{
 "receipt": "ITEM51_DYSON_WORDS",
 "stamp_utc": "2026-09-06T13:44:51Z",
 "stamp_source": "date -u inside this python",
 "producer": {
  "script": "dyson_words.py",
  "script_sha256": "91c466befb7d3612977d043e72c4f066bf1f466a00dfadf72aa2e65efbc5c3b7",
  "sympy": "1.14.0"
 },
 "connection_object": {
  "path": "Aform.json",
  "sha256": "13e392bf9fe099e747584f16608ec08ff7b18ce9995ba1c9e2a85737e2579ada",
  "matrix_M": [
   [
    "0",
    "0",
    "0",
    "0"
   ],
   [
    "0",
    "-f_2a-f_2b",
    "1",
    "0"
   ],
   [
    "0",
    "f_4b",
    "-f_2a+2*f_2b",
    "1"
   ],
   [
    "f_4a",
    "f_6",
    "f_4b",
    "-f_2a-f_2b"
   ]
  ],
  "alphabet": [
   "1",
   "f_2a",
   "f_2b",
   "f_4a",
   "f_4b",
   "f_6"
  ],
  "modular_weights": {
   "f_2a": 2,
   "f_2b": 2,
   "f_4a": 4,
   "f_4b": 4,
   "f_6": 6
  }
 },
 "boundary_grading_by_object": {
  "b0=g4": "eps^0 (I1 = eps^3 I_1110, I_1110 = -Gamma(eps)^3)",
  "b1=g1": "eps^3 (I2 = eps^3 (pi^2/varpi_0) I_1111)",
  "b2=g2": "eps^2 (I3 = (1/(2 pi i eps)) d/dtau I2 + F32 I2)",
  "b3=g3": "eps^1 (I4 = (1/(2 pi i eps)) d/dtau I3 + ...)",
  "source": "build_Aform.py L92-96 (sha256 7a08e88c4498d3b6...)"
 },
 "word_count_tower_g1": [
  1,
  3,
  10,
  36,
  131,
  476,
  1726
 ],
 "record_tower_EXPLICIT_K3": [
  1,
  3,
  10,
  36,
  131,
  476
 ],
 "tower_matches_record_through_eps5": true,
 "letter_first_physical_order": {
  "one": 0,
  "f4a": 0,
  "f2a": 1,
  "f2b": 1,
  "f4b": 2,
  "f6": 3
 },
 "physical_layers": {
  "m1_eps^0": {
   "n_words_structural": 4,
   "n_words_after_record_zeros": 2,
   "letters_active_after_record_zeros": [
    "f4a",
    "one"
   ],
   "words": [
    {
     "coeff": 1,
     "word_outer_to_inner": [],
     "boundary": "b1",
     "boundary_order": 3,
     "boundary_factor": "b1[eps^3]",
     "known_zero": null
    },
    {
     "coeff": 1,
     "word_outer_to_inner": [
      "one"
     ],
     "boundary": "b2",
     "boundary_order": 2,
     "boundary_factor": "b2[eps^2]",
     "known_zero": "C_{3,2} = 0 (regularized; CLOSE_K3_A.json MUM_cusp_constants_literature)"
    },
    {
     "coeff": 1,
     "word_outer_to_inner": [
      "one",
      "one"
     ],
     "boundary": "b3",
     "boundary_order": 1,
     "boundary_factor": "b3[eps^1]",
     "known_zero": "C_{4,1} = 0 (regularized; CLOSE_K3_A.json MUM_cusp_constants_literature)"
    },
    {
     "coeff": 1,
     "word_outer_to_inner": [
      "one",
      "one",
      "f4a"
     ],
     "boundary": "b0",
     "boundary_order": 0,
     "boundary_factor": "b0[eps^0]",
     "known_zero": null
    }
   ]
  },
  "m1_eps^1": {
   "n_words_structural": 22,
   "n_words_after_record_zeros": 12,
   "letters_active_after_record_zeros": [
    "f2a",
    "f2b",
    "f4a",
    "one"
   ],
   "words": [
    {
     "coeff": 1,
     "word_outer_to_inner": [],
     "boundary": "b1",
     "boundary_order": 4,
     "boundary_factor": "b1[eps^4]",
     "known_zero": null
    },
    {
     "coeff": -1,
     "word_outer_to_inner": [
      "f2a"
     ],
     "boundary": "b1",
     "boundary_order": 3,
     "boundary_factor": "b1[eps^3]",
     "known_zero": null
    },
    {
     "coeff": -1,
     "word_outer_to_inner": [
      "f2b"
     ],
     "boundary": "b1",
     "boundary_order": 3,
     "boundary_factor": "b1[eps^3]",
     "known_zero": null
    },
    {
     "coeff": 1,
     "word_outer_to_inner": [
