schema_version: 1 contribution_id: con_c2c1e3918cf941b38aca71bbe91c7472 revision_id: rev_788ef24bd41046408e76679a89d7bd78 expected_predecessor: null type: attempt home_problem_id: prb_88fb7854aa574122913745e92367cf66 targets: - target_kind: problem problem_id: prb_88fb7854aa574122913745e92367cf66 statement_revision_id: stm_e6bca88c4e4846f1a659be908acf615f scope: whole_statement title: Partial result on TOP-30005893 profiles: - id: mathematical_argument version: 1 required: true claim: type: partial_result scope_statement: |- For the exact Kümmerle–Maly Algorithm 2.1 in arXiv:2306.04961v2, with target orders r=s=1, prescribed identity initial weight and infinite initial smoothing parameters, we construct a rational sensing Gram on R^(4×2) with joint doubled-order RIP constant δ_(2,2)<2/3. The target is the unique one-row rank-one feasible matrix, yet every iterate from the first onward is the same incorrect matrix, with strictly positive smoothing parameters. A companion geometric proposition proves a sharp 1/√2 lower bound for a specified first-step flat-row mechanism under scalar partial-isometry sensing, including arbitrary kernel dimension. This bound does not apply to general sensing metrics; the counterexample uses such a metric. This is not a full disproof of the open question: sufficiently smaller RIP constants, other related conditions, and global recovery for useful operator classes remain open. No optimal failure threshold, perturbation-stable attraction, or exhaustive literature novelty claim is made. The result goes beyond the existing CS-421-A1 identifiability discussion by proving failure of the exact initialized recurrence despite doubled-order restricted injectivity and target uniqueness. assumptions: [] limitations: [] attribution: submitter: person_ref: per_af8d978512094eff842edb39e170201a github_id: 51691872 login_at_event: yuningyang19 display_name: yuningyang19 roles: - submission - prompting authorship_confirmation: confirmed humans: - person_ref: per_af8d978512094eff842edb39e170201a github_id: 51691872 login_at_event: yuningyang19 display_name: yuningyang19 roles: - prompting - submission authorship_confirmation: confirmed organisations: [] contribution_mode: ai_only model_uses: - provider: openai declared_name: gpt 6 astra family: null version: gpt-6-astra; serving revision unknown role: proof_search settings: thinking_level: Medium thinking_time: unknown generation_date: null provenance: level: declared evidence: - kind: statement note: The generator's Astra/Medium run is not represented as meeting the listed High-setting example. The submitted claims receive a new correctness check by GPT 6.1 Sol at High, a model/setting explicitly listed by the contribution policy. This comprises the source weight/initialization interface, exact rational PSD/rank/kernel and restricted spectra, target uniqueness, full initialized stagnation induction, arbitrary-kernel projection obstruction, and its attaining example. The fresh-context reviewer is separate from the proof-generating contexts. No human or formal verification is claimed. The complete proof and explicit certificates are included above so the submission does not rely on inaccessible logs. The separate High review completed with a PASS on 19 October 2026; it independently reconstructed these arguments and checked every displayed rational pair determinant. The checking model and setting were verified from its own runtime turn_context metadata, rather than inferred from a gl - kind: statement note: obal configuration. The mathematical evidence being submitted is the complete proof and exact table above; private review logs are not required to verify it. - provider: openai declared_name: gpt 6.1 sol family: null version: gpt-6.1-sol; serving revision unknown role: review_assistance settings: thinking_level: High thinking_time: no preset budget; elapsed duration not used as a capability claim generation_date: null provenance: level: declared evidence: - kind: statement note: The generator's Astra/Medium run is not represented as meeting the listed High-setting example. The submitted claims receive a new correctness check by GPT 6.1 Sol at High, a model/setting explicitly listed by the contribution policy. This comprises the source weight/initialization interface, exact rational PSD/rank/kernel and restricted spectra, target uniqueness, full initialized stagnation induction, arbitrary-kernel projection obstruction, and its attaining example. The fresh-context reviewer is separate from the proof-generating contexts. No human or formal verification is claimed. The complete proof and explicit certificates are included above so the submission does not rely on inaccessible logs. The separate High review completed with a PASS on 19 October 2026; it independently reconstructed these arguments and checked every displayed rational pair determinant. The checking model and setting were verified from its own runtime turn_context metadata, rather than inferred from a gl - kind: statement note: obal configuration. The mathematical evidence being submitted is the complete proof and exact table above; private review logs are not required to verify it. - provider: openai declared_name: chatgpt (underlying model unknown) family: null version: unknown role: generated_draft settings: thinking_level: unknown thinking_time: unknown generation_date: null provenance: level: declared evidence: - kind: statement note: The generator's Astra/Medium run is not represented as meeting the listed High-setting example. The submitted claims receive a new correctness check by GPT 6.1 Sol at High, a model/setting explicitly listed by the contribution policy. This comprises the source weight/initialization interface, exact rational PSD/rank/kernel and restricted spectra, target uniqueness, full initialized stagnation induction, arbitrary-kernel projection obstruction, and its attaining example. The fresh-context reviewer is separate from the proof-generating contexts. No human or formal verification is claimed. The complete proof and explicit certificates are included above so the submission does not rely on inaccessible logs. The separate High review completed with a PASS on 19 October 2026; it independently reconstructed these arguments and checked every displayed rational pair determinant. The checking model and setting were verified from its own runtime turn_context metadata, rather than inferred from a gl - kind: statement note: obal configuration. The mathematical evidence being submitted is the complete proof and exact table above; private review logs are not required to verify it. lineage: [] artifacts: - role: manuscript location: in_repository path: files/attempt.md media_type: text/markdown - role: supplementary location: in_repository path: files/disclosures.md media_type: text/markdown rights: licence: CC-BY-4.0 redistribution: permitted holders: - yuningyang19 declarations: rights: confirmed: true source: form_field actor: per_af8d978512094eff842edb39e170201a recorded_at: '2026-10-19T08:07:38Z' evidence_url: https://github.com/We-Solve/research/issues/352 public_disclosure: confirmed: true source: form_field actor: per_af8d978512094eff842edb39e170201a recorded_at: '2026-10-19T08:07:38Z' evidence_url: https://github.com/We-Solve/research/issues/352 ai_disclosure: confirmed: true source: form_field actor: per_af8d978512094eff842edb39e170201a recorded_at: '2026-10-19T08:07:38Z' evidence_url: https://github.com/We-Solve/research/issues/352