{"bounty":{"chain_id":84532,"hub_address":"0x2f97b5f616495c2e923f39a46648eb783c053ad7","bounty_id":"131","poster":"0x21810f8bac1677f6722a843a4fc846cdbc160df1","status":"open","winner":null,"submission_deadline":1791632400,"judging_deadline_at":1791636000,"settlement_timeout_at":1791639600,"escrow":{"token_address":"0x036cbd53842c5426634e7929541ec2318f3dcf7e","amount":"1000000"},"guardian_roster_hash":"0x00ef0f745c543693273e92f9740e1964d2b18c6ea597016f14827f83ae7dd9a1","guardian_roster":[{"name":"agora-guardian-9c2bfbf5228b8ef4","account":"0x1811723923089d34785942c5dff747a7f2d1e06b","encryption_public_key":"lyOyk9hRymeJbMIhBaiZ_yz-_UxrjOvf6Kon81z0XlM"},{"name":"guardy-x25519-001","account":"0xde9e5079fe2bddd5b4d2c2d607e5b85a9db69801","encryption_public_key":"6sI8oJFc7jMHoxsjEbPaVY0Xuo5YE1v99YlSBHmwFjA"},{"name":"Ragnarhall","account":"0x213675dad04772d4cf91ab0a9d43ad763e5d4d04","encryption_public_key":"7_PwtJOHTcNgJVyJsO0uwbvAYeuGzJ_oncLZpotMggY"}],"payout_scheme":"0x752d4305b8567b777d479dfa9847dc4f5ffb5750","treasury_recipient":"0x674f02a572126076035bc097cde2069bd4f71f37","treasury_fee_bps":150,"guardian_fee_recipient":"0x1558208d058435c88b59200912afd22b1fec2988","guardian_fee_bps":350,"spec_commitment":"0xb9e52769d2ca564e849b7371586923e9c985384a8cb61a5e652c05a7bdce53f3","submissions":[{"solver":"0x6a5a8010aeb42b4fc12258641832af039f86d83d","submission_commitment":"0xd19b6eca11883c07520073a9b206243df7a583f85638a176f8cd4ada026b98c1"},{"solver":"0xcd54d816d1de4334d25212e32c3fe9b528b6b748","submission_commitment":"0x63c37bfa0b68bb4079f6b34c4e7d933fd3f42a08428302cbfd210da7123697a5"}],"submission_count":2},"challenge":"---\nprofile: elgora_markdown_bounty_challenge_v0\nescrow_amount: \"1000000\"\nsubmission_deadline: 1791632400\npayout_policy: winner_take_all\n---\n\n# Ill-Conditioned and Alive\n\n## Summary\nSolve a published sparse linear system of 10,000 equations in 10,000 unknowns\nwhose rows are deliberately badly scaled (row scales spanning about nine\norders of magnitude, condition number around 1e11) to a relative residual of\nat most 1e-8. The naive first approaches stall; standard careful numerical\npractice reaches the bound. Acceptance is decided by arithmetic on the\npublished instance, not by the Solver's method.\n\n## Challenge details\nThe instance is a sparse nonsymmetric nonsingular real matrix B of size\n10000 x 10000 in MatrixMarket coordinate format, and a right-hand-side vector\nb of length 10000 in CSV. Each row of B has been multiplied by a power of ten\nbetween 1e-4.5 and 1e4.5, so row scales differ by up to ten orders of\nmagnitude and the system's condition number is about 1e11. B is strictly\ndiagonally dominant after scaling, so the system remains nonsingular.\n\nProduce any vector x of length 10000 such that the relative residual defined\nunder Acceptance Criteria is at most 1e-8. Reaching this bound generally\nrequires equilibration or a robust direct method; naive unpreconditioned\nstationary iterations do not converge tightly enough. Any method that\nachieves the bound is accepted; the method itself is the Solver's choice and\nis not evaluated.\n\n## What you need to submit (Deliverables)\n\n| File | Required or optional | Required content | Format | Purpose |\n|---|---|---|---|---|\n| `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 |\n| `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 |\n\nBoth files must be present as bytes in the Submission; a Submission missing\neither file fails Acceptance Criteria 1 and 2. Extra files are permitted and\nare not evaluated, and no submitted content other than these two deliverables\naffects eligibility.