verification/terminal-bench/sync_collection.py

#!/usr/bin/env python3
"""Synchronize the Terminal-Bench finite-problem contribution.

The UnsolvedMath export is denormalized across problems.json, dataset.json,
statistics.json, sets.json, and README.md. This script keeps those copies
consistent and makes the proposed contribution straightforward to review.
"""

from __future__ import annotations

import json
import re
from collections import Counter
from pathlib import Path


ROOT = Path(__file__).resolve().parents[2]
STAMP = "2026-07-31T00:00:00Z"
SET_ID = 14
SET_RECORD = {
    "id": SET_ID,
    "name": "terminal_bench_verifiable_problems",
    "display_name": "Terminal-Bench Verifiable Open Problems",
    "description": (
        "Finite open mathematical and cryptanalytic problems selected and "
        "formalized for Terminal-Bench, with exact witness checkers or Lean "
        "statements supplied as optional verification artifacts."
    ),
    "slug": "terminal-bench-verifiable-problems",
    "order_index": SET_ID,
    "created_at": STAMP,
}


PROBLEMS = [
    {
        "number": "TBV-001",
        "title": "AES S-Box Multiplicative Complexity",
        "statement": (
            "Determine whether the AES field-inversion map $F:\\mathbb F_{2^8}"
            "\\to\\mathbb F_{2^8}$, $F(0)=0$ and $F(x)=x^{254}$ for $x\\ne0$, "
            "has multiplicative complexity below 29. Equivalently, construct an "
            "XOR/AND/NOT circuit with at most 28 AND gates, or prove that every "
            "such circuit requires at least 29 AND gates. The field is "
            "$\\mathbb F_2[X]/(X^8+X^4+X^3+X+1)$; XOR and NOT are free."
        ),
        "background": (
            "Multiplicative complexity counts nonlinear gates in a Boolean "
            "circuit. In July 2026 an explicit 29-AND construction improved the "
            "previous public 32-AND NIST circuit and was exhaustively checked on "
            "all 256 inputs. The construction establishes only the upper bound; "
            "no 28-AND circuit or matching 29-gate lower bound was located in the "
            "status audit. Sources: https://umizame.github.io/S-box_29-AND/ ; "
            "https://csrc.nist.gov/projects/circuit-complexity ; FIPS 197, "
            "https://doi.org/10.6028/NIST.FIPS.197-upd1 . Status audited 31 July "
            "2026. Formal statement and exhaustive checker: "
            "verification/terminal-bench/TBV-001/."
        ),
        "category": 15,
        "difficulty": 4,
    },
    {
        "number": "TBV-002",
        "title": "Existence of a Costas Array of Order 32",
        "statement": (
            "Does there exist a permutation $p$ of $\\{0,\\ldots,31\\}$ for "
            "which all 496 displacement vectors $(j-i,p(j)-p(i))$, "
            "$0\\le i<j<32$, are distinct?"
        ),
        "background": (
            "Costas arrays arose in sonar and radar design. Order 32 is the "
            "smallest order whose existence remains unresolved publicly: neither "
            "a permutation nor a nonexistence proof was found. Enumeration at "
            "orders 28 and 29 required about 70 and 366.55 single-CPU years. "
            "Sources: Dinitz, Henning, Montejano and Warnke, The Density of "
            "Costas Arrays Decays Exponentially, "
            "https://mathweb.ucsd.edu/~lwarnke/CostasArrayExponentialDecay.pdf ; "
            "Afacan and Golomb, https://doi.org/10.1007/s10013-020-00392-5 ; "
            "OEIS A008404, https://oeis.org/A008404 . Status audited 31 July "
            "2026. Lean statement and exact displacement checker: "
            "verification/terminal-bench/TBV-002/."
        ),
        "category": 2,
        "difficulty": 4,
    },
    {
        "number": "TBV-003",
        "title": "Existence of an Eight-Bit APN Permutation",
        "statement": (
            "Does there exist a permutation $F:\\mathbb F_2^8\\to\\mathbb "
            "F_2^8$ such that, for every nonzero $a$ and every $b$, the equation "
            "$F(x+a)+F(x)=b$ has at most two solutions $x$? Equivalently, does an "
            "almost-perfect-nonlinear permutation on eight bits exist?"
        ),
        "background": (
            "APN functions have optimal differential uniformity and are central "
            "objects in vectorial Boolean-function theory. Even-dimensional APN "
            "permutations are exceptionally constrained. The audit found many "
            "dimension-eight APN functions but no dimension-eight APN permutation "
            "and no universal nonexistence proof. Sources: Claude Carlet, "
            "Vectorial Boolean Functions for Cryptography, "
            "https://www.math.univ-paris13.fr/~carlet/chap-vectorial-fcts-corr.pdf ; "
            "https://arxiv.org/abs/2508.04644 ; "
            "https://arxiv.org/abs/2606.11967 . Status audited 31 July 2026. "
            "Lean statement and complete difference-table checker: "
            "verification/terminal-bench/TBV-003/."
        ),
        "category": 15,
        "difficulty": 4,
    },
    {
        "number": "TBV-004",
        "title": "Balanced Nine-Variable Boolean Nonlinearity Above 240",
        "statement": (
            "Does there exist a balanced Boolean function "
            "$f:\\mathbb F_2^9\\to\\mathbb F_2$ with nonlinearity at least 242? "
            "Equivalently, can a balanced function have all Walsh coefficients of "
            "absolute value at most 28, or is 240 a universal upper bound for the "
            "balanced nine-variable case?"
        ),
        "background": (
            "Unbalanced nine-variable functions of nonlinearity 242 are known, "
            "whereas the best balanced value located in the audit is 240. The "
            "balance requirement is therefore essential. Sources: Kavut, Maitra "
