{
  "asserted_counts": {
    "checks_min": 17,
    "dod_engines_min": 2,
    "dod_exact_rows_min": 2,
    "engines_min": 12,
    "exact_byte_min": 21,
    "exact_rows_min": 56,
    "exact_token_min": 35,
    "foils_min": 32,
    "frontier_codes_min": 3,
    "known_limits_min": 6,
    "refused_rows_min": 6,
    "rows_min": 64,
    "vocabulary_min": 9
  },
  "boundary": {
    "does_not_hold": [
      "that any named engine would accept these bytes: nothing here links vLLM, TensorRT-LLM, SGLang, llama.cpp, FlashInfer, LMDeploy or transformers",
      "that the exhaustive index argument extends to another geometry: it is a statement about THIS shape, and the arbitrary-parameter content lives in the Lean primitives",
      "that the Lean primitives are what layouts.py implements: that link is a Python restatement pinned by the index probe, not a proof",
      "anything at all about throughput, latency, memory or cost"
    ],
    "holds": [
      "the eight layouts are DECLARED SHAPES with citations; no engine, kernel or GPU runs anywhere in this item",
      "the canonical tensor is [removed].decode_harness's (2, T, n_kv_heads, head_dim) numpy GQA geometry: 3 layers, 2 kv-heads, head_dim 8, float16",
      "token identity is measured against a reference this same run computes from the untranslated state through the same harness, with fixed seeded weights",
      "every index-level claim is checked over EVERY position of the declared geometry, and the certificate carries positions_checked and positions_total so a reader can see it"
    ],
    "note": "An enumerated list of exact transformations is a claim about a family and its edge. The REFUSED rows are as much the deliverable as the EXACT ones."
  },
  "checks": [
    {
      "detail": "64 rows against the 19 proof fields restated in specs/[removed]/verify_exact_transformations.py; offenders []",
      "name": "every_proof_matches_the_published_verifiers_field_set",
      "passed": true
    },
    {
      "detail": "56 exact rows; each one's checked-position count equals the product of the destination layout's own declared native shapes, computed independently; offenders []",
      "name": "every_exact_row_is_proved_over_its_whole_re_derived_index_space",
      "passed": true
    },
    {
      "detail": "every exact row needs at least one vocabulary word; offenders []",
      "name": "no_exact_row_is_a_relabelling",
      "passed": true
    },
    {
      "detail": "byte-identical 21, token-identical 35 \u2014 the DoD offers both and a list carrying only one of them has answered half the question",
      "name": "both_of_the_DoDs_exactness_classes_are_non_empty",
      "passed": true
    },
    {
      "detail": "9 of 9 words appear in some row; missing []",
      "name": "the_whole_transformation_vocabulary_is_exercised",
      "passed": true
    },
    {
      "detail": "the family's 3 edges are all demonstrated: ['X1_LATENT_KV', 'X2_HEAD_GATHER', 'X4_GEOMETRY_UNREPRESENTABLE']. Requantisation is deliberately NOT among them: it RUNS, and is graded NOT_EXACT",
      "name": "every_frontier_code_is_reached_by_a_row",
      "passed": true
    },
    {
      "detail": "corrupting one cached K position changes the decode: [2, 27, 60, 51, 2, 27, 60, 51] -> [2, 59, 39, 38, 59, 39, 38, 59]",
      "name": "the_token_leg_is_not_vacuous",
      "passed": true
    },
    {
      "detail": "reference tokens [2, 27, 60, 51, 2, 27, 60, 51] carry 4 distinct values",
      "name": "the_reference_sequence_is_not_degenerate",
      "passed": true
    },
    {
      "detail": "the relabelling translator round-trips A->B->A byte-identically (True) and is graded NOT_EXACT; its decode emits [52, 52, 52, 52, 52, 52, 52, 52] against the reference [2, 27, 60, 51, 2, 27, 60, 51]",
      "name": "a_perfect_round_trip_does_not_make_a_transformation_exact",
      "passed": true
    },
    {
      "detail": "35 token-identical rows, each differing on exactly its source's unread block-tail positions and nowhere else; offenders []",
      "name": "token_identical_means_the_padding_and_nothing_else",
      "passed": true
    },
    {
      "detail": "12 declared layouts, all distinct as DESCRIPTORS; collisions []",
      "name": "no_two_declared_engines_are_the_same_layout",
      "passed": true
    },
    {
      "detail": "8 distinct native images across the lossless layouts; two names for one image would be a relabelling, not a cross-engine pair. Collisions []",
      "name": "no_two_declared_engines_have_the_same_native_image",
      "passed": true
    },
    {
      "detail": "each layout names the engine structure it models, so a reader can check the shape against the engine rather than against this file",
      "name": "every_engine_carries_a_citation_for_the_shape_it_claims",
      "passed": true
    },
    {
      "detail": "8 of 8 lossless layouts carry a generated `decide` lemma over the whole 64-element small geometry; the pair statement follows by ExactTransform.comp_roundtrip",
      "name": "every_lossless_engine_has_a_kernel_checked_round_trip_lemma_THAT_EXISTS",
      "passed": true
    },
    {
      "detail": "ExactTransform.swapAt, transcribed into Python, produces the SAME flat index map as numpy's own adjacent-axis transpose over 165 axis stacks of 2-5 axes; divergences []. The two-axis `swap` it generalises does NOT: on a (2,3,4) tensor it disagrees with numpy, which is why the general form exists",
      "name": "the_lean_axis_exchange_is_the_operation_numpy_performs",
      "passed": true
    },
    {
      "detail": "over all 81 assignments of the four observations to {True, False, None}, weakening any one never raises a row's rank, and NULLING any one drops the row to UNPROVEN \u2014 the bottom of the scale, strictly below the NOT_EXACT that forward=False earns",
      "name": "no_missing_observation_can_improve_a_row",
      "passed": true
    },
    {
      "detail": "8 lossless layouts -> 56 ordered pairs, 56 present; the frontier and lossy layouts are paired against the anchor in both directions on top of that",
      "name": "the_hunt_covers_every_ordered_pair_of_the_lossless_engines",
      "passed": true
    }
  ],
  "engines": [
    {
      "attention": "gqa",
      "block": 16,
      "cite": "vLLM FlashAttention backend KV cache [2, num_blocks, block_size, num_kv_heads, head_size]; block_size default 16",
      "engine": "vllm-fa",
      "is_the_identity_map": false,
      "k_axes": [
        "KV",
        "Tb",
        "Ti",
        "H",
        "D"
      ],
      "k_x": 0,
      "kv": "interleaved",
      "lean_lemma": "ExactTransformCert.roundtrip_vllm_fa",
      "n_kv_heads": 0,
      "native_shapes": {
        "kv": [
          2,
          3,
          16,
          2,
          8
        ]
      },
      "quant": "none",
      "realisable_at_this_geometry": true,
      "v_axes": [
        "KV",
        "Tb",
        "Ti",
        "H",
        "D"
      ],
      "v_x": 0
    },
    {
      "attention": "gqa",
      "block": 16,
      "cite": "vLLM PagedAttention kernel: K [num_blocks, num_kv_heads, head_size//x, block_size, x], V [num_blocks, num_kv_heads, head_size, block_size]. The kernel's own x = 16 bytes / element size gives 8 for fp16, and x = 8 IS realisable at head_dim 8 ([.., .., 1, 16, 8]); 4 is declared here for NON-DEGENERACY, so the factored axis has two groups instead of one, and not because the real value does not fit",
      "engine": "vllm-paged-x",
      "is_the_identity_map": false,
      "k_axes": [
        "Tb",
        "H",
        "Dg",
        "Ti",
        "Dx"
      ],
      "k_x": 4,
      "kv": "separate",
      "lean_lemma": "ExactTransformCert.roundtrip_vllm_paged_x",
      "n_kv_heads": 0,
      "native_shapes": {
        "k": [
          3,
          2,
          2,
          16,
          4
        ],
        "v": [
          3,
          2,
          8,
          16
        ]
      },
      "quant": "none",
      "realisable_at_this_geometry": true,
      "v_axes": [
        "Tb",
        "H",
        "D",
        "Ti"
      ],
      "v_x": 0
    },
    {
      "attention": "gqa",
      "block": 32,
      "cite": "TensorRT-LLM paged KV block [num_blocks, 2, num_kv_heads, tokens_per_block, head_dim]; tokens_per_block 32",
      "engine": "trtllm",
      "is_the_identity_map": false,
      "k_axes": [
        "Tb",
        "KV",
        "H",
        "Ti",
        "D"
      ],
      "k_x": 0,
      "kv": "interleaved",
      "lean_lemma": "ExactTransformCert.roundtrip_trtllm",
      "n_kv_heads": 0,
      "native_shapes": {
        "kv": [
          2,
          2,
          2,
          32,
          8
        ]
      },
      "quant": "none",
      "realisable_at_this_geometry": true,
      "v_axes": [
        "Tb",
        "KV",
        "H",
        "Ti",
        "D"
      ],
      "v_x": 0
    },
    {
      "attention": "gqa",
      "block": 0,
      "cite": "SGLang RadixAttention token-indexed pools: separate K and V, each [num_tokens, num_kv_heads, head_dim]; paging is an index, not a layout",
      "engine": "sglang",
      "is_the_identity_map": true,
      "k_axes": [
        "T",
        "H",
        "D"
      ],
      "k_x": 0,
      "kv": "separate",
      "lean_lemma": "ExactTransformCert.roundtrip_sglang",
      "n_kv_heads": 0,
      "native_shapes": {
        "k": [
          40,
          2,
          8
        ],
        "v": [
          40,
          2,
          8
        ]
      },
      "quant": "none",
      "realisable_at_this_geometry": true,
      "v_axes": [
        "T",
        "H",
        "D"
      ],
      "v_x": 0
    },
    {
      "attention": "gqa",
      "block": 0,
      "cite": "Hugging Face transformers DynamicCache: key_cache/value_cache each [batch, num_kv_heads, seq_len, head_dim]; batch 1 here",
      "engine": "hf-dynamic-cache",
      "is_the_identity_map": false,
      "k_axes": [
        "H",
