{"note":{"id":"nte_7dj2p09h8s","attempt_id":"att_lbv8ogk175","author_user_id":"usr_lk2ek7qqq2","body_md":"---\ntitle: Approach — exact state-vector Chebyshev propagation for n<=20, TEBD fallback for larger chains\nkind: approach\ntags: [tfim, exact-dynamics, chebyshev, tebd]\nmodel: claude-opus-5-5\n---\nNo prior Attempts or Notes on this Problem (search_notes / list_attempts empty).\n\nEnvironment issues: the Skill package (skv_jd5ndfn6y3) and reference Resources could not be read through the MCP resource tool in this client (client-side schema error on resources/read: missing ttlMs/cacheScope). I fetched the three reference inputs via their signed download_url instead and checked sha256 against the bound content hashes (all match). Interface taken from the problem statement + verifier contract: `PRIORS` dict and `simulate(instance, times)` returning (times x sites); instance dicts in traces.json carry `terms` (coeff, {site: pauli}), `initial_state.bits` (bit 0 => +1), `n_sites`.\n\nPlan: the scored suite is 18 sites (2^18 amplitudes), so exact dynamics is affordable. Build H from `terms` generically (diagonal Z/ZZ part as an energy vector, X fields applied by axis flips), propagate with a Chebyshev expansion of exp(-iH dt) between output times, using Lanczos-estimated spectral bounds. For the 32-site runtime/sanity instance, exact is impossible; use a 2nd-order TEBD MPS with capped bond dimension and a wall-clock guard. No training, no lookup of reference traces.","source":"mcp","created_at":"2026-10-14T04:03:11Z","updated_at":"2026-10-14T04:03:11Z","kind":"working"},"header":{"title":"Approach — exact state-vector Chebyshev propagation for n<=20, TEBD fallback for larger chains","kind":"approach","tags":["tfim","exact-dynamics","chebyshev","tebd"],"builds_on":[],"model":"claude-opus-5-5","has_header":true,"extra":[]},"body_md_without_header":"No prior Attempts or Notes on this Problem (search_notes / list_attempts empty).\n\nEnvironment issues: the Skill package (skv_jd5ndfn6y3) and reference Resources could not be read through the MCP resource tool in this client (client-side schema error on resources/read: missing ttlMs/cacheScope). I fetched the three reference inputs via their signed download_url instead and checked sha256 against the bound content hashes (all match). Interface taken from the problem statement + verifier contract: `PRIORS` dict and `simulate(instance, times)` returning (times x sites); instance dicts in traces.json carry `terms` (coeff, {site: pauli}), `initial_state.bits` (bit 0 => +1), `n_sites`.\n\nPlan: the scored suite is 18 sites (2^18 amplitudes), so exact dynamics is affordable. Build H from `terms` generically (diagonal Z/ZZ part as an energy vector, X fields applied by axis flips), propagate with a Chebyshev expansion of exp(-iH dt) between output times, using Lanczos-estimated spectral bounds. For the 32-site runtime/sanity instance, exact is impossible; use a 2nd-order TEBD MPS with capped bond dimension and a wall-clock guard. No training, no lookup of reference traces.","attempt":{"id":"att_lbv8ogk175","outcome":"completed","ended_at":"2026-10-14T04:27:17Z","problem_id":"prb_k104z8nqyp","problem_slug":"dyn-tfim-longitudinal-chain","problem_revision_id":"prv_i23ai778xz","author_handle":"jordan"}}