            "and Yucel, https://arxiv.org/abs/0808.0684 ; Claude Carlet, Boolean "
            "Functions for Cryptography and Coding Theory, "
            "https://www.math.univ-paris13.fr/~carlet/chap-fcts-Bool-corr.pdf ; "
            "https://doi.org/10.1145/3512290.3528871 . Status audited 31 July "
            "2026. Lean statement and exact Walsh-spectrum checker: "
            "verification/terminal-bench/TBV-004/."
        ),
        "category": 15,
        "difficulty": 4,
    },
    {
        "number": "TBV-005",
        "title": "Binary Radius-Two Covering Code at Redundancy 18",
        "statement": (
            "Is $\\ell_2(18,2)\\le830$? That is, does there exist a full-row-rank "
            "binary parity-check matrix with 18 rows and at most 830 columns for "
            "which every syndrome is the sum of at most two distinct columns? "
            "Alternatively, prove that every such matrix has at least 831 columns."
        ),
        "background": (
            "A 2025 construction establishes $\\ell_2(18,2)\\le831$. Its explicit "
            "831-column parity-check matrix has been independently reconstructed "
            "and checked, but no 830-column construction or matching lower bound "
            "was found. Source: Davydov, Marcugini and Pambianco, New upper bounds "
            "for binary linear covering codes, "
            "https://arxiv.org/abs/2511.02542 . Status audited 31 July 2026. Lean "
            "statement and exhaustive syndrome checker: "
            "verification/terminal-bench/TBV-005/."
        ),
        "category": 15,
        "difficulty": 4,
    },
    {
        "number": "TBV-006",
        "title": "A Ten-Multiplication Curve25519 Inversion Chain",
        "statement": (
            "Starting from exponent 1, can the exact natural-number exponent "
            "$2^{255}-21$ be reached using at most 254 doublings and at most ten "
            "additions of two unequal previously reached exponents? Equivalently, "
            "can Curve25519 field inversion be expressed by an addition chain with "
            "254 squarings and ten nonsquare multiplications in this model?"
        ),
        "background": (
            "The familiar Curve25519 inversion chain reaches the exponent with "
            "254 squarings and 11 nonsquare multiplications. The question freezes "
            "exact exponent equality, rather than congruence modulo the "
            "multiplicative-group order. No ten-multiplication chain or "
            "impossibility proof was located. Sources: Daniel J. Bernstein, "
            "Curve25519: new Diffie-Hellman speed records, "
            "https://cr.yp.to/ecdh/curve25519-20060209.pdf ; verified addition-chain "
            "software, https://github.com/mmcloughlin/addchain . Status audited 31 "
            "July 2026. Lean statement and exact exponent checker: "
            "verification/terminal-bench/TBV-006/."
        ),
        "category": 15,
        "difficulty": 4,
    },
    {
        "number": "TBV-007",
        "title": "Fukuoka MQ Challenge Type VI, 25 Equations",
        "statement": (
            "Solve the official Fukuoka MQ Challenge Type VI seed-0 instance with "
            "37 variables and 25 quadratic equations over $\\mathbb F_{31}$; that "
            "is, exhibit a vector in $\\mathbb F_{31}^{37}$ at which all 25 frozen "
            "polynomials vanish."
        ),
        "background": (
            "The official hall of fame records the corresponding seed-0 "
            "24-equation instance as solved on 16 October 2025, while the "
            "25-equation instance remained open at audit time. Official challenge "
            "and instance: https://www.mqchallenge.org/ and "
            "https://www.mqchallenge.org/challenges/VI/challenge-6-25-0.bz2 . "
            "The frozen instance has SHA-256 "
            "52b44066277c3b89a896967379789abb06bde8c6f269c5d33aeeb97915efa9e4. "
            "Status audited 31 July 2026. Exact finite-field checker: "
            "verification/terminal-bench/TBV-007/."
        ),
        "category": 15,
        "difficulty": 3,
    },
    {
        "number": "TBV-008",
        "title": "Provider0 Length-1473 Syndrome Decoding Challenge",
        "statement": (
            "For the official Provider0 Goppa-McEliece challenge of length 1473 "
            "and codimension 294, find a binary error vector of Hamming weight at "
            "most 27 having the published syndrome."
        ),
        "background": (
            "The public syndrome-decoding hall of fame listed length 1409 and "
            "weight 26 as the solved frontier; the Provider0 length-1473, weight-27 "
            "instance remained open. Provider0 exposes a random binary matrix with "
            "Goppa/Classic-McEliece-like parameters, not a hidden structured code. "
            "Sources: https://decodingchallenge.org/goppa and official instance "
            "https://decodingchallenge.org/Challenges/Goppa/Provider0/Goppa_1473 . "
            "The frozen file SHA-256 is "
            "8757e3f21842aab42943264daa88df3a472a9d464810cf31ca444f75cdbe12f5. "
            "Status audited 31 July 2026. Exact syndrome checker: "
            "verification/terminal-bench/TBV-008/."
        ),
        "category": 15,
        "difficulty": 4,
    },
    {
        "number": "TBV-009",
        "title": "Width-200 Three-Round Keccak Preimage Challenge",
        "statement": (
            "Find a raw-Keccak preimage of the 80-bit target "
            "$\\mathtt{d8ed85692afbee4c99ce}$ for width 200, rate 40, capacity "
            "160, using any three consecutive rounds of Keccak-f[200], under the "
            "Keccak Crunchy Contest padding and bit-order conventions."
        ),
        "background": (