        "T",
        "D"
      ],
      "k_x": 0,
      "kv": "separate",
      "lean_lemma": "ExactTransformCert.roundtrip_hf_dynamic_cache",
      "n_kv_heads": 0,
      "native_shapes": {
        "k": [
          2,
          40,
          8
        ],
        "v": [
          2,
          40,
          8
        ]
      },
      "quant": "none",
      "realisable_at_this_geometry": true,
      "v_axes": [
        "H",
        "T",
        "D"
      ],
      "v_x": 0
    },
    {
      "attention": "gqa",
      "block": 0,
      "cite": "llama.cpp llama_kv_cache: k_l is ggml-shaped [n_embd_k_gqa, kv_size] and v_l is TRANSPOSED to [kv_size, n_embd_v_gqa] unless flash_attn is set. ggml's ne[0] is the FASTEST-VARYING axis, so in C row-major terms K is token-major [n_tokens, n_head_kv, head_dim] and V is [n_head_kv, head_dim, n_tokens] \u2014 the reversal is a real trap and is why it is spelled out here",
      "engine": "llamacpp",
      "is_the_identity_map": false,
      "k_axes": [
        "T",
        "H",
        "D"
      ],
      "k_x": 0,
      "kv": "separate",
      "lean_lemma": "ExactTransformCert.roundtrip_llamacpp",
      "n_kv_heads": 0,
      "native_shapes": {
        "k": [
          40,
          2,
          8
        ],
        "v": [
          2,
          8,
          40
        ]
      },
      "quant": "none",
      "realisable_at_this_geometry": true,
      "v_axes": [
        "H",
        "D",
        "T"
      ],
      "v_x": 0
    },
    {
      "attention": "gqa",
      "block": 16,
      "cite": "FlashInfer paged KV cache, NHD layout [max_num_pages, 2, page_size, num_kv_heads, head_dim]; page_size 16",
      "engine": "flashinfer-nhd",
      "is_the_identity_map": false,
      "k_axes": [
        "Tb",
        "KV",
        "Ti",
        "H",
        "D"
      ],
      "k_x": 0,
      "kv": "interleaved",
      "lean_lemma": "ExactTransformCert.roundtrip_flashinfer_nhd",
      "n_kv_heads": 0,
      "native_shapes": {
        "kv": [
          3,
          2,
          16,
          2,
          8
        ]
      },
      "quant": "none",
      "realisable_at_this_geometry": true,
      "v_axes": [
        "Tb",
        "KV",
        "Ti",
        "H",
        "D"
      ],
      "v_x": 0
    },
    {
      "attention": "gqa",
      "block": 64,
      "cite": "LMDeploy TurboMind blocked KV: separate K/V blocks [num_blocks, num_kv_heads, block_seq_len, head_dim], block_seq_len 64. WEAKEST CITATION IN THIS TABLE \u2014 TurboMind's block layout has changed across releases and no version is pinned; what this row demonstrates is a 64-token blocked separate HND layout, whoever ships it",
      "engine": "lmdeploy-turbomind",
      "is_the_identity_map": false,
      "k_axes": [
        "Tb",
        "H",
        "Ti",
        "D"
      ],
      "k_x": 0,
      "kv": "separate",
      "lean_lemma": "ExactTransformCert.roundtrip_lmdeploy_turbomind",
      "n_kv_heads": 0,
      "native_shapes": {
        "k": [
          1,
          2,
          64,
          8
        ],
        "v": [
          1,
          2,
          64,
          8
        ]
      },
      "quant": "none",
      "realisable_at_this_geometry": true,
      "v_axes": [
        "Tb",
        "H",
        "Ti",
        "D"
      ],
      "v_x": 0
    },
    {
      "attention": "mla",
      "block": 16,
      "cite": "DeepSeek-V2/V3 Multi-head Latent Attention: the cache is a per-token compressed latent c_KV plus a decoupled rope key, NOT a per-head K/V tensor. There is no layout permutation between it and any of the above, at any block size",
      "engine": "deepseek-mla",
      "is_the_identity_map": false,
      "k_axes": [
        "KV",
        "Tb",
        "Ti",
        "H",
        "D"
      ],
      "k_x": 0,
      "kv": "interleaved",
      "lean_lemma": null,
      "n_kv_heads": 0,
      "native_shapes": {
        "kv": [
          2,
          3,
          16,
          2,
          8
        ]
      },
      "quant": "none",
      "realisable_at_this_geometry": true,
      "v_axes": [
        "KV",
        "Tb",
        "Ti",
        "H",
        "D"
      ],
      "v_x": 0
    },
    {
      "attention": "gqa",
      "block": 16,
      "cite": "vLLM with tensor_parallel_size 2 over a 2-kv-head model: each rank holds ONE kv-head. One rank's cache is a PROJECTION of the whole, so the map back is a gather with no inverse",
      "engine": "vllm-tp2",
      "is_the_identity_map": false,
      "k_axes": [
        "KV",
        "Tb",
        "Ti",
        "H",
        "D"
      ],
      "k_x": 0,
      "kv": "interleaved",
      "lean_lemma": null,
      "n_kv_heads": 1,
      "native_shapes": {},
      "quant": "none",
      "realisable_at_this_geometry": false,
      "v_axes": [
        "KV",
        "Tb",
        "Ti",
        "H",
        "D"
      ],
      "v_x": 0
    },
    {
      "attention": "gqa",
      "block": 16,
      "cite": "the SAME vLLM PagedAttention K layout with x = 16, which is what it is for fp8 or for a 1-byte element. At head_dim 8 the factorisation does not divide, so this layout DOES NOT EXIST at this geometry \u2014 the same engine, refused for the geometry and not for the engine",
      "engine": "vllm-paged-x16",
      "is_the_identity_map": false,
      "k_axes": [
        "Tb",
        "H",
        "Dg",
        "Ti",
        "Dx"
      ],
      "k_x": 16,
      "kv": "separate",
      "lean_lemma": null,
      "n_kv_heads": 0,
      "native_shapes": {},
      "quant": "none",
      "realisable_at_this_geometry": false,
      "v_axes": [
        "Tb",
        "H",
        "D",
        "Ti"
      ],
      "v_x": 0
    },
    {
      "attention": "gqa",
      "block": 16,
      "cite": "vLLM --kv-cache-dtype fp8_e4m3: the same block shape over an 8-bit element. The POSITION map is a permutation and the ELEMENT map is not injective",
      "engine": "vllm-fp8",
      "is_the_identity_map": false,
      "k_axes": [
        "KV",
        "Tb",
        "Ti",
        "H",
        "D"
      ],
      "k_x": 0,
      "kv": "interleaved",
      "lean_lemma": null,
      "n_kv_heads": 0,
      "native_shapes": {
        "kv": [
          2,
          3,
          16,
          2,
          8
        ]
      },
      "quant": "fp8_e4m3",
      "realisable_at_this_geometry": true,
      "v_axes": [
        "KV",
        "Tb",
        "Ti",
        "H",
        "D"
      ],
      "v_x": 0
    }
  ],
  "falsifications": [
    {
      "actual": "NOT_EXACT",
      "declared_guard": "NOT_EXACT",
      "detail": "a translator that reinterprets the source's bytes as the destination's shape. A->B->A is the IDENTITY, so it is byte-perfect on every input; the forward image is not what the destination produces and the decode emits [52, 52, 52, 52, 52, 52, 52, 52] instead of [2, 27, 60, 51, 2, 27, 60, 51]",
      "guard_ok": true,
      "name": "roundtrip-only-proof",
      "passed": true
    },
    {
      "actual": "NOT_EXACT",
      "declared_guard": "NOT_EXACT",
      "detail": "the same pair with the source's unread block tail allowed into the trimmed state: the decode emits [18, 12, 18, 12, 18, 12, 18, 12] against [2, 27, 60, 51, 2, 27, 60, 51]. This is why 'token-identical' is a measurement and not a consequence of the padding being there",
      "guard_ok": true,
      "name": "padding-read",
      "passed": true
    },
    {
      "actual": "H5_TRIVIAL_TRANSFORMATION",
      "declared_guard": "H5_TRIVIAL_TRANSFORMATION",
      "detail": "an engine declared with vllm-fa's exact layout under a different name needs [] transformations \u2014 the cheapest way to lengthen this list is to invent engines, and an empty transformation set is what catches it",
      "guard_ok": true,
      "name": "relabelled-engine",
      "passed": true
    },
    {
      "actual": "X4_GEOMETRY_UNREPRESENTABLE",
      "declared_guard": "X4_GEOMETRY_UNREPRESENTABLE",
      "detail": "sglang->vllm-paged-x is EXACT at head_dim 8 and does not exist at head_dim 6, where vLLM's x=4 split does not divide. Exactness is a property of the pair AND the geometry, and this list is a list about one geometry",
      "guard_ok": true,
      "name": "the-same-pair-at-a-geometry-that-does-not-admit-it",
      "passed": true
    },
    {
      "actual": "X1_LATENT_KV",
      "declared_guard": "X1_LATENT_KV",
      "detail": "the destination or source caches a compressed per-token latent, not a per-head K/V tensor; there is no permutation between the two at any block size",
      "guard_ok": true,
      "name": "mla-destination",
      "passed": true
    },
    {
      "actual": "X2_HEAD_GATHER",
      "declared_guard": "X2_HEAD_GATHER",
      "detail": "the two layouts hold different numbers of kv-heads, so one is a PROJECTION of the other; the map back is a gather and has no inverse",
      "guard_ok": true,
      "name": "tp-shard-destination",
      "passed": true
    },
    {
      "actual": "X4_GEOMETRY_UNREPRESENTABLE",
      "declared_guard": "X4_GEOMETRY_UNREPRESENTABLE",
      "detail": "the layout does not exist at this geometry (a factorisation that does not divide), so there is nothing to be exact about (vllm-paged-x16: head_dim 8 % x 16 != 0)",
      "guard_ok": true,
      "name": "x16-destination",
      "passed": true
    },
    {
      "actual": "NOT_EXACT",
      "declared_guard": "NOT_EXACT",
      "detail": "the fp8 destination produces EXACTLY the image it would independently have produced (forward True), and the round trip differs at 4603 positions against 768 unread padding slots. Its decode emits [2, 59, 2, 27, 11, 6, 31, 31] against the reference [2, 27, 60, 51, 2, 27, 60, 51]. This is the row that separates 'cannot be attempted' from 'will be deployed and is not exact'",
      "guard_ok": true,
      "name": "fp8-destination-runs-and-is-not-exact",
      "passed": true
    },
    {
      "actual": "UNPROVEN",
