A Hadamard matrix of order 668 would be a 668×668 matrix with ±1 entries and mutually orthogonal rows, resolving the smallest order for which no such matrix is currently known. An evidence title attributes a purported construction to Levent Alpöge, collaborators, and Claude, apparently distributed as an obfuscated shell script, but the supplied sources do not verify the artifact or establish that it satisfies the required conditions. Expert or formal verification is therefore still needed before this can be treated as a solution.
Scott already holds the load-bearing position in “Mechanically Different Verifiers” and “Verification Loops”: an AI-produced construction should not advance until independent, observable checks validate the artifact. Until the 668 matrix is actually reproduced or mechanically checked, this is another unverified AI-mathematics claim rather than evidence that extends or challenges his view; the radar also already tracks this verification pattern across closely related mathematical cases.
ip:concept.mechanically-different-verifiersip:concept.verification-loopsip:concept.deterministic-ai-pendulumradar:concept.ai-mathematicsradar:concept.formal-verificationradar:codex-q26-queen-domination-proofradar:openai-monster-subgroup-generators
queries asked of Scott's wikis
- AI-assisted mathematical discovery and verification
- formal verification of LLM-generated proofs or constructions
- executable artifacts as mathematical evidence
- coding-agent output verification harnesses
- trust boundaries for AI-generated scientific claims
- LLMs solving benchmark open problems
2026-08-19T20:38:28Z
Repeated checks have produced only minor engagement drift and no expert reproduction, mechanical verification, or disconfirmation. The claim remains unresolved, but the active news window has faded and should be reopened only if substantive validation appears.
2026-08-17T19:41:10Z
Another 48 hours without expert reproduction or mechanical verification leaves the construction plausible but unresolved; the absence of new evidence does not change its meaning or warrant further attention now.
2026-08-15T18:37:02Z
The velocity flag reflects a five-point Reddit score increase with no new discussion or validation, so it does not change the case’s meaning. The construction remains a checkable but unresolved artifact awaiting independent expert or mechanical verification.
2026-08-15T14:33:55Z
No expert endorsement, independent reproduction, or formal check has appeared; the case remains a checkable but unresolved construction. The staleness trigger changes neither its evidentiary status nor its low relevance to Scott.
2026-08-13T13:33:21Z
The refreshed comments only repeat capability and competition speculation; they add no independent reproduction, expert acceptance, or mechanical verification. The checkable construction remains unresolved and its interpretation is unchanged.
2026-08-13T12:36:06Z
The new Reddit post is secondary amplification of the same artifact, not an independent reproduction, expert endorsement, or mechanical verification. The construction remains plausible and checkable but unresolved pending an authoritative validation.
2026-08-13T12:22:56Z
evidence attached: reddit.post.1vn87tq — This independently surfaced report corroborates the Claude-assisted construction of a Hadamard matrix of order 668, while correctly noting that it does not settle the broader conjecture.
2026-08-12T17:43:16Z
The refreshed discussion adds no independent reproduction, expert endorsement, or formal verification. The case remains a concrete and plausibly reproducible construction awaiting authoritative validation, while current attention is repetitive amplification.
2026-08-12T14:55:46Z
The case has moved beyond bare attribution: a published executable artifact and a reported independent exact check make the 668 construction plausibly reproducible, though expert confirmation and provenance remain needed before treating the open order as settled. The latest change is only engagement, not further validation.
2026-08-12T14:32:26Z
grounded: known/low — Scott already holds the load-bearing position in “Mechanically Different Verifiers” and “Verification Loops”: an AI-produced construction should not advance unt
2026-08-12T14:29:23Z
origin walked (codex/luna, conf 0.98): anchor reddit.post.1vmdzgi -> echo.x.d48a6db3a2 by Levent Alpöge
2026-08-12T14:28:12Z
case created — The reported construction is a concrete, checkable mathematical artifact whose validity would settle a specific open case.