement in the optical field is likelier to be a real hit than a uniformly random one.
Numbers, transcripts and the acceptance boundary for the bench receipt live in the paper — see §07 below. This page is deliberately not a benchmark sheet.
§04 · Claim boundary
What the papers say. What they do not.
Five lines so you never have to guess the tier of a statement.
Local patches + collar agreement ⇒ one global witness
Patch Equalizer Theorem. This is the load-bearing statement for the whole approach.
SHA-256d factors into four constraint patches
SHA-256d search is equivalent to finding a zero-energy state of a bounded-locality Hamiltonian.
Chamber biases the candidate stream on the bench
There is one measured lane (kHeavyHash / Kaspa) with a defined acceptance boundary. The paper carries the numbers.
Full SHA-256d speedup on OMEGA-I1
The full-route enrichment on network-difficulty SHA-256d has not been measured. Everything downstream of that number is conditional on it.
SHA-256d cryptographic break or complexity-class shortcut
Never. The exact verifier stays in the loop and query counts still obey classical / Grover bounds.
§05 · Papers this page draws from
The three that carry the weight.
Everything else in the OPH corpus is background. These three carry the arguments on this page.
Observers Are All You Need
open paper →connection ·The Patch Equalizer Theorem lives here. It says that if every local energy is zero and every collar agrees, the local stories glue to one global witness. That is why bad candidates die at collars instead of at the verifier.
Screen Microphysics and Observer Synchronization
open paper →connection ·Why the chambers are wired the way they are: the twelve-port carrier boundary and the observer-visible signature that a federation of chambers has to preserve for the consensus to mean anything.
Photonic Fixed-Point Consensus for SHA-256d Proof of Work
open paper →connection ·Worked example. Compiles SHA-256d into four constraint patches and specifies the OMEGA-I1 five-module route used on this page as a concrete instance of the general idea.
The full 12-paper corpus lives on the FloatingPragma/observer-patch-holography repository.