      "declared_guard": "UNPROVEN",
      "detail": "three observations green and the fourth NOT MADE grades UNPROVEN \u2014 the bottom of the scale \u2014 while the same three with the fourth MADE AND FALSE grades NOT_EXACT. Declining to look is strictly worse than looking and failing, which is what stops a hunt growing its list by measuring less",
      "guard_ok": true,
      "name": "withholding-an-observation",
      "passed": true
    },
    {
      "actual": "H2_VERDICT_NOT_DERIVED@exit3",
      "declared_guard": "H2_VERDICT_NOT_DERIVED@exit3",
      "detail": "reference H2_VERDICT_NOT_DERIVED@exit3, published H2_VERDICT_NOT_DERIVED@exit3",
      "guard_ok": true,
      "name": "verifier:verdict-relabelled",
      "passed": true
    },
    {
      "actual": "H2_VERDICT_NOT_DERIVED@exit3",
      "declared_guard": "H2_VERDICT_NOT_DERIVED@exit3",
      "detail": "reference H2_VERDICT_NOT_DERIVED@exit3, published H2_VERDICT_NOT_DERIVED@exit3",
      "guard_ok": true,
      "name": "verifier:observation-withheld",
      "passed": true
    },
    {
      "actual": "H2_VERDICT_NOT_DERIVED@exit3",
      "declared_guard": "H2_VERDICT_NOT_DERIVED@exit3",
      "detail": "reference H2_VERDICT_NOT_DERIVED@exit3, published H2_VERDICT_NOT_DERIVED@exit3",
      "guard_ok": true,
      "name": "verifier:corroboration-nulled",
      "passed": true
    },
    {
      "actual": "H4_PROOF_NOT_EXHAUSTIVE@exit3",
      "declared_guard": "H4_PROOF_NOT_EXHAUSTIVE@exit3",
      "detail": "reference H4_PROOF_NOT_EXHAUSTIVE@exit3, published H4_PROOF_NOT_EXHAUSTIVE@exit3",
      "guard_ok": true,
      "name": "verifier:one-position-is-the-whole-space",
      "passed": true
    },
    {
      "actual": "H8_FLOOR_BELOW_OBSERVATION@exit3",
      "declared_guard": "H8_FLOOR_BELOW_OBSERVATION@exit3",
      "detail": "reference H8_FLOOR_BELOW_OBSERVATION@exit3, published H8_FLOOR_BELOW_OBSERVATION@exit3",
      "guard_ok": true,
      "name": "verifier:guard-set-shrunk-to-one-each",
      "passed": true
    },
    {
      "actual": "H0_DOCUMENT_UNREADABLE@exit1",
      "declared_guard": "H0_DOCUMENT_UNREADABLE@exit1",
      "detail": "reference H0_DOCUMENT_UNREADABLE@exit1, published H0_DOCUMENT_UNREADABLE@exit1",
      "guard_ok": true,
      "name": "verifier:unhashable-in-a-signed-list",
      "passed": true
    },
    {
      "actual": "H2_VERDICT_NOT_DERIVED@exit3",
      "declared_guard": "H2_VERDICT_NOT_DERIVED@exit3",
      "detail": "reference H2_VERDICT_NOT_DERIVED@exit3, published H2_VERDICT_NOT_DERIVED@exit3",
      "guard_ok": true,
      "name": "verifier:bijection-denied",
      "passed": true
    },
    {
      "actual": "H3_PROOF_MISSING@exit3",
      "declared_guard": "H3_PROOF_MISSING@exit3",
      "detail": "reference H3_PROOF_MISSING@exit3, published H3_PROOF_MISSING@exit3",
      "guard_ok": true,
      "name": "verifier:no-kernel-checked-lemma",
      "passed": true
    },
    {
      "actual": "H3_PROOF_MISSING@exit3",
      "declared_guard": "H3_PROOF_MISSING@exit3",
      "detail": "reference H3_PROOF_MISSING@exit3, published H3_PROOF_MISSING@exit3",
      "guard_ok": true,
      "name": "verifier:proof-deleted",
      "passed": true
    },
    {
      "actual": "H4_PROOF_NOT_EXHAUSTIVE@exit3",
      "declared_guard": "H4_PROOF_NOT_EXHAUSTIVE@exit3",
      "detail": "reference H4_PROOF_NOT_EXHAUSTIVE@exit3, published H4_PROOF_NOT_EXHAUSTIVE@exit3",
      "guard_ok": true,
      "name": "verifier:sampled-proof",
      "passed": true
    },
    {
      "actual": "H5_TRIVIAL_TRANSFORMATION@exit3",
      "declared_guard": "H5_TRIVIAL_TRANSFORMATION@exit3",
      "detail": "reference H5_TRIVIAL_TRANSFORMATION@exit3, published H5_TRIVIAL_TRANSFORMATION@exit3",
      "guard_ok": true,
      "name": "verifier:trivial-transformation",
      "passed": true
    },
    {
      "actual": "H6_HUNT_FOUND_NOTHING@exit3",
      "declared_guard": "H6_HUNT_FOUND_NOTHING@exit3",
      "detail": "reference H6_HUNT_FOUND_NOTHING@exit3, published H6_HUNT_FOUND_NOTHING@exit3",
      "guard_ok": true,
      "name": "verifier:hunt-emptied",
      "passed": true
    },
    {
      "actual": "H7_VOCABULARY_NOT_EXERCISED@exit3",
      "declared_guard": "H7_VOCABULARY_NOT_EXERCISED@exit3",
      "detail": "reference H7_VOCABULARY_NOT_EXERCISED@exit3, published H7_VOCABULARY_NOT_EXERCISED@exit3",
      "guard_ok": true,
      "name": "verifier:vocabulary-thinned",
      "passed": true
    },
    {
      "actual": "H14_NO_FRONTIER@exit3",
      "declared_guard": "H14_NO_FRONTIER@exit3",
      "detail": "reference H14_NO_FRONTIER@exit3, published H14_NO_FRONTIER@exit3",
      "guard_ok": true,
      "name": "verifier:no-frontier",
      "passed": true
    },
    {
      "actual": "H8_FLOOR_BELOW_OBSERVATION@exit3",
      "declared_guard": "H8_FLOOR_BELOW_OBSERVATION@exit3",
      "detail": "reference H8_FLOOR_BELOW_OBSERVATION@exit3, published H8_FLOOR_BELOW_OBSERVATION@exit3",
      "guard_ok": true,
      "name": "verifier:floor-above-observation",
      "passed": true
    },
    {
      "actual": "H9_GUARD_FAILED_OPEN@exit3",
      "declared_guard": "H9_GUARD_FAILED_OPEN@exit3",
      "detail": "reference H9_GUARD_FAILED_OPEN@exit3, published H9_GUARD_FAILED_OPEN@exit3",
      "guard_ok": true,
      "name": "verifier:check-failed-open",
      "passed": true
    },
    {
      "actual": "H10_COUNTS_DO_NOT_RECOMPUTE@exit3",
      "declared_guard": "H10_COUNTS_DO_NOT_RECOMPUTE@exit3",
      "detail": "reference H10_COUNTS_DO_NOT_RECOMPUTE@exit3, published H10_COUNTS_DO_NOT_RECOMPUTE@exit3",
      "guard_ok": true,
      "name": "verifier:counts-do-not-recompute",
      "passed": true
    },
    {
      "actual": "H11_ENGINE_UNDECLARED@exit3",
      "declared_guard": "H11_ENGINE_UNDECLARED@exit3",
      "detail": "reference H11_ENGINE_UNDECLARED@exit3, published H11_ENGINE_UNDECLARED@exit3",
      "guard_ok": true,
      "name": "verifier:undeclared-engine",
      "passed": true
    },
    {
      "actual": "H12_PAIR_DECLARED_TWICE@exit3",
      "declared_guard": "H12_PAIR_DECLARED_TWICE@exit3",
      "detail": "reference H12_PAIR_DECLARED_TWICE@exit3, published H12_PAIR_DECLARED_TWICE@exit3",
      "guard_ok": true,
      "name": "verifier:pair-declared-twice",
      "passed": true
    },
    {
      "actual": "H13_TOKEN_CLAIM_WITHOUT_A_DECODE@exit3",
      "declared_guard": "H13_TOKEN_CLAIM_WITHOUT_A_DECODE@exit3",
      "detail": "reference H13_TOKEN_CLAIM_WITHOUT_A_DECODE@exit3, published H13_TOKEN_CLAIM_WITHOUT_A_DECODE@exit3",
      "guard_ok": true,
      "name": "verifier:token-claim-without-a-decode",
      "passed": true
    },
    {
      "actual": "H1_SIGNATURE_INVALID@exit3",
      "declared_guard": "H1_SIGNATURE_INVALID@exit3",
      "detail": "reference H1_SIGNATURE_INVALID@exit3, published H1_SIGNATURE_INVALID@exit3",
      "guard_ok": true,
      "name": "verifier:forged-signer",
      "passed": true
    },
    {
      "actual": "H1_SIGNATURE_INVALID@exit3",
      "declared_guard": "H1_SIGNATURE_INVALID@exit3",
      "detail": "reference H1_SIGNATURE_INVALID@exit3, published H1_SIGNATURE_INVALID@exit3",
      "guard_ok": true,
      "name": "verifier:mutated-document",
      "passed": true
    },
    {
      "actual": "H0_DOCUMENT_UNREADABLE@exit1",
      "declared_guard": "H0_DOCUMENT_UNREADABLE@exit1",
      "detail": "reference H0_DOCUMENT_UNREADABLE@exit1, published H0_DOCUMENT_UNREADABLE@exit1",
      "guard_ok": true,
      "name": "verifier:torn-document",
      "passed": true
    }
  ],
  "geometry": {
    "canonical_axes": [
      "KV",
      "T",
      "H",
      "D"
    ],
    "decode_steps": 8,
    "dtype": "float16",
    "head_dim": 8,
    "kv_heads": 2,
    "layers": 3,
    "lean_slice": {
      "head_dim": 8,
      "kv_heads": 2,
      "tokens": 2
    },
    "pad_model": "non-zero block tail (a real engine's tail holds whatever the last request left); the value is fixed so the round-trip difference is a set identity and not a probability",
    "tokens": 40
  },
  "hunt_id": "sf-exact-transformation-hunt-v1",
  "known_limits": [
    {
      "detail": "an engine whose layout was made up on the spot grades EXACT_BYTE with 1280 positions checked. Everything in this document is a statement about DECLARED SHAPES; that a shape matches a real engine's is a citation, not a measurement",
      "name": "no-engine-runs-here",
      "passed": true
    },
    {
      "detail": "a translator that behaves exactly like the real one except on a single element VALUE passes the exhaustive index probe and all 6 gather payloads and is graded EXACT_BYTE \u2014 and on a payload that actually contains that value it silently zeroes 1280 elements. The index argument is about POSITIONS; that the layout is a pure gather is probed on the payloads this run happened to use, not proved",
      "name": "a-data-dependent-layout-passes-the-gather-probe",
      "passed": true
    },
    {
      "detail": "sglang->vllm-paged-x is EXACT_BYTE at head_dim 8 and X4_GEOMETRY_UNREPRESENTABLE at head_dim 6. The enumerated list is a list about THIS geometry; the arbitrary-parameter statements are the Lean primitives and they are about index arithmetic, not about these engines",
      "name": "exactness-is-a-property-of-the-geometry-too",
      "passed": true
    },
    {
      "detail": "the same prompt through the same harness with a different weight seed decodes to [63, 26, 25, 18, 25, 18, 25, 18] instead of [2, 27, 60, 51, 2, 27, 60, 51]. 'Token-identical' means identical to a reference this run computed, not to any engine's output",
      "name": "token-identity-is-relative-to-this-model",
      "passed": true
    },
    {
      "detail": "re-run with a ZERO block tail, 35 of the token-identical rows become byte-identical. A real engine's block tail holds whatever the last request left, which is why the hunt uses a non-zero tail; an engine that zeroes its tails would move the whole EXACT_TOKEN class into EXACT_BYTE and neither the layouts nor the proofs would have changed",