      "one"
     ],
     "boundary": "b2",
     "boundary_order": 3,
     "boundary_factor": "b2[eps^3]",
     "known_zero": null
    },
    {
     "coeff": -1,
     "word_outer_to_inner": [
      "f2a",
      "one"
     ],
     "boundary": "b2",
     "boundary_order": 2,
     "boundary_factor": "b2[eps^2]",
     "known_zero": "C_{3,2} = 0 (regularized; CLOSE_K3_A.json MUM_cusp_constants_literature)"
    },
    {
     "coeff": -1,
     "word_outer_to_inner": [
      "f2b",
      "one"
     ],
     "boundary": "b2",
     "boundary_order": 2,
     "boundary_factor": "b2[eps^2]",
     "known_zero": "C_{3,2} = 0 (regularized; CLOSE_K3_A.json MUM_cusp_constants_literature)"
    },
    {
     "coeff": -1,
     "word_outer_to_inner": [
      "one",
      "f2a"
     ],
     "boundary": "b2",
     "boundary_order": 2,
     "boundary_factor": "b2[eps^2]",
     "known_zero": "C_{3,2} = 0 (regularized; CLOSE_K3_A.json MUM_cusp_constants_literature)"
    },
    {
     "coeff": 2,
     "word_outer_to_inner": [
      "one",
      "f2b"
     ],
     "boundary": "b2",
     "boundary_order": 2,
     "boundary_factor": "b2[eps^2]",
     "known_zero": "C_{3,2} = 0 (regularized; CLOSE_K3_A.json MUM_cusp_constants_literature)"
    },
    {
     "coeff": 1,
     "word_outer_to_inner": [
      "one",
      "one"
     ],
     "boundary": "b3",
     "boundary_order": 2,
     "boundary_factor": "b3[eps^2]",
     "known_zero": null
    },
    {
     "coeff": -1,
     "word_outer_to_inner": [
      "f2a",
      "one",
      "one"
     ],
     "boundary": "b3",
     "boundary_order": 1,
     "boundary_factor": "b3[eps^1]",
     "known_zero": "C_{4,1} = 0 (regularized; CLOSE_K3_A.json MUM_cusp_constants_literature)"
    },
    {
     "coeff": -1,
     "word_outer_to_inner": [
      "f2b",
      "one",
      "one"
     ],
     "boundary": "b3",
     "boundary_order": 1,
     "boundary_factor": "b3[eps^1]",
     "known_zero": "C_{4,1} = 0 (regularized; CLOSE_K3_A.json MUM_cusp_constants_literature)"
    },
    {
     "coeff": -1,
     "word_outer_to_inner": [
      "one",
      "f2a",
      "one"
     ],
     "boundary": "b3",
     "boundary_order": 1,
     "boundary_factor": "b3[eps^1]",
     "known_zero": "C_{4,1} = 0 (regularized; CLOSE_K3_A.json MUM_cusp_constants_literature)"
    },
    {
     "coeff": 2,
     "word_outer_to_inner": [
      "one",
      "f2b",
      "one"
     ],
     "boundary": "b3",
     "boundary_order": 1,
     "boundary_factor": "b3[eps^1]",
     "known_zero": "C_{4,1} = 0 (regularized; CLOSE_K3_A.json MUM_cusp_constants_literature)"
    },
    {
     "coeff": -1,
     "word_outer_to_inner": [
      "one",
      "one",
      "f2a"
     ],
     "boundary": "b3",
     "boundary_order": 1,
     "boundary_factor": "b3[eps^1]",
     "known_zero": "C_{4,1} = 0 (regularized; CLOSE_K3_A.json MUM_cusp_constants_literature)"
    },
    {
     "coeff": -1,
     "word_outer_to_inner": [
      "one",
      "one",
      "f2b"
     ],
     "boundary": "b3",
     "boundary_order": 1,
     "boundary_factor": "b3[eps^1]",
     "known_zero": "C_{4,1} = 0 (regularized; CLOSE_K3_A.json MUM_cusp_constants_literature)"
    },
    {
     "coeff": 1,
     "word_outer_to_inner": [
      "one",
      "one",
      "f4a"
     ],
     "boundary": "b0",
     "boundary_order": 1,
     "boundary_factor": "b0[eps^1]",
