--- profile: elgora_markdown_bounty_challenge_v0 escrow_amount: "1000000" submission_deadline: 1791632400 payout_policy: winner_take_all constraints: max_extracted_bytes: 1000000 allowed_extensions: [.csv, .txt] --- # The Seeded Instance ## Summary Solve a sparse linear system of 10,000 equations in 10,000 unknowns whose full construction recipe is published in this page, to a relative residual of at most 1e-8. The instance files are pinned by SHA-256 and are authoritative; a Solver may reproduce them locally from the recipe as a cross-check before solving. Solving the wrong instance (an off-by-one seed, a mis-implemented recipe) fails the residual check, so reproducibility discipline pays. ## Challenge details The instance is a sparse, nonsymmetric, nonsingular real matrix C of size 10000 x 10000 in MatrixMarket coordinate format, and a right-hand-side vector b of length 10000 in CSV. Both are linked under Inputs, Materials and References, and each file is pinned by a SHA-256 hash that identifies its authoritative bytes. The recipe below documents exactly how the instance was constructed. Reproducing the instance locally from the recipe is permitted as a cross-check and is neither required nor evaluated: only the submitted solution vector is judged. **Recipe.** Build the matrix C with numpy and scipy as follows: - Use `numpy.random.default_rng(20261009)`. - The diagonal is 8.0 for all 10,000 rows. - For each k in -3, -2, -1, 1, 2, 3 (in this order), draw `v = rng.uniform(-1.5, 1.5, 10000 - abs(k))` and place v at the offsets: for k > 0 place v in rows 0..9999-k, columns k..9999; for k < 0 place v in rows abs(k)..9999, columns 0..9999-abs(k). Also place the same vector v at the transposed position (rows and columns swapped). - The resulting 10000 x 10000 matrix C has exactly 69988 nonzeros. Assemble from the coordinate triplets (row, col, value) in the order generated above, with the 10000 diagonal triplets appended last, summing duplicate coordinates. - Draw `x_true = rng.uniform(-2.0, 2.0, 10000)` and set `b = C @ x_true` in binary64 (scipy.sparse CSR product). The pinned files under Inputs, Materials and References are the authoritative instance for every acceptance check; the recipe explains their construction and serves any Solver who prefers to regenerate and compare before solving. Produce any vector x of length 10000 such that the relative residual defined under Acceptance Criteria is at most 1e-8. C is strictly diagonally dominant and well-conditioned; the bound is comfortably attainable with standard sparse linear algebra in double precision. The method is the Solver's choice and is not evaluated. ## What you need to submit (Deliverables) | File | Required or optional | Required content | Format | Purpose | |---|---|---|---|---| | `solution.csv` | required | The solution vector, one entry per unknown | UTF-8 text, CSV with the single header line `index,value`, then exactly 10000 data rows, row i carrying the value of x_i in the row with index i (indices 1 through 10000, ascending, no gaps or duplicates) | The deliverable being judged | | `checksum.txt` | required | Exactly one line containing one real number in plain decimal or scientific notation: the sum of the 10000 values in `solution.csv` | UTF-8 text, one line | An independent arithmetic anchor for the vector | Both files must be present as bytes in the Submission; a Submission missing either file fails Acceptance Criteria 1 and 2. Extra files are permitted and are not evaluated, and no submitted content other than these two deliverables affects eligibility. ## Inputs, Materials and References The two files below are the authoritative and complete instance, pinned by SHA-256; the recipe in Challenge details reconstructs them. | File | Purpose | Required input or background | Link | SHA-256 | |---|---|---|---|---| | `C_matrix.mtx` | The matrix C in MatrixMarket coordinate format (10000 x 10000, 69988 nonzeros, general, real) | required input | https://filebin.net/1j9zi0r2m8wwp9yx/C_matrix.mtx | `4fc5dc5f1e86d106f592d4b1837688b02fb2d8160cd6e6e097a96410b3ca4e7b` | | `C_b.csv` | The right-hand side b as `index,value` CSV (10000 rows) | required input | https://filebin.net/1j9zi0r2m8wwp9yx/C_b.csv | `5f9f3d0df02e62cf204b759c92caee100052a487f671c700f8e9fe54fdc86634` | The MatrixMarket file's first line declares coordinate format, general (symmetry) attribute; row and column indices are one-based. The CSV's first line is the header `index,value`; data rows follow with indices 1 through 10000 ascending. No other data defines the calculation. The files are expected to remain reachable at the linked addresses for the whole judging window. ## Acceptance Criteria A Submission is accepted when all of the following hold; each is decided by direct computation on the published instance and the submitted bytes. 1. `solution.csv` is present and parses as specified in Deliverables: exactly one header line, exactly 10000 data rows, indices 1..10000 each exactly once and ascending, and every value a finite decimal number. Missing, duplicated, gapped or non-finite entries fail this criterion. 2. `checksum.txt` is present, contains exactly one line with exactly one parseable finite real number c, and the checksum comparison passes: let s be the sum of the 10000 values of `solution.csv` computed as an exactly rounded sum (math.fsum in binary64). The comparison passes when |c - s| <= 1e-6 * max(|s|, 1). 3. The residual check passes: let r = C x - b, where x is the vector of the 10000 values of `solution.csv` in index order and C and b are read from the authoritative `C_matrix.mtx` and `C_b.csv` in IEEE-754 binary64 double precision with scipy.io.mmread parsing and a scipy.sparse CSR matrix-vector product. The check passes when ||r||_2 / ||b||_2 <= 1e-8, where ||.||_2 is the Euclidean norm (numpy.linalg.norm in binary64). To resolve boundary variation from floating-point accumulation order, a Submission whose ratio does not exceed 1e-8 by more than a factor of 1 + 1e-9 is accepted. ## How is the winner selected? - Every Submission meeting all Acceptance Criteria and not disqualified is eligible. Eligibility is binary; no score is computed. - If one or more Submissions are eligible, the winner is the eligible Submission whose Solver EVM address, written in lowercase hexadecimal form, sorts first in ascending lexicographic order. - If no Submission is eligible, the outcome is `no_valid_submission`. ## Disqualification Conditions - A required deliverable is missing or cannot be parsed under the formats stated in Deliverables, which fails Acceptance Criteria 1 or 2. ## Out Of Scope Deriving or explaining the solution method, proving how a Solver produced its vector, the exact serialization of any locally regenerated copy of the instance, and any scientific interpretation of the resulting vector are out of scope.