      "name": "the-byte-token-split-is-the-padding-model",
      "passed": true
    },
    {
      "detail": "a layout mutated into a DIFFERENT permutation is still a permutation, so the generated `decide` lemma for it would kernel-check exactly as well (64 canonical elements over 512 native positions, all distinct, and a different permutation from the real one). The Lean leg establishes that these index maps are bijections; it cannot establish that they are the maps the engines use, and nothing in this repository closes that",
      "name": "the-lean-lemmas-are-about-index-arithmetic-not-about-layouts_py",
      "passed": true
    }
  ],
  "observed": {
    "distinct_index_spaces": 8,
    "distinct_positions": 12544,
    "engines": [
      "vllm-fa",
      "vllm-paged-x",
      "trtllm",
      "sglang",
      "hf-dynamic-cache",
      "llamacpp",
      "flashinfer-nhd",
      "lmdeploy-turbomind",
      "deepseek-mla",
      "vllm-tp2",
      "vllm-paged-x16",
      "vllm-fp8"
    ],
    "exact_pairs": [
      "flashinfer-nhd->hf-dynamic-cache",
      "flashinfer-nhd->llamacpp",
      "flashinfer-nhd->lmdeploy-turbomind",
      "flashinfer-nhd->sglang",
      "flashinfer-nhd->trtllm",
      "flashinfer-nhd->vllm-fa",
      "flashinfer-nhd->vllm-paged-x",
      "hf-dynamic-cache->flashinfer-nhd",
      "hf-dynamic-cache->llamacpp",
      "hf-dynamic-cache->lmdeploy-turbomind",
      "hf-dynamic-cache->sglang",
      "hf-dynamic-cache->trtllm",
      "hf-dynamic-cache->vllm-fa",
      "hf-dynamic-cache->vllm-paged-x",
      "llamacpp->flashinfer-nhd",
      "llamacpp->hf-dynamic-cache",
      "llamacpp->lmdeploy-turbomind",
      "llamacpp->sglang",
      "llamacpp->trtllm",
      "llamacpp->vllm-fa",
      "llamacpp->vllm-paged-x",
      "lmdeploy-turbomind->flashinfer-nhd",
      "lmdeploy-turbomind->hf-dynamic-cache",
      "lmdeploy-turbomind->llamacpp",
      "lmdeploy-turbomind->sglang",
      "lmdeploy-turbomind->trtllm",
      "lmdeploy-turbomind->vllm-fa",
      "lmdeploy-turbomind->vllm-paged-x",
      "sglang->flashinfer-nhd",
      "sglang->hf-dynamic-cache",
      "sglang->llamacpp",
      "sglang->lmdeploy-turbomind",
      "sglang->trtllm",
      "sglang->vllm-fa",
      "sglang->vllm-paged-x",
      "trtllm->flashinfer-nhd",
      "trtllm->hf-dynamic-cache",
      "trtllm->llamacpp",
      "trtllm->lmdeploy-turbomind",
      "trtllm->sglang",
      "trtllm->vllm-fa",
      "trtllm->vllm-paged-x",
      "vllm-fa->flashinfer-nhd",
      "vllm-fa->hf-dynamic-cache",
      "vllm-fa->llamacpp",
      "vllm-fa->lmdeploy-turbomind",
      "vllm-fa->sglang",
      "vllm-fa->trtllm",
      "vllm-fa->vllm-paged-x",
      "vllm-paged-x->flashinfer-nhd",
      "vllm-paged-x->hf-dynamic-cache",
      "vllm-paged-x->llamacpp",
      "vllm-paged-x->lmdeploy-turbomind",
      "vllm-paged-x->sglang",
      "vllm-paged-x->trtllm",
      "vllm-paged-x->vllm-fa"
    ],
    "frontier_codes": [
      "X1_LATENT_KV",
      "X2_HEAD_GATHER",
      "X4_GEOMETRY_UNREPRESENTABLE"
    ],
    "identity_map_engines": [
      "sglang"
    ],
    "lossless_engines": [
      "vllm-fa",
      "vllm-paged-x",
      "trtllm",
      "sglang",
      "hf-dynamic-cache",
      "llamacpp",
      "flashinfer-nhd",
      "lmdeploy-turbomind"
    ],
    "positions_checked_total": 90880,
    "source_positions_checked_total": 90880,
    "verdict_counts": {
      "EXACT_BYTE": 21,
      "EXACT_TOKEN": 35,
      "NOT_EXACT": 2,
      "REFUSED": 6,
      "UNPROVEN": 0
    },
    "vocabulary_exercised": [
      "axis_permute",
      "head_dim_devectorize",
      "head_dim_vectorize",
      "head_order_transpose",
      "kv_merge",
      "kv_split",
      "reblock",
      "requantize",
      "v_dim_transpose"
    ]
  },
  "rows": [
    {
      "dst": "vllm-fa",
      "frontier_code": "X1_LATENT_KV",
      "frontier_reason": "the destination or source caches a compressed per-token latent, not a per-head K/V tensor; there is no permutation between the two at any block size",
      "native_bytes": {
        "dst": null,
        "src": null
      },
      "observations": {
        "forward_reproduces_target": null,
        "roundtrip_byte_identical": null,
        "roundtrip_diff_is_exactly_unread_padding": null,
        "tokens_identical": null
      },
      "pair_id": "deepseek-mla->vllm-fa",
      "proof": {
        "command": "make exact-hunt-frontier",
        "decoded_tokens": null,
        "dest_bijective": null,
        "dest_padding_positions": null,
        "detail": "the destination or source caches a compressed per-token latent, not a per-head K/V tensor; there is no permutation between the two at any block size",
        "gather_agrees": null,
        "gather_payloads": null,
        "kind": "frontier",
        "layers": null,
        "lean_lemmas": [
          "ExactTransform.latent_kv_not_a_permutation"
        ],
        "positions_checked": null,
        "positions_total": null,
        "reference_tokens": null,
        "roundtrip_diff_positions": null,
        "source_bijective": null,
        "source_padding_positions": null,
        "source_positions_checked": null,
        "source_positions_total": null,
        "unread_padding_positions": null
      },
      "src": "deepseek-mla",
      "transformations": [],
      "verdict": "REFUSED"
    },
    {
      "dst": "hf-dynamic-cache",
      "frontier_code": null,
      "frontier_reason": null,
      "native_bytes": {
        "dst": 2560,
        "src": 3072
      },
      "observations": {
        "forward_reproduces_target": true,
        "roundtrip_byte_identical": false,
        "roundtrip_diff_is_exactly_unread_padding": true,
        "tokens_identical": true
      },
      "pair_id": "flashinfer-nhd->hf-dynamic-cache",
      "proof": {
        "command": "make exact-hunt",
        "decoded_tokens": [
          2,
          27,
          60,
          51,
          2,
          27,
          60,
          51
        ],
        "dest_bijective": true,
        "dest_padding_positions": 0,
        "detail": null,
        "gather_agrees": true,
        "gather_payloads": 6,
        "kind": "index-permutation-exhaustive",
        "layers": 3,
        "lean_lemmas": [
          "ExactTransformCert.roundtrip_flashinfer_nhd",
          "ExactTransformCert.roundtrip_hf_dynamic_cache",
          "ExactTransform.comp_roundtrip",
          "ExactTransform.swap_involutive",
          "ExactTransform.factor_unfactor_id"
        ],
        "positions_checked": 1280,
        "positions_total": 1280,
        "reference_tokens": [
          2,
          27,
          60,
          51,
          2,
          27,
          60,
          51
        ],
        "roundtrip_diff_positions": 768,
        "source_bijective": true,
        "source_padding_positions": 256,
        "source_positions_checked": 1536,
        "source_positions_total": 1536,
        "unread_padding_positions": 768
      },
      "src": "flashinfer-nhd",
      "transformations": [
        "head_order_transpose",
        "kv_split",
        "reblock"
      ],
      "verdict": "EXACT_TOKEN"
    },
    {
      "dst": "llamacpp",
      "frontier_code": null,
      "frontier_reason": null,
      "native_bytes": {
        "dst": 2560,
        "src": 3072
      },
      "observations": {
        "forward_reproduces_target": true,
        "roundtrip_byte_identical": false,
        "roundtrip_diff_is_exactly_unread_padding": true,
        "tokens_identical": true
      },
      "pair_id": "flashinfer-nhd->llamacpp",
      "proof": {
        "command": "make exact-hunt",
        "decoded_tokens": [
          2,
          27,
          60,
          51,
          2,
          27,
          60,
          51
        ],
        "dest_bijective": true,
        "dest_padding_positions": 0,
        "detail": null,
        "gather_agrees": true,
        "gather_payloads": 6,
        "kind": "index-permutation-exhaustive",
        "layers": 3,
        "lean_lemmas": [
          "ExactTransformCert.roundtrip_flashinfer_nhd",
          "ExactTransformCert.roundtrip_llamacpp",
          "ExactTransform.comp_roundtrip",
          "ExactTransform.swap_involutive",
          "ExactTransform.factor_unfactor_id"
        ],
        "positions_checked": 1280,
        "positions_total": 1280,
        "reference_tokens": [
          2,
          27,
          60,
          51,
          2,
          27,
          60,
          51
        ],
        "roundtrip_diff_positions": 768,
        "source_bijective": true,
        "source_padding_positions": 256,
        "source_positions_checked": 1536,
        "source_positions_total": 1536,
        "unread_padding_positions": 768
      },
      "src": "flashinfer-nhd",
      "transformations": [
        "axis_permute",
        "head_order_transpose",
        "kv_split",
        "reblock",
        "v_dim_transpose"
      ],
      "verdict": "EXACT_TOKEN"
    },
    {
      "dst": "lmdeploy-turbomind",
      "frontier_code": null,
      "frontier_reason": null,
      "native_bytes": {
        "dst": 4096,
        "src": 3072
      },
      "observations": {
        "forward_reproduces_target": true,
        "roundtrip_byte_identical": false,
        "roundtrip_diff_is_exactly_unread_padding": true,
        "tokens_identical": true
      },
      "pair_id": "flashinfer-nhd->lmdeploy-turbomind",
      "proof": {
        "command": "make exact-hunt",
        "decoded_tokens": [
          2,
          27,
          60,
          51,
          2,
          27,
          60,
          51
        ],
        "dest_bijective": true,
        "dest_padding_positions": 768,
        "detail": null,
        "gather_agrees": true,
        "gather_payloads": 6,
        "kind": "index-permutation-exhaustive",
        "layers": 3,
        "lean_lemmas": [