     "known_zero": null
    },
    {
     "coeff": -1,
     "word_outer_to_inner": [
      "f2a",
      "one",
      "one",
      "f4a"
     ],
     "boundary": "b0",
     "boundary_order": 0,
     "boundary_factor": "b0[eps^0]",
     "known_zero": null
    },
    {
     "coeff": -1,
     "word_outer_to_inner": [
      "f2b",
      "one",
      "one",
      "f4a"
     ],
     "boundary": "b0",
     "boundary_order": 0,
     "boundary_factor": "b0[eps^0]",
     "known_zero": null
    },
    {
     "coeff": -1,
     "word_outer_to_inner": [
      "one",
      "f2a",
      "one",
      "f4a"
     ],
     "boundary": "b0",
     "boundary_order": 0,
     "boundary_factor": "b0[eps^0]",
     "known_zero": null
    },
    {
     "coeff": 2,
     "word_outer_to_inner": [
      "one",
      "f2b",
      "one",
      "f4a"
     ],
     "boundary": "b0",
     "boundary_order": 0,
     "boundary_factor": "b0[eps^0]",
     "known_zero": null
    },
    {
     "coeff": -1,
     "word_outer_to_inner": [
      "one",
      "one",
      "f2a",
      "f4a"
     ],
     "boundary": "b0",
     "boundary_order": 0,
     "boundary_factor": "b0[eps^0]",
     "known_zero": null
    },
    {
     "coeff": -1,
     "word_outer_to_inner": [
      "one",
      "one",
      "f2b",
      "f4a"
     ],
     "boundary": "b0",
     "boundary_order": 0,
     "boundary_factor": "b0[eps^0]",
     "known_zero": null
    }
   ]
  },
  "m1_eps^2": {
   "n_words_structural": 93,
   "n_words_after_record_zeros": 53,
   "letters_active_after_record_zeros": [
    "f2a",
    "f2b",
    "f4a",
    "f4b",
    "one"
   ],
   "words": [
    {
     "coeff": 1,
     "word_outer_to_inner": [],
     "boundary": "b1",
     "boundary_order": 5,
     "boundary_factor": "b1[eps^5]",
     "known_zero": null
    },
    {
     "coeff": -1,
     "word_outer_to_inner": [
      "f2a"
     ],
     "boundary": "b1",
     "boundary_order": 4,
     "boundary_factor": "b1[eps^4]",
     "known_zero": null
    },
    {
     "coeff": -1,
     "word_outer_to_inner": [
      "f2b"
     ],
     "boundary": "b1",
     "boundary_order": 4,
     "boundary_factor": "b1[eps^4]",
     "known_zero": null
    },
    {
     "coeff": 1,
     "word_outer_to_inner": [
      "one"
     ],
     "boundary": "b2",
     "boundary_order": 4,
     "boundary_factor": "b2[eps^4]",
     "known_zero": null
    },
    {
     "coeff": 1,
     "word_outer_to_inner": [
      "f2a",
      "f2b"
     ],
     "boundary": "b1",
     "boundary_order": 3,
     "boundary_factor": "b1[eps^3]",
     "known_zero": null
    },
    {
     "coeff": -1,
     "word_outer_to_inner": [
      "f2a",
      "one"
     ],
     "boundary": "b2",
     "boundary_order": 3,
     "boundary_factor": "b2[eps^3]",
     "known_zero": null
    },
    {
     "coeff": 1,
     "word_outer_to_inner": [
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      "f2a"
     ],
     "boundary": "b1",
     "boundary_order": 3,
     "boundary_factor": "b1[eps^3]",
     "known_zero": null
    },
    {
     "coeff": 1,
     "word_outer_to_inner": [
      "f2b",
      "f2a"
     ],
     "boundary": "b1",
     "boundary_order": 3,
     "boundary_factor": "b1[eps^3]",
     "known_zero": null
    },
    {
     "coeff": -1,
     "word_outer_to_inner": [
      "f2b",
      "one"
     ],
     "boundary": "b2",
     "boundary_order": 3,
     "boundary_factor": "b2