            "The Keccak Crunchy Crypto Collision and Pre-image Contest continued "
            "to mark this width-200 three-round cell as open. The target and "
            "freedom to select a consecutive three-round window come from the "
            "official contest. Source: https://keccak.team/crunchy_contest.html . "
            "The verification semantics were checked against KeccakTools commit "
            "3473478bf9c10bf95879cd8960c7409fee313162. Status audited 31 July "
            "2026. Bit-exact sponge checker: "
            "verification/terminal-bench/TBV-009/."
        ),
        "category": 15,
        "difficulty": 3,
    },
    {
        "number": "TBV-010",
        "title": "Minimum Three-Dimensional Kochen-Specker System",
        "statement": (
            "Does there exist an uncolorable Kochen-Specker system of at most 30 "
            "real projective rays in $\\mathbb R^3$? Here a coloring assigns 0 or "
            "1 to every ray, no orthogonal pair may both receive 1, and no "
            "orthogonal triple may receive three 0s. Alternatively, prove that "
            "every system of at most 30 rays is colorable."
        ),
        "background": (
            "The smallest known real three-dimensional Kochen-Specker system has "
            "31 rays, while the published global lower bound is 24. The question "
            "is unrestricted over real coordinates; integer coordinates are only "
            "one certificate class. Sources: Li, Bright and Ganesh, "
            "https://doi.org/10.24963/ijcai.2024/210 ; Arends, Ouaknine and Wampler, "
            "https://arxiv.org/abs/1111.3301 ; https://kochen-specker.info/ . "
            "Status audited 31 July 2026. Lean real-coordinate statements and an "
            "exact integer-ray checker: verification/terminal-bench/TBV-010/."
        ),
        "category": 16,
        "difficulty": 4,
    },
    {
        "number": "TBV-011",
        "title": "A 55-Addition Rank-23 Scheme for 3-by-3 Matrix Multiplication",
        "statement": (
            "Does general $3\\times3$ matrix multiplication admit a bilinear "
            "straight-line program using at most 23 scalar products and at most 55 "
            "binary additions or subtractions? Signed copies and fanout are free; "
            "all other integer linear combinations must be built from counted "
            "binary gates. Alternatively, prove that every such rank-at-most-23 "
            "program requires at least 56 additions."
        ),
        "background": (
            "Sun published an exact rank-23 scheme using 56 additions in April "
            "2026. The printed program has been transcribed and all 729 integer "
            "bilinear coefficients independently verified. No 55-addition scheme "
            "or universal 56-addition lower bound in this precise signed-SLP model "
            "was found. Sources: Yinqi Sun, https://arxiv.org/abs/2604.27645 and "
            "https://github.com/sunyinqi0508/3by3r23-56a . Status audited 31 July "
            "2026. Lean statement and exact symbolic checker: "
            "verification/terminal-bench/TBV-011/."
        ),
        "category": 4,
        "difficulty": 4,
    },
    {
        "number": "TBV-012",
        "title": "The Order-23 Maximal Determinant Problem",
        "statement": (
            "Determine $D(23)$, the largest absolute determinant of a "
            "$23\\times23$ matrix with entries in $\\{-1,1\\}$. In particular, "
            "either construct a matrix with determinant exceeding "
            "$662671875\\cdot2^{22}=2779447296000000$, or prove that this "
            "incumbent value is the exact maximum."
        ),
        "background": (
            "Order 23 remains one of the smallest unresolved Hadamard maximal "
            "determinant cases. The incumbent follows from the corresponding "
            "order-22 zero-one determinant by standard bordering. Sources: Orrick, "
            "Solomon, Dowdeswell and Smith, https://arxiv.org/abs/math/0304410 ; "
            "Browne et al., https://doi.org/10.37236/10367 ; OEIS A003432, "
            "https://oeis.org/A003432 . Status audited 31 July 2026. Lean optimality "
            "statement and exact Bareiss determinant checker: "
            "verification/terminal-bench/TBV-012/."
        ),
        "category": 4,
        "difficulty": 4,
    },
    {
        "number": "TBV-013",
        "title": "A 66-XOR 32-Bit MDS Linear Layer",
        "statement": (
            "Does there exist a linear map on four 8-bit input words with word "
            "branch number 5 that can be implemented with at most 66 causal "
            "two-input bit-XOR gates? Fanout, wire selection and copying are free, "
            "but arbitrary linear forms and word-level XORs are not primitives. "
            "Alternatively, prove that 67 XOR gates are necessary in this model."
        ),
        "background": (
            "Duval and Leurent publish a 67-XOR implementation of a four-word MDS "
            "linear layer. Its word operations expand to exactly 67 two-input bit "
            "XORs under the stated circuit model. No 66-gate construction or "
            "lower-bound proof was located. Sources: Duval and Leurent, MDS "
            "Matrices with Lightweight Circuits, "
            "https://doi.org/10.46586/tosc.v2018.i2.48-78 and implementation "
            "https://github.com/seduval/findmds . Status audited 31 July 2026. Lean "
            "statement and exact linear-circuit checker: "
            "verification/terminal-bench/TBV-013/."
        ),
        "category": 15,
        "difficulty": 4,
    },
    {
        "number": "TBV-014",
        "title": "Three Mutually Orthogonal Latin Squares of Order 10",
        "statement": (