          "ExactTransformCert.roundtrip_flashinfer_nhd",
          "ExactTransformCert.roundtrip_lmdeploy_turbomind",
          "ExactTransform.comp_roundtrip",
          "ExactTransform.swap_involutive",
          "ExactTransform.factor_unfactor_id"
        ],
        "positions_checked": 2048,
        "positions_total": 2048,
        "reference_tokens": [
          2,
          27,
          60,
          51,
          2,
          27,
          60,
          51
        ],
        "roundtrip_diff_positions": 768,
        "source_bijective": true,
        "source_padding_positions": 256,
        "source_positions_checked": 1536,
        "source_positions_total": 1536,
        "unread_padding_positions": 768
      },
      "src": "flashinfer-nhd",
      "transformations": [
        "axis_permute",
        "kv_split",
        "reblock"
      ],
      "verdict": "EXACT_TOKEN"
    },
    {
      "dst": "sglang",
      "frontier_code": null,
      "frontier_reason": null,
      "native_bytes": {
        "dst": 2560,
        "src": 3072
      },
      "observations": {
        "forward_reproduces_target": true,
        "roundtrip_byte_identical": false,
        "roundtrip_diff_is_exactly_unread_padding": true,
        "tokens_identical": true
      },
      "pair_id": "flashinfer-nhd->sglang",
      "proof": {
        "command": "make exact-hunt",
        "decoded_tokens": [
          2,
          27,
          60,
          51,
          2,
          27,
          60,
          51
        ],
        "dest_bijective": true,
        "dest_padding_positions": 0,
        "detail": null,
        "gather_agrees": true,
        "gather_payloads": 6,
        "kind": "index-permutation-exhaustive",
        "layers": 3,
        "lean_lemmas": [
          "ExactTransformCert.roundtrip_flashinfer_nhd",
          "ExactTransformCert.roundtrip_sglang",
          "ExactTransform.comp_roundtrip",
          "ExactTransform.swap_involutive",
          "ExactTransform.factor_unfactor_id"
        ],
        "positions_checked": 1280,
        "positions_total": 1280,
        "reference_tokens": [
          2,
          27,
          60,
          51,
          2,
          27,
          60,
          51
        ],
        "roundtrip_diff_positions": 768,
        "source_bijective": true,
        "source_padding_positions": 256,
        "source_positions_checked": 1536,
        "source_positions_total": 1536,
        "unread_padding_positions": 768
      },
      "src": "flashinfer-nhd",
      "transformations": [
        "axis_permute",
        "kv_split",
        "reblock"
      ],
      "verdict": "EXACT_TOKEN"
    },
    {
      "dst": "trtllm",
      "frontier_code": null,
      "frontier_reason": null,
      "native_bytes": {
        "dst": 4096,
        "src": 3072
      },
      "observations": {
        "forward_reproduces_target": true,
        "roundtrip_byte_identical": false,
        "roundtrip_diff_is_exactly_unread_padding": true,
        "tokens_identical": true
      },
      "pair_id": "flashinfer-nhd->trtllm",
      "proof": {
        "command": "make exact-hunt",
        "decoded_tokens": [
          2,
          27,
          60,
          51,
          2,
          27,
          60,
          51
        ],
        "dest_bijective": true,
        "dest_padding_positions": 768,
        "detail": null,
        "gather_agrees": true,
        "gather_payloads": 6,
        "kind": "index-permutation-exhaustive",
        "layers": 3,
        "lean_lemmas": [
          "ExactTransformCert.roundtrip_flashinfer_nhd",
          "ExactTransformCert.roundtrip_trtllm",
          "ExactTransform.comp_roundtrip",
          "ExactTransform.swap_involutive",
          "ExactTransform.factor_unfactor_id"
        ],
        "positions_checked": 2048,
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      "verdict": "EXACT_BYTE"
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      "verdict": "EXACT_BYTE"
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      "verdict": "EXACT_BYTE"
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      "verdict": "EXACT_BYTE"
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      "verdict": "EXACT_TOKEN"
    },
    {
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      "verdict": "EXACT_TOKEN"
    },
    {
      "dst": "llamacpp",
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          "ExactTransform.swap_involutive",
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        "v_dim_transpose"
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      "verdict": "EXACT_TOKEN"
    },
    {
      "dst": "lmdeploy-turbomind",
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      "verdict": "EXACT_TOKEN"
    },
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      "verdict": "EXACT_TOKEN"
    },
    {
      "dst": "vllm-fa",
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          "ExactTransform.comp_roundtrip",
          "ExactTransform.swap_involutive",
          "ExactTransform.factor_unfactor_id"
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        "reblock"
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      "verdict": "EXACT_TOKEN"
    },
    {
      "dst": "vllm-paged-x",
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          "ExactTransform.comp_roundtrip",
          "ExactTransform.swap_involutive",
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      "verdict": "EXACT_TOKEN"
    },
    {
      "dst": "deepseek-mla",
      "frontier_code": "X1_LATENT_KV",
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      "src": "vllm-fa",
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      "verdict": "REFUSED"
    },
    {
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          "ExactTransform.swap_involutive",
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      "src": "vllm-fa",
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      "verdict": "EXACT_TOKEN"
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    {
      "dst": "hf-dynamic-cache",
      "frontier_code": null,
      "frontier_reason": null,
      "native_bytes": {
        "dst": 2560,
        "src": 3072
      },
      "observations": {
        "forward_reproduces_target": true,
        "roundtrip_byte_identical": false,
        "roundtrip_diff_is_exactly_unread_padding": true,
        "tokens_identical": true
      },
      "pair_id": "vllm-fa->hf-dynamic-cache",
      "proof": {
        "command": "make exact-hunt",
        "decoded_tokens": [
          2,
          27,
          60,
          51,
          2,
          27,
          60,
          51
        ],
        "dest_bijective": true,
        "dest_padding_positions": 0,
        "detail": null,
        "gather_agrees": true,
        "gather_payloads": 6,
        "kind": "index-permutation-exhaustive",
        "layers": 3,
        "lean_lemmas": [
          "ExactTransformCert.roundtrip_vllm_fa",
          "ExactTransformCert.roundtrip_hf_dynamic_cache",
          "ExactTransform.comp_roundtrip",
          "ExactTransform.swap_involutive",
          "ExactTransform.factor_unfactor_id"
        ],
        "positions_checked": 1280,
        "positions_total": 1280,
        "reference_tokens": [
          2,
          27,
          60,
          51,
          2,
          27,
          60,
          51
        ],
        "roundtrip_diff_positions": 768,
        "source_bijective": true,
        "source_padding_positions": 256,
        "source_positions_checked": 1536,
        "source_positions_total": 1536,
        "unread_padding_positions": 768
      },
      "src": "vllm-fa",
      "transformations": [
        "head_order_transpose",
        "kv_split",
        "reblock"
      ],
      "verdict": "EXACT_TOKEN"
    },
    {
      "dst": "llamacpp",
      "frontier_code": null,
      "frontier_reason": null,
      "native_bytes": {
        "dst": 2560,
        "src": 3072
      },
      "observations": {
        "forward_reproduces_target": true,
        "roundtrip_byte_identical": false,
        "roundtrip_diff_is_exactly_unread_padding": true,
        "tokens_identical": true
      },
      "pair_id": "vllm-fa->llamacpp",
      "proof": {
        "command": "make exact-hunt",
        "decoded_tokens": [
          2,
          27,
          60,
          51,
          2,
          27,
          60,
          51
        ],
        "dest_bijective": true,
        "dest_padding_positions": 0,
        "detail": null,
        "gather_agrees": true,
        "gather_payloads": 6,
        "kind": "index-permutation-exhaustive",
        "layers": 3,
        "lean_lemmas": [
          "ExactTransformCert.roundtrip_vllm_fa",
          "ExactTransformCert.roundtrip_llamacpp",
          "ExactTransform.comp_roundtrip",
          "ExactTransform.swap_involutive",
          "ExactTransform.factor_unfactor_id"
        ],
        "positions_checked": 1280,
        "positions_total": 1280,
        "reference_tokens": [
          2,
          27,
          60,
          51,
          2,
          27,
          60,
          51
        ],
        "roundtrip_diff_positions": 768,
        "source_bijective": true,
        "source_padding_positions": 256,
        "source_positions_checked": 1536,
        "source_positions_total": 1536,
        "unread_padding_positions": 768
      },
      "src": "vllm-fa",
      "transformations": [
        "head_order_transpose",
        "kv_split",
        "reblock",
        "v_dim_transpose"
      ],
      "verdict": "EXACT_TOKEN"
    },
    {
      "dst": "lmdeploy-turbomind",
      "frontier_code": null,
      "frontier_reason": null,
      "native_bytes": {
        "dst": 4096,
        "src": 3072
      },
      "observations": {
        "forward_reproduces_target": true,
        "roundtrip_byte_identical": false,
        "roundtrip_diff_is_exactly_unread_padding": true,
