{
  "schema": "OMEGA_CURRENT_RELATIONSHIP/2",
  "date": "2026-11-07",
  "status": "CURRENT_INDEX",
  "purpose": "Current index of the expanded joining evidence, the retained earlier package, and the separate treeOS finite replay. Not a new proof and not a mutation of a frozen map.",
  "not": [
    "not a mutation of /tga/2.1/graph-report.json",
    "not a mutation of atlas release 1.0",
    "not a joining of the nine source works",
    "not a written-proof review",
    "not an SRSD conformance review of Paper III",
    "not an attachment of INSTANCE_CHECKED to the compact record"
  ],
  "current": {
    "package": {
      "path": "/dynamics/joining/1.1.0/OMEGA_Explicit_Joining_Theorem_2026-11-07.zip",
      "filename": "OMEGA_Explicit_Joining_Theorem_2026-11-07.zip",
      "version": "1.1.0",
      "bytes": 254716,
      "sha256": "80d058b1807c4bb3b9ab7ba53163df3e18a5c0cb70ab2befb5cbbb2824f378e9",
      "replay": "Extract; python3 verify.py --self-test"
    },
    "typed_maps": {
      "path": "/dynamics/joining/1.1.0/CONNECTIONS.json",
      "schema": "OMEGA_JOINING_PROOF_RELATIONS/1",
      "bytes": 10933,
      "sha256": "75df2714b86fe76b844354cef39d2bc8d0c57fa503ab7f78e89c9cf6cee9460c",
      "maps": [
        {
          "id": "J01",
          "from": "selected positive scale",
          "to": "affine scalar state",
          "map": "chi(a)=1+a/a_ref; chi(lambda*a)=Omega_lambda(chi(a))",
          "written_proof": "PROOF.md, section 3"
        },
        {
          "id": "J02",
          "from": "600-cell vertex coordinates",
          "to": "four real network modes",
          "map": "2C=C0+phi*C1; A*C=6phi*C",
          "written_proof": "PROOF.md, section 2"
        },
        {
          "id": "J03",
          "from": "Z x Z^4 x Z^4",
          "to": "Z^120",
          "map": "E_Z(u)=B_enc*u; M*B_enc=B_enc*K",
          "written_proof": "PROOF.md, section 2"
        },
        {
          "id": "J04",
          "from": "real geometric signal family",
          "to": "real network F_gamma",
          "map": "F_gamma(E(t,w))=E(Omega_gamma(t),gamma*(13+6phi)*w/25)",
          "written_proof": "PROOF.md, section 3"
        },
        {
          "id": "J05",
          "from": "nonzero integer difference k",
          "to": "M*k",
          "map": "||M*k||_infinity >= 10",
          "written_proof": "PROOF.md, section 4"
        },
        {
          "id": "J06",
          "from": "integer input d",
          "to": "valid record (T(d),d mod8)",
          "map": "d -> (floor(Q*M*d/D),d mod8)",
          "written_proof": "PROOF.md, section 4"
        },
        {
          "id": "J07",
          "from": "valid full record (y,r)",
          "to": "valid mod8 record (y,s)",
          "map": "J(y,r)=(y,D_full(y,r) mod8); H(y,s)=(y,QM*D8(y,s)-Dy)",
          "written_proof": "PROOF.md, section 5"
        },
        {
          "id": "J08",
          "from": "scalar integer dynamics",
          "to": "constant-vector network dynamics",
          "map": "T(n*1)=floor(Q*n/S)*1; r(n*1)=25rho(n)*1",
          "written_proof": "PROOF.md, section 6"
        },
        {
          "id": "J09",
          "from": "nine geometric integers",
          "to": "terminal state plus ordered witnesses",
          "map": "E_Z^-1 o DecodeHistory8 o EncodeHistory8 o E_Z=Id",
          "written_proof": "PROOF.md, section 6"
        },
        {
          "id": "J10",
          "from": "ideal lambda evolution",
          "to": "rational quantized trajectory and remainders",
          "map": "F_lambda(1+d)=1+T(d)+r(d)/D+(lambda-q)*P*d",
          "written_proof": "PROOF.md, section 7"
        },
        {
          "id": "J11",
          "from": "floor(q*n)",
          "to": "floor(lambda*n)",
          "map": "n=2*10^15 gives 679899542689556 versus 679899542689557",
          "written_proof": "PROOF.md, section 7"
        },
        {
          "id": "J12",
          "from": "quantized output and residue",
          "to": "at-most-one exact lattice candidate",
          "map": "C_net^-1(y+[0,1)^120) intersect (s+8Z^120)",
          "written_proof": "PROOF.md, section 5"
        }
      ]
    },
    "compact_record": {
      "path": "/dynamics/joining/treeos/treeOS_LOG_OMEGA_Joining.v1.1.json",
      "filename": "treeOS_LOG_OMEGA_Joining.json",
      "version": "1.1",
      "bytes": 3276,
      "sha256": "15a2931cec9df25a7588417917f0817be75d3e9deb7dc5ba5337d163b3640b18",
      "embedded_kernel": false,
      "instance_checked_receipt": "not attached"
    },
    "this_archive_replay": {
      "path": "/dynamics/joining/1.1.0/evidence/2026-11-07-site/EXECUTION.json",
      "python": "3.10.21",
      "status": "PASS",
      "stdout_sha256": "67794f3070ab6a83c7c446762e7a22e5918c8bb4a4e126419b7ae07f6e8c83c1",
      "supplied_report_python": "3.12.14",
      "report_body_excluding_python_matches_supplied": true
    }
  },
  "retained": {
    "earlier_package": {
      "path": "/dynamics/joining/OMEGA_Explicit_Joining_Theorem_2026-11-07.zip",
      "bytes": 26470,
      "sha256": "7b7ba1b75025f74451c5960793f88f6a4fa5b2fe08274bbe2a846636c5b6e649",
      "role": "historical package; not replaced"
    },
    "executable_log": {
      "path": "/dynamics/joining/treeos/treeOS_LOG_OMEGA_Joining.json",
      "bytes": 24941,
      "sha256": "0b7a7715e49f5519a9d1e5088ca11eab8c3f2bef202ecd85b72fa2753c451133",
      "contract": "treeOS_LOG/OMEGA-SRSD/1.0",
      "receipt": "INSTANCE_CHECKED applies only to the finite replay of this log"
    }
  },
  "pages": [
    {
      "path": "/dynamics/joining",
      "role": "written note, both packages, finite replay"
    },
    {
      "path": "/dynamics/600cell",
      "role": "600-cell signals; separate from this note"
    },
    {
      "path": "/papers/ix",
      "role": "Zenodo preprint version 0.6; not this note"
    },
    {
      "path": "/network",
      "role": "5 September typed-interface dossier; frozen relative to this note"
    },
    {
      "path": "/proofs",
      "role": "navigator; link only"
    },
    {
      "path": "/reproduce",
      "role": "named commands; link only"
    }
  ],
  "frozen_unchanged": [
    "/tga/2.1/graph-report.json",
    "/atlas/index.html",
    "/atlas/releases/1.0/omega-atlas.html"
  ],
  "intervals_unchanged": [
    "306 <= ell* <= 360",
    "307 <= ell* <= 352"
  ],
  "source_works": 9
}