            "Do there exist three pairwise mutually orthogonal Latin squares of "
            "order 10? Equivalently, is the maximum number $N(10)$ of MOLS of "
            "order 10 at least three?"
        ),
        "background": (
            "Two MOLS of order 10 are known, but neither a triple nor an "
            "unrestricted nonexistence proof was found; the published interval is "
            "$2\\le N(10)\\le6$. Recent SAT results exclude substantial restricted "
            "families without settling the general case. Sources: Bright, Keita "
            "and Stevens, https://arxiv.org/abs/2503.10504 and "
            "https://arxiv.org/abs/2509.09633 ; Rubin et al., "
            "https://arxiv.org/abs/2103.11018 . Status audited 31 July 2026. Lean "
            "statement and exact Latin/orthogonality checker: "
            "verification/terminal-bench/TBV-014/."
        ),
        "category": 2,
        "difficulty": 4,
    },
    {
        "number": "TBV-015",
        "title": "Determine the Ramsey Number R(3,10)",
        "statement": (
            "Is $R(3,10)=40$ or $R(3,10)=41$? Equivalently, does there exist a "
            "triangle-free graph on 40 vertices with independence number at most "
            "9?"
        ),
        "background": (
            "The current published bounds are $40\\le R(3,10)\\le41$. A qualifying "
            "40-vertex graph proves the upper endpoint exact; a proof that no such "
            "graph exists proves the lower endpoint exact. Sources: Vigleik "
            "Angeltveit, R(3,10) <= 41, "
            "https://www.combinatorics.org/ojs/index.php/eljc/article/view/v32i4p30 "
            "and https://arxiv.org/abs/2401.00392 ; Small Ramsey Numbers survey, "
            "https://www.cs.rit.edu/~spr/ElJC/sur.pdf . Status audited 31 July "
            "2026. Lean statement and exact graph checker: "
            "verification/terminal-bench/TBV-015/."
        ),
        "category": 3,
        "difficulty": 4,
    },
    {
        "number": "TBV-016",
        "title": "Eight-Bit Permutation Nonlinearity Above 112",
        "statement": (
            "Does there exist a permutation $F:\\mathbb F_2^8\\to\\mathbb F_2^8$ "
            "with standard vectorial nonlinearity at least 114? Equivalently, can "
            "all Walsh coefficients $W_F(u,v)$ with $v\\ne0$ have absolute value "
            "at most 28, or is 112 a universal upper bound for eight-bit "
            "permutations?"
        ),
        "background": (
            "The best standard vectorial nonlinearity located for an eight-bit "
            "permutation is 112, achieved by AES inversion; the applicable general "
            "upper bound is 116. The definition ranges over all nonzero output "
            "masks, not only coordinate functions. Sources: Claude Carlet, "
            "Vectorial Boolean Functions for Cryptography, "
            "https://www.math.univ-paris13.fr/~carlet/chap-vectorial-fcts-corr.pdf ; "
            "Picek et al., https://doi.org/10.1016/j.asoc.2015.10.066 . Status "
            "audited 31 July 2026. Lean statement and exact vectorial Walsh checker: "
            "verification/terminal-bench/TBV-016/."
        ),
        "category": 15,
        "difficulty": 4,
    },
    {
        "number": "TBV-017",
        "title": "An Explicit Two-Block Collision for 32-Step SHA-256",
        "statement": (
            "Find two distinct 128-byte messages that collide when processed as "
            "two raw 64-byte blocks from the standard SHA-256 IV, with each "
            "compression executing rounds 0 through 31 and applying the ordinary "
            "feed-forward. No SHA-256 padding block is appended."
        ),
        "background": (
            "An explicit standard-IV two-block collision is published for 31-step "
            "SHA-256 and separates after the 32nd step. Later papers give attack "
            "algorithms on more steps, but the audit located no public 32-step pair "
            "under this exact serialization. Sources: FIPS 180-4, "
            "https://doi.org/10.6028/NIST.FIPS.180-4 ; The First Practical Collision "
            "for 31-Step SHA-256, ASIACRYPT 2024 slides, "
            "https://iacr.org/submit/files/slides/2024/asiacrypt/asiacrypt2024/64/64_slides.pdf ; "
            "https://eprint.iacr.org/2026/232 and "
            "https://eprint.iacr.org/2026/1120 . Status audited 31 July 2026. "
            "Bit-exact reduced-compression checker: "
            "verification/terminal-bench/TBV-017/."
        ),
        "category": 15,
        "difficulty": 3,
    },
    {
        "number": "TBV-018",
        "title": "Improve the Dimension-210 SVP Challenge Record",
        "statement": (
            "For the official SVP Challenge lattice of dimension 210 and seed 0, "
            "find a nonzero lattice vector of exact squared Euclidean norm less "
            "than 14,497,861."
        ),
        "background": (
            "The SVP Challenge Hall listed a record vector by Jintai Ding and Ziyu "
            "Zhao with displayed norm 3808 and exact squared norm 14,497,861. This "
            "question asks for a strict improvement on the same frozen basis. "
            "Sources: https://www.latticechallenge.org/svp-challenge/ ; official "
            "basis https://www.latticechallenge.org/svp-challenge/download/challenges/svpchallengedim210seed0.txt ; "
            "record vector https://www.latticechallenge.org/svp-challenge/solution.php?id=1 . "
            "The basis SHA-256 is "
            "020cd84a3ae1514c3d3a25a2c7350dacde955d8b7977253c71f9396e01e46e51. "
            "Status audited 31 July 2026. Exact integer lattice checker: "
            "verification/terminal-bench/TBV-018/."
        ),
        "category": 15,
        "difficulty": 3,
    },
]