        "tokens_identical": true
      },
      "pair_id": "vllm-fa->lmdeploy-turbomind",
      "proof": {
        "command": "make exact-hunt",
        "decoded_tokens": [
          2,
          27,
          60,
          51,
          2,
          27,
          60,
          51
        ],
        "dest_bijective": true,
        "dest_padding_positions": 768,
        "detail": null,
        "gather_agrees": true,
        "gather_payloads": 6,
        "kind": "index-permutation-exhaustive",
        "layers": 3,
        "lean_lemmas": [
          "ExactTransformCert.roundtrip_vllm_fa",
          "ExactTransformCert.roundtrip_lmdeploy_turbomind",
          "ExactTransform.comp_roundtrip",
          "ExactTransform.swap_involutive",
          "ExactTransform.factor_unfactor_id"
        ],
        "positions_checked": 2048,
        "positions_total": 2048,
        "reference_tokens": [
          2,
          27,
          60,
          51,
          2,
          27,
          60,
          51
        ],
        "roundtrip_diff_positions": 768,
        "source_bijective": true,
        "source_padding_positions": 256,
        "source_positions_checked": 1536,
        "source_positions_total": 1536,
        "unread_padding_positions": 768
      },
      "src": "vllm-fa",
      "transformations": [
        "axis_permute",
        "kv_split",
        "reblock"
      ],
      "verdict": "EXACT_TOKEN"
    },
    {
      "dst": "sglang",
      "frontier_code": null,
      "frontier_reason": null,
      "native_bytes": {
        "dst": 2560,
        "src": 3072
      },
      "observations": {
        "forward_reproduces_target": true,
        "roundtrip_byte_identical": false,
        "roundtrip_diff_is_exactly_unread_padding": true,
        "tokens_identical": true
      },
      "pair_id": "vllm-fa->sglang",
      "proof": {
        "command": "make exact-hunt",
        "decoded_tokens": [
          2,
          27,
          60,
          51,
          2,
          27,
          60,
          51
        ],
        "dest_bijective": true,
        "dest_padding_positions": 0,
        "detail": null,
        "gather_agrees": true,
        "gather_payloads": 6,
        "kind": "index-permutation-exhaustive",
        "layers": 3,
        "lean_lemmas": [
          "ExactTransformCert.roundtrip_vllm_fa",
          "ExactTransformCert.roundtrip_sglang",
          "ExactTransform.comp_roundtrip",
          "ExactTransform.swap_involutive",
          "ExactTransform.factor_unfactor_id"
        ],
        "positions_checked": 1280,
        "positions_total": 1280,
        "reference_tokens": [
          2,
          27,
          60,
          51,
          2,
          27,
          60,
          51
        ],
        "roundtrip_diff_positions": 768,
        "source_bijective": true,
        "source_padding_positions": 256,
        "source_positions_checked": 1536,
        "source_positions_total": 1536,
        "unread_padding_positions": 768
      },
      "src": "vllm-fa",
      "transformations": [
        "kv_split",
        "reblock"
      ],
      "verdict": "EXACT_TOKEN"
    },
    {
      "dst": "trtllm",
      "frontier_code": null,
      "frontier_reason": null,
      "native_bytes": {
        "dst": 4096,
        "src": 3072
      },
      "observations": {
        "forward_reproduces_target": true,
        "roundtrip_byte_identical": false,
        "roundtrip_diff_is_exactly_unread_padding": true,
        "tokens_identical": true
      },
      "pair_id": "vllm-fa->trtllm",
      "proof": {
        "command": "make exact-hunt",
        "decoded_tokens": [
          2,
          27,
          60,
          51,
          2,
          27,
          60,
          51
        ],
        "dest_bijective": true,
        "dest_padding_positions": 768,
        "detail": null,
        "gather_agrees": true,
        "gather_payloads": 6,
        "kind": "index-permutation-exhaustive",
        "layers": 3,
        "lean_lemmas": [
          "ExactTransformCert.roundtrip_vllm_fa",
          "ExactTransformCert.roundtrip_trtllm",
          "ExactTransform.comp_roundtrip",
          "ExactTransform.swap_involutive",
          "ExactTransform.factor_unfactor_id"
        ],
        "positions_checked": 2048,
        "positions_total": 2048,
        "reference_tokens": [
          2,
          27,
          60,
          51,
          2,
          27,
          60,
          51
        ],
        "roundtrip_diff_positions": 768,
        "source_bijective": true,
        "source_padding_positions": 256,
        "source_positions_checked": 1536,
        "source_positions_total": 1536,
        "unread_padding_positions": 768
      },
      "src": "vllm-fa",
      "transformations": [
        "axis_permute",
        "reblock"
      ],
      "verdict": "EXACT_TOKEN"
    },
    {
      "dst": "vllm-fp8",
      "frontier_code": null,
      "frontier_reason": null,
      "native_bytes": {
        "dst": 3072,
        "src": 3072
      },
      "observations": {
        "forward_reproduces_target": true,
        "roundtrip_byte_identical": false,
        "roundtrip_diff_is_exactly_unread_padding": false,
        "tokens_identical": false
      },
      "pair_id": "vllm-fa->vllm-fp8",
      "proof": {
        "command": "make exact-hunt",
        "decoded_tokens": [
          2,
          59,
          2,
          27,
          11,
          6,
          31,
          31
        ],
        "dest_bijective": true,
        "dest_padding_positions": 256,
        "detail": "the element type changes. The POSITION map is still a bijection \u2014 the certificate records it as one \u2014 and the ELEMENT map is not injective, so no arrangement of the bytes makes the transfer exact. This row is NOT_EXACT rather than REFUSED because the transfer runs.",
        "gather_agrees": true,
        "gather_payloads": 6,
        "kind": "index-permutation-exhaustive",
        "layers": 3,
        "lean_lemmas": [
          "ExactTransformCert.roundtrip_vllm_fa",
          "ExactTransform.comp_roundtrip",
          "ExactTransform.swap_involutive",
          "ExactTransform.factor_unfactor_id"
        ],
        "positions_checked": 1536,
        "positions_total": 1536,
        "reference_tokens": [
          2,
          27,
          60,
          51,
          2,
          27,
          60,
          51
        ],
        "roundtrip_diff_positions": 4603,
        "source_bijective": true,
        "source_padding_positions": 256,
        "source_positions_checked": 1536,
        "source_positions_total": 1536,
        "unread_padding_positions": 768
      },
      "src": "vllm-fa",
      "transformations": [
        "requantize"
      ],
      "verdict": "NOT_EXACT"
    },
    {
      "dst": "vllm-paged-x",
      "frontier_code": null,
      "frontier_reason": null,
      "native_bytes": {
        "dst": 3072,
        "src": 3072
      },
      "observations": {
        "forward_reproduces_target": true,
        "roundtrip_byte_identical": false,
        "roundtrip_diff_is_exactly_unread_padding": true,
        "tokens_identical": true
      },
      "pair_id": "vllm-fa->vllm-paged-x",
      "proof": {
        "command": "make exact-hunt",
        "decoded_tokens": [
          2,
          27,
          60,
          51,
          2,
          27,
          60,
          51
        ],
        "dest_bijective": true,
        "dest_padding_positions": 256,
        "detail": null,
        "gather_agrees": true,
        "gather_payloads": 6,
        "kind": "index-permutation-exhaustive",
        "layers": 3,
        "lean_lemmas": [
          "ExactTransformCert.roundtrip_vllm_fa",
          "ExactTransformCert.roundtrip_vllm_paged_x",
          "ExactTransform.comp_roundtrip",
          "ExactTransform.swap_involutive",
          "ExactTransform.factor_unfactor_id"
        ],
        "positions_checked": 1536,
        "positions_total": 1536,
        "reference_tokens": [
          2,
          27,
          60,
          51,
          2,
          27,
          60,
          51
        ],
        "roundtrip_diff_positions": 768,
        "source_bijective": true,
        "source_padding_positions": 256,
        "source_positions_checked": 1536,
        "source_positions_total": 1536,
        "unread_padding_positions": 768
      },
      "src": "vllm-fa",
      "transformations": [
        "axis_permute",
        "head_dim_vectorize",
        "kv_split"
      ],
      "verdict": "EXACT_TOKEN"
    },
    {
      "dst": "vllm-paged-x16",
      "frontier_code": "X4_GEOMETRY_UNREPRESENTABLE",
      "frontier_reason": "the layout does not exist at this geometry (a factorisation that does not divide), so there is nothing to be exact about (vllm-paged-x16: head_dim 8 % x 16 != 0)",
      "native_bytes": {
        "dst": null,
        "src": null
      },
      "observations": {
        "forward_reproduces_target": null,
        "roundtrip_byte_identical": null,
        "roundtrip_diff_is_exactly_unread_padding": null,
        "tokens_identical": null
      },
      "pair_id": "vllm-fa->vllm-paged-x16",
      "proof": {
        "command": "make exact-hunt-frontier",
        "decoded_tokens": null,
        "dest_bijective": null,
        "dest_padding_positions": null,
        "detail": "the layout does not exist at this geometry (a factorisation that does not divide), so there is nothing to be exact about (vllm-paged-x16: head_dim 8 % x 16 != 0)",
        "gather_agrees": null,
        "gather_payloads": null,
        "kind": "frontier",
        "layers": null,
        "lean_lemmas": [
          "ExactTransform.factor_needs_divisibility"
        ],
        "positions_checked": null,
        "positions_total": null,
        "reference_tokens": null,
        "roundtrip_diff_positions": null,
        "source_bijective": null,
        "source_padding_positions": null,