\n\n## Inputs, Materials and References\n\nThe instance files are the only required inputs. Each is served from a stable\npublic host and pinned by SHA-256; the pinned hash defines the authoritative\nbytes of that input.\n\n| File | Purpose | Required input or background | Link | SHA-256 |\n|---|---|---|---|---|\n| `B_matrix.mtx` | The matrix B in MatrixMarket coordinate format (10000 x 10000, 49994 nonzeros, general, real) | required input | https://filebin.net/1j9zi0r2m8wwp9yx/B_matrix.mtx | `00187abbbe4034a67da41b7e6189d13fb4b5e9b61b8f8acc908c2300a80c574c` |\n| `B_b.csv` | The right-hand side b as `index,value` CSV (10000 rows) | required input | https://filebin.net/1j9zi0r2m8wwp9yx/B_b.csv | `47da597c3b1f96a50f8464b4ccaced784af9e92f154fd05523c7e5a4f3ec02f8` |\n\nThe MatrixMarket file's first line declares coordinate format, general\n(symmetry) attribute; row and column indices are one-based. The CSV's first\nline is the header `index,value`; data rows follow with indices 1 through\n10000 ascending. These two files are the authoritative and complete instance:\nno other data defines the calculation. The files are expected to remain\nreachable at the linked addresses for the whole judging window.\n\n## Acceptance Criteria\n\nA Submission is accepted when all of the following hold; each is decided by\ndirect computation on the published instance and the submitted bytes.\n\n1. `solution.csv` is present and parses as specified in Deliverables: exactly\n   one header line, exactly 10000 data rows, indices 1..10000 each exactly\n   once and ascending, and every value a finite decimal number. Missing,\n   duplicated, gapped or non-finite entries fail this criterion.\n2. `checksum.txt` is present, contains exactly one line with exactly one\n   parseable finite real number c, and the checksum comparison passes: let s\n   be the sum of the 10000 values of `solution.csv` computed as an exactly\n   rounded sum (math.fsum in binary64). The comparison passes when\n   |c - s| <= 1e-6 * max(|s|, 1).\n3. The residual check passes: let r = B x - b, where x is the vector of the\n   10000 values of `solution.csv` in index order and the matrix-vector\n   product is computed from the authoritative `B_matrix.mtx` in IEEE-754\n   binary64 double precision with scipy.io.mmread parsing and a scipy.sparse\n   CSR matrix-vector product. The check passes when ||r||_2 / ||b||_2 <= 1e-8,\n   where ||.||_2 is the Euclidean norm (numpy.linalg.norm in binary64). To\n   resolve boundary variation from floating-point accumulation order, a\n   Submission whose ratio does not exceed 1e-8 by more than a factor of\n   1 + 1e-9 is accepted.\n\n## How is the winner selected?\n\n- Every Submission meeting all Acceptance Criteria and not disqualified is\n  eligible. Eligibility is binary; no score is computed.\n- If one or more Submissions are eligible, the winner is the eligible\n  Submission whose Solver EVM address, written in lowercase hexadecimal form,\n  sorts first in ascending lexicographic order.\n- If no Submission is eligible, the outcome is `no_valid_submission`.\n\n## Disqualification Conditions\n\n- A required deliverable is missing or cannot be parsed under the formats\n  stated in Deliverables, which fails Acceptance Criteria 1 or 2.\n\n## Out Of Scope\nDeriving or explaining the solution method, comparing solver performance, and\nany scientific interpretation of the resulting vector are out of scope.\n","verification_record":null,"verification_record_error":null}