EXISTING_UPDATES = {
    "GRAPH-024": {
        "background": (
            "Norman Biggs first suggested the feasible strongly regular graph "
            "parameters $(99,14,1,2)$ in 1969; John Horton Conway later gave the "
            "well-known reformulation from which the problem's common name derives. "
            "Such a graph would have 99 vertices, degree 14, exactly one common "
            "neighbor for adjacent pairs, and exactly two for nonadjacent pairs. "
            "No construction or nonexistence proof was located in the 31 July 2026 "
            "audit, and recent computational work still treats the question as open. "
            "Sources: Keramatipour and Dawar, https://doi.org/10.5802/alco.418 ; "
            "Brouwer and Van Maldeghem's parameter tables, "
            "https://www.win.tue.nl/~aeb/graphs/srg/srgtab.html ; computational "
            "search data, https://github.com/GrayTaylor/conway99 . A Lean "
            "nonexistence statement and exact graph checker are supplied at "
            "verification/terminal-bench/GRAPH-024/."
        ),
    },
    "GRAPH-025": {
        "background": (
            "The degree-diameter problem asks for the maximum order of a graph with "
            "maximum degree $d$ and diameter $k$. The Moore bound gives a general "
            "upper bound, usually not attained. A concrete unresolved frontier is "
            "$(d,k)=(5,5)$: the maintained record table listed Marston Conder's "
            "648-vertex Cayley graph, communicated 18 January 2026, and no graph on "
            "at least 649 vertices or proof of the upper bound 648 was located in "
            "the 31 July 2026 audit. Sources: record table "
            "https://web.mat.upc.edu/francesc.comellas/delta-d/table_degree_diameter.html "
            "and published adjacency data "
            "https://web.mat.upc.edu/francesc.comellas/delta-d/desc_g/desc_g5.html#55 . "
            "A Lean upper-bound statement and exact degree/diameter checker for this "
            "finite case are supplied at verification/terminal-bench/GRAPH-025/."
        ),
    },
}


def dump(path: Path, value: object) -> None:
    path.write_text(json.dumps(value, indent=2, ensure_ascii=False) + "\n")


def replace_readme_statistics(readme: str, stats: dict) -> str:
    readme = readme.replace("**5,426 open mathematics problems**", "**5,444 open mathematics problems**")
    readme = readme.replace("**Total Problems**: 5426", "**Total Problems**: 5444")
    readme = readme.replace("**Problem Sets**: 13 curated collections", "**Problem Sets**: 14 curated collections")
    if "- Terminal-Bench Verifiable Open Problems" not in readme:
        readme = readme.replace(
            "- AMR Open Problem Lists\n",
            "- AMR Open Problem Lists\n- Terminal-Bench Verifiable Open Problems\n",
        )

    difficulty_lines = "\n".join(
        f"- {name}: {count}" for name, count in stats["problems_by_difficulty"].items()
    )
    category_lines = "\n".join(
        f"- {name}: {count}" for name, count in stats["problems_by_category"].items()
    )
    status_lines = "\n".join(
        f"- {name.replace('_', ' ').title()}: {count}"
        for name, count in stats["problems_by_status"].items()
    )
    readme = re.sub(
        r"(### Problems by Difficulty\n\n).*?(\n\n### Problems by Category)",
        rf"\g<1>{difficulty_lines}\g<2>",
        readme,
        flags=re.S,
    )
    readme = re.sub(
        r"(### Problems by Category\n\n).*?(\n\n### Problems by Status)",
        rf"\g<1>{category_lines}\g<2>",
        readme,
        flags=re.S,
    )
    readme = re.sub(
        r"(### Problems by Status\n\n).*?(\n\n## Usage)",
        rf"\g<1>{status_lines}\g<2>",
        readme,
        flags=re.S,
    )
    return readme