        "source_positions_checked": null,
        "source_positions_total": null,
        "unread_padding_positions": null
      },
      "src": "vllm-fa",
      "transformations": [
        "axis_permute",
        "head_dim_vectorize",
        "kv_split"
      ],
      "verdict": "REFUSED"
    },
    {
      "dst": "vllm-tp2",
      "frontier_code": "X2_HEAD_GATHER",
      "frontier_reason": "the two layouts hold different numbers of kv-heads, so one is a PROJECTION of the other; the map back is a gather and has no inverse",
      "native_bytes": {
        "dst": null,
        "src": null
      },
      "observations": {
        "forward_reproduces_target": null,
        "roundtrip_byte_identical": null,
        "roundtrip_diff_is_exactly_unread_padding": null,
        "tokens_identical": null
      },
      "pair_id": "vllm-fa->vllm-tp2",
      "proof": {
        "command": "make exact-hunt-frontier",
        "decoded_tokens": null,
        "dest_bijective": null,
        "dest_padding_positions": null,
        "detail": "the two layouts hold different numbers of kv-heads, so one is a PROJECTION of the other; the map back is a gather and has no inverse",
        "gather_agrees": null,
        "gather_payloads": null,
        "kind": "frontier",
        "layers": null,
        "lean_lemmas": [
          "ExactTransform.head_gather_not_injective"
        ],
        "positions_checked": null,
        "positions_total": null,
        "reference_tokens": null,
        "roundtrip_diff_positions": null,
        "source_bijective": null,
        "source_padding_positions": null,
        "source_positions_checked": null,
        "source_positions_total": null,
        "unread_padding_positions": null
      },
      "src": "vllm-fa",
      "transformations": [],
      "verdict": "REFUSED"
    },
    {
      "dst": "vllm-fa",
      "frontier_code": null,
      "frontier_reason": null,
      "native_bytes": {
        "dst": 3072,
        "src": 3072
      },
      "observations": {
        "forward_reproduces_target": false,
        "roundtrip_byte_identical": false,
        "roundtrip_diff_is_exactly_unread_padding": true,
        "tokens_identical": false
      },
      "pair_id": "vllm-fp8->vllm-fa",
      "proof": {
        "command": "make exact-hunt",
        "decoded_tokens": [
          2,
          59,
          2,
          27,
          11,
          6,
          31,
          31
        ],
        "dest_bijective": true,
        "dest_padding_positions": 256,
        "detail": "the element type changes. The POSITION map is still a bijection \u2014 the certificate records it as one \u2014 and the ELEMENT map is not injective, so no arrangement of the bytes makes the transfer exact. This row is NOT_EXACT rather than REFUSED because the transfer runs.",
        "gather_agrees": true,
        "gather_payloads": 6,
        "kind": "index-permutation-exhaustive",
        "layers": 3,
        "lean_lemmas": [
          "ExactTransformCert.roundtrip_vllm_fa",
          "ExactTransform.comp_roundtrip",
          "ExactTransform.swap_involutive",
          "ExactTransform.factor_unfactor_id"
        ],
        "positions_checked": 1536,
        "positions_total": 1536,
        "reference_tokens": [
          2,
          27,
          60,
          51,
          2,
          27,
          60,
          51
        ],
        "roundtrip_diff_positions": 768,
        "source_bijective": true,
        "source_padding_positions": 256,
        "source_positions_checked": 1536,
        "source_positions_total": 1536,
        "unread_padding_positions": 768
      },
      "src": "vllm-fp8",
      "transformations": [
        "requantize"
      ],
      "verdict": "NOT_EXACT"
    },
    {
      "dst": "flashinfer-nhd",
      "frontier_code": null,
      "frontier_reason": null,
      "native_bytes": {
        "dst": 3072,
        "src": 3072
      },
      "observations": {
        "forward_reproduces_target": true,
        "roundtrip_byte_identical": false,
        "roundtrip_diff_is_exactly_unread_padding": true,
        "tokens_identical": true
      },
      "pair_id": "vllm-paged-x->flashinfer-nhd",
      "proof": {
        "command": "make exact-hunt",
        "decoded_tokens": [
          2,
          27,
          60,
          51,
          2,
          27,
          60,
          51
        ],
        "dest_bijective": true,
        "dest_padding_positions": 256,
        "detail": null,
        "gather_agrees": true,
        "gather_payloads": 6,
        "kind": "index-permutation-exhaustive",
        "layers": 3,
        "lean_lemmas": [
          "ExactTransformCert.roundtrip_vllm_paged_x",
          "ExactTransformCert.roundtrip_flashinfer_nhd",
          "ExactTransform.comp_roundtrip",
          "ExactTransform.swap_involutive",
          "ExactTransform.factor_unfactor_id"
        ],
        "positions_checked": 1536,
        "positions_total": 1536,
        "reference_tokens": [
          2,
          27,
          60,
          51,
          2,
          27,
          60,
          51
        ],
        "roundtrip_diff_positions": 768,
        "source_bijective": true,
        "source_padding_positions": 256,
        "source_positions_checked": 1536,
        "source_positions_total": 1536,
        "unread_padding_positions": 768
      },
      "src": "vllm-paged-x",
      "transformations": [
        "axis_permute",
        "head_dim_devectorize",
        "kv_merge"
      ],
      "verdict": "EXACT_TOKEN"
    },
    {
      "dst": "hf-dynamic-cache",
      "frontier_code": null,
      "frontier_reason": null,
      "native_bytes": {
        "dst": 2560,
        "src": 3072
      },
      "observations": {
        "forward_reproduces_target": true,
        "roundtrip_byte_identical": false,
        "roundtrip_diff_is_exactly_unread_padding": true,
        "tokens_identical": true
      },
      "pair_id": "vllm-paged-x->hf-dynamic-cache",
      "proof": {
        "command": "make exact-hunt",
        "decoded_tokens": [
          2,
          27,
          60,
          51,
          2,
          27,
          60,
          51
        ],
        "dest_bijective": true,
        "dest_padding_positions": 0,
        "detail": null,
        "gather_agrees": true,
        "gather_payloads": 6,
        "kind": "index-permutation-exhaustive",
        "layers": 3,
        "lean_lemmas": [
          "ExactTransformCert.roundtrip_vllm_paged_x",
          "ExactTransformCert.roundtrip_hf_dynamic_cache",
          "ExactTransform.comp_roundtrip",
          "ExactTransform.swap_involutive",
          "ExactTransform.factor_unfactor_id"
        ],
        "positions_checked": 1280,
        "positions_total": 1280,
        "reference_tokens": [
          2,
          27,
          60,
          51,
          2,
          27,
          60,
          51
        ],
        "roundtrip_diff_positions": 768,
        "source_bijective": true,
        "source_padding_positions": 256,
        "source_positions_checked": 1536,
        "source_positions_total": 1536,
        "unread_padding_positions": 768
      },
      "src": "vllm-paged-x",
      "transformations": [
        "head_dim_devectorize",
        "head_order_transpose",
        "reblock"
      ],
      "verdict": "EXACT_TOKEN"
    },
    {
      "dst": "llamacpp",
      "frontier_code": null,
      "frontier_reason": null,
      "native_bytes": {
        "dst": 2560,
        "src": 3072
      },
      "observations": {
        "forward_reproduces_target": true,
        "roundtrip_byte_identical": false,
        "roundtrip_diff_is_exactly_unread_padding": true,
        "tokens_identical": true
      },
      "pair_id": "vllm-paged-x->llamacpp",
      "proof": {
        "command": "make exact-hunt",
        "decoded_tokens": [
          2,
          27,
          60,
          51,
          2,
          27,
          60,
          51
        ],
        "dest_bijective": true,
        "dest_padding_positions": 0,
        "detail": null,
        "gather_agrees": true,
        "gather_payloads": 6,
        "kind": "index-permutation-exhaustive",
        "layers": 3,
        "lean_lemmas": [
          "ExactTransformCert.roundtrip_vllm_paged_x",
          "ExactTransformCert.roundtrip_llamacpp",
          "ExactTransform.comp_roundtrip",
          "ExactTransform.swap_involutive",
          "ExactTransform.factor_unfactor_id"
        ],
        "positions_checked": 1280,
        "positions_total": 1280,
        "reference_tokens": [
          2,
          27,
          60,
          51,
          2,
          27,
          60,
          51
        ],
        "roundtrip_diff_positions": 768,
        "source_bijective": true,
        "source_padding_positions": 256,
        "source_positions_checked": 1536,
        "source_positions_total": 1536,
        "unread_padding_positions": 768
      },
      "src": "vllm-paged-x",
      "transformations": [
        "axis_permute",
        "head_dim_devectorize",
        "head_order_transpose",
        "reblock",
        "v_dim_transpose"
      ],
      "verdict": "EXACT_TOKEN"
    },
    {
      "dst": "lmdeploy-turbomind",
      "frontier_code": null,
      "frontier_reason": null,
      "native_bytes": {
        "dst": 4096,
        "src": 3072
      },
      "observations": {
        "forward_reproduces_target": true,
        "roundtrip_byte_identical": false,
        "roundtrip_diff_is_exactly_unread_padding": true,
        "tokens_identical": true
      },
      "pair_id": "vllm-paged-x->lmdeploy-turbomind",
      "proof": {
        "command": "make exact-hunt",
        "decoded_tokens": [
          2,
          27,
          60,
          51,
          2,
          27,
          60,
          51
        ],
        "dest_bijective": true,
        "dest_padding_positions": 768,
        "detail": null,
        "gather_agrees": true,
        "gather_payloads": 6,
        "kind": "index-permutation-exhaustive",
        "layers": 3,
        "lean_lemmas": [
          "ExactTransformCert.roundtrip_vllm_paged_x",
          "ExactTransformCert.roundtrip_lmdeploy_turbomind",
          "ExactTransform.comp_roundtrip",
          "ExactTransform.swap_involutive",
          "ExactTransform.factor_unfactor_id"
        ],
        "positions_checked": 2048,
        "positions_total": 2048,
        "reference_tokens": [
          2,
          27,
          60,
          51,
          2,
          27,
          60,
          51
        ],
        "roundtrip_diff_positions": 768,
        "source_bijective": true,
        "source_padding_positions": 256,
        "source_positions_checked": 1536,
        "source_positions_total": 1536,
        "unread_padding_positions": 768
      },
      "src": "vllm-paged-x",
      "transformations": [
        "axis_permute",
        "head_dim_devectorize",
        "reblock"
      ],
      "verdict": "EXACT_TOKEN"
    },
    {
      "dst": "sglang",
      "frontier_code": null,
      "frontier_reason": null,
      "native_bytes": {
        "dst": 2560,
        "src": 3072
      },
      "observations": {
        "forward_reproduces_target": true,
        "roundtrip_byte_identical": false,
        "roundtrip_diff_is_exactly_unread_padding": true,
        "tokens_identical": true
      },
      "pair_id": "vllm-paged-x->sglang",
      "proof": {
        "command": "make exact-hunt",
        "decoded_tokens": [
          2,
          27,
          60,
          51,
          2,
          27,
          60,
          51
        ],
        "dest_bijective": true,
        "dest_padding_positions": 0,
        "detail": null,
        "gather_agrees": true,
        "gather_payloads": 6,
        "kind": "index-permutation-exhaustive",
        "layers": 3,
        "lean_lemmas": [
          "ExactTransformCert.roundtrip_vllm_paged_x",
          "ExactTransformCert.roundtrip_sglang",
          "ExactTransform.comp_roundtrip",
          "ExactTransform.swap_involutive",
          "ExactTransform.factor_unfactor_id"
        ],
        "positions_checked": 1280,
        "positions_total": 1280,
        "reference_tokens": [
          2,
          27,
          60,
          51,
          2,
          27,
          60,
          51
        ],
        "roundtrip_diff_positions": 768,
        "source_bijective": true,
        "source_padding_positions": 256,
        "source_positions_checked": 1536,
        "source_positions_total": 1536,
        "unread_padding_positions": 768
      },
      "src": "vllm-paged-x",
      "transformations": [
        "axis_permute",
        "head_dim_devectorize",
        "reblock"
      ],
      "verdict": "EXACT_TOKEN"
    },
    {
      "dst": "trtllm",
      "frontier_code": null,
      "frontier_reason": null,
      "native_bytes": {
        "dst": 4096,
        "src": 3072
      },
      "observations": {
        "forward_reproduces_target": true,
        "roundtrip_byte_identical": false,
        "roundtrip_diff_is_exactly_unread_padding": true,
        "tokens_identical": true
      },
      "pair_id": "vllm-paged-x->trtllm",
      "proof": {
        "command": "make exact-hunt",
        "decoded_tokens": [
          2,
          27,
          60,
          51,
          2,
          27,
          60,
          51
        ],
        "dest_bijective": true,
        "dest_padding_positions": 768,
        "detail": null,
        "gather_agrees": true,
        "gather_payloads": 6,
        "kind": "index-permutation-exhaustive",
        "layers": 3,
        "lean_lemmas": [
          "ExactTransformCert.roundtrip_vllm_paged_x",
          "ExactTransformCert.roundtrip_trtllm",
          "ExactTransform.comp_roundtrip",
          "ExactTransform.swap_involutive",
          "ExactTransform.factor_unfactor_id"
        ],
        "positions_checked": 2048,
        "positions_total": 2048,
        "reference_tokens": [
          2,
          27,
          60,
          51,
          2,
          27,
          60,
          51
        ],
        "roundtrip_diff_positions": 768,
        "source_bijective": true,
        "source_padding_positions": 256,
        "source_positions_checked": 1536,
        "source_positions_total": 1536,
        "unread_padding_positions": 768
      },
      "src": "vllm-paged-x",
      "transformations": [
        "axis_permute",
        "head_dim_devectorize",
        "kv_merge",
        "reblock"
      ],
      "verdict": "EXACT_TOKEN"
    },
    {
      "dst": "vllm-fa",
      "frontier_code": null,
      "frontier_reason": null,
      "native_bytes": {
        "dst": 3072,
        "src": 3072
      },
      "observations": {
        "forward_reproduces_target": true,
        "roundtrip_byte_identical": false,
        "roundtrip_diff_is_exactly_unread_padding": true,
        "tokens_identical": true
      },
      "pair_id": "vllm-paged-x->vllm-fa",
      "proof": {
        "command": "make exact-hunt",
        "decoded_tokens": [
          2,
          27,
          60,
          51,
          2,
          27,
          60,
          51
        ],
        "dest_bijective": true,
        "dest_padding_positions": 256,
        "detail": null,
        "gather_agrees": true,
        "gather_payloads": 6,
        "kind": "index-permutation-exhaustive",
        "layers": 3,
        "lean_lemmas": [
          "ExactTransformCert.roundtrip_vllm_paged_x",
          "ExactTransformCert.roundtrip_vllm_fa",
          "ExactTransform.comp_roundtrip",
          "ExactTransform.swap_involutive",
          "ExactTransform.factor_unfactor_id"
        ],
        "positions_checked": 1536,
        "positions_total": 1536,
        "reference_tokens": [
          2,
          27,
          60,
          51,
          2,
          27,
          60,
          51
        ],
        "roundtrip_diff_positions": 768,
        "source_bijective": true,
        "source_padding_positions": 256,
        "source_positions_checked": 1536,
        "source_positions_total": 1536,
        "unread_padding_positions": 768
      },
      "src": "vllm-paged-x",
      "transformations": [
        "axis_permute",
        "head_dim_devectorize",
        "kv_merge"
      ],
      "verdict": "EXACT_TOKEN"
    },
    {
      "dst": "vllm-fa",
      "frontier_code": "X4_GEOMETRY_UNREPRESENTABLE",
      "frontier_reason": "the layout does not exist at this geometry (a factorisation that does not divide), so there is nothing to be exact about (vllm-paged-x16: head_dim 8 % x 16 != 0)",
      "native_bytes": {
        "dst": null,
        "src": null
      },
      "observations": {
        "forward_reproduces_target": null,
        "roundtrip_byte_identical": null,
        "roundtrip_diff_is_exactly_unread_padding": null,
        "tokens_identical": null
      },
      "pair_id": "vllm-paged-x16->vllm-fa",
      "proof": {
        "command": "make exact-hunt-frontier",
        "decoded_tokens": null,
        "dest_bijective": null,
        "dest_padding_positions": null,
        "detail": "the layout does not exist at this geometry (a factorisation that does not divide), so there is nothing to be exact about (vllm-paged-x16: head_dim 8 % x 16 != 0)",
        "gather_agrees": null,
        "gather_payloads": null,
        "kind": "frontier",
        "layers": null,
        "lean_lemmas": [
          "ExactTransform.factor_needs_divisibility"
        ],
        "positions_checked": null,
        "positions_total": null,
        "reference_tokens": null,
        "roundtrip_diff_positions": null,
        "source_bijective": null,
        "source_padding_positions": null,
        "source_positions_checked": null,
        "source_positions_total": null,
        "unread_padding_positions": null
      },
      "src": "vllm-paged-x16",
      "transformations": [
        "axis_permute",
        "head_dim_devectorize",
        "kv_merge"
      ],
      "verdict": "REFUSED"
    },
    {
      "dst": "vllm-fa",
      "frontier_code": "X2_HEAD_GATHER",
      "frontier_reason": "the two layouts hold different numbers of kv-heads, so one is a PROJECTION of the other; the map back is a gather and has no inverse",
      "native_bytes": {
        "dst": null,
        "src": null
      },
      "observations": {
        "forward_reproduces_target": null,
        "roundtrip_byte_identical": null,
        "roundtrip_diff_is_exactly_unread_padding": null,
        "tokens_identical": null
      },
      "pair_id": "vllm-tp2->vllm-fa",
      "proof": {
        "command": "make exact-hunt-frontier",
        "decoded_tokens": null,
        "dest_bijective": null,
        "dest_padding_positions": null,
        "detail": "the two layouts hold different numbers of kv-heads, so one is a PROJECTION of the other; the map back is a gather and has no inverse",
        "gather_agrees": null,
        "gather_payloads": null,
        "kind": "frontier",
        "layers": null,
        "lean_lemmas": [
          "ExactTransform.head_gather_not_injective"
        ],
        "positions_checked": null,
        "positions_total": null,
        "reference_tokens": null,
        "roundtrip_diff_positions": null,
        "source_bijective": null,
        "source_padding_positions": null,
        "source_positions_checked": null,
        "source_positions_total": null,
        "unread_padding_positions": null
      },
      "src": "vllm-tp2",
      "transformations": [],
      "verdict": "REFUSED"
    }
  ],
  "schema": "[removed].exact-transformations/v1",
  "signature": "77d70225eae39641d242386303be0fd6ed0c8149ba6a46af4ebc9785af7e8b93946cb1ae466f5b0a3b43eb5a378d078ec8e368f32920452e4330fba52eaa710f",
  "vocabulary": [
    "reblock",
    "head_order_transpose",
    "kv_split",
    "kv_merge",
    "head_dim_vectorize",
    "head_dim_devectorize",
    "v_dim_transpose",
    "axis_permute",
    "requantize"
  ]
}
