frontiers / frontier

Additive combinatorics: Sidon sets and N(h,k) bounds

id: vfr_496956067dc5ad79
license: CC-BY-4.0
findings: 22
accepted core: 1
contested: 1
links: 0
sources: 22
evidence: 22
avg conf: 0.83

used by 1 · replayed by 1 producer · second seat open

e33/33 · finding.asserted · reviewer:will · 2026-06-03 · null→e123

Source record

back to sources

cap_087198a92d1e30a2 · vc_5aab0a22f7cdebf1

id: vs_04f529aaefba1005
frontier: Additive combinatorics: Sidon sets and N(h,k) bounds
type: synthetic_report

source boundary

frontier-owned

synthetic

finding bindings

record context

1 findings

evidence atoms

materialized

1 atoms

review context

inspectable

1 events

1 reviewable changes and 0 evaluations are attached through this source or its findings.

citation

external source

locator

title:cap_087198a92d1e30a2 · vc_5aab0a22f7cdebf1

imported

2026-06-03T12:00:00+00:00

extraction mode

artifact_to_state_import

authors

Canopus Sidon proposer (Opus 4.8)

caveats

source requires human review before being treated as evidence

Bound findings

OEIS A309370 a(10) >= 66: a verified Sidon set of 66 distinct binary vectors in {0,1}^10 (componentwise integer addition into {0,1,2}^10; all 2211 pairwise sums a+b (a<=b) distinct), improving the live OEIS public lower bound a(10) >= 63 by +3 and the prior local best 65 by +1. Found by an Opus-4.8 Canopus-loop proposer (no-context arm, local search); re-verified from scratch by verify_construction.verify_sidon (frozen gate). Witness sha256:6a358e229f98b723…
theoretical · vf_c9ab5970cdbcb6af

Evidence atoms

vea_260ba1d40fa518abcomputational · supports
{"artifact_id":"va_6a358e229f98b723","artifact_packet_id":"cap_087198a92d1e30a2","candidate_claim_id":"vc_5aab0a22f7cdebf1"}

Review, event, and evaluation records

events

vev_d30acf067ad58787finding.asserted
Candidate claim vc_5aab0a22f7cdebf1 imported from artifact packet cap_087198a92d1e30a2
reviewer:will · 2026-06-03

reviewable changes

vpr_1879d8894dd07e64finding.add
Candidate claim vc_5aab0a22f7cdebf1 imported from artifact packet cap_087198a92d1e30a2
applied · agent:canopus-lean-2026-06-03 · 2026-06-03

evaluations

No evaluation rows are attached.