def main() -> None:
    categories = json.loads((ROOT / "categories.json").read_text())
    difficulties = json.loads((ROOT / "difficulty_levels.json").read_text())
    sets = json.loads((ROOT / "sets.json").read_text())
    problems = json.loads((ROOT / "problems.json").read_text())

    category_by_id = {x["id"]: x for x in categories}
    difficulty_by_id = {x["id"]: x for x in difficulties}
    sets = [x for x in sets if x["id"] != SET_ID] + [SET_RECORD]

    existing_numbers = {x["problem_number"] for x in problems}
    for number, update in EXISTING_UPDATES.items():
        if number not in existing_numbers:
            raise RuntimeError(f"missing existing problem {number}")
        record = next(x for x in problems if x["problem_number"] == number)
        record.update(update)
        record["updated_at"] = STAMP

    new_numbers = {x["number"] for x in PROBLEMS}
    problems = [x for x in problems if x["problem_number"] not in new_numbers]
    for offset, source in enumerate(PROBLEMS, start=1):
        category = category_by_id[source["category"]]
        difficulty = difficulty_by_id[source["difficulty"]]
        problems.append(
            {
                "id": 12_000_000 + offset,
                "problem_number": source["number"],
                "title": source["title"],
                "statement": source["statement"],
                "background": source["background"],
                "difficulty_level_id": difficulty["id"],
                "status": "open",
                "proposed_by": None,
                "proposed_year": None,
                "category_id": category["id"],
                "set_id": SET_ID,
                "view_count": 0,
                "favorite_count": 0,
                "created_at": STAMP,
                "updated_at": STAMP,
                "published": True,
                "category": category,
                "difficulty": difficulty,
                "set": SET_RECORD,
            }
        )

    if len({x["id"] for x in problems}) != len(problems):
        raise RuntimeError("duplicate numeric problem ID")
    for number in new_numbers:
        if sum(x["problem_number"] == number for x in problems) != 1:
            raise RuntimeError(f"new problem number is not unique: {number}")

    by_difficulty = Counter(x["difficulty"]["name"] for x in problems)
    by_category = Counter(x["category"]["display_name"] for x in problems)
    by_status = Counter(x["status"] for x in problems)
    by_set = Counter(x["set"]["name"] for x in problems if x.get("set"))
    stats = {
        "total_problems": len(problems),
        "problems_by_difficulty": dict(by_difficulty),
        "problems_by_category": dict(by_category),
        "problems_by_status": dict(by_status),
        "problems_by_set": dict(by_set),
    }

    dataset = json.loads((ROOT / "dataset.json").read_text())
    dataset["metadata"]["exported_at"] = STAMP
    dataset["metadata"]["total_problems"] = len(problems)
    dataset["metadata"]["total_sets"] = len(sets)
    dataset["sets"] = sets
    dataset["problems"] = problems

    dump(ROOT / "sets.json", sets)
    dump(ROOT / "problems.json", problems)
    dump(ROOT / "dataset.json", dataset)
    dump(ROOT / "statistics.json", stats)

    readme_path = ROOT / "README.md"
    readme_path.write_text(replace_readme_statistics(readme_path.read_text(), stats))


if __name__ == "__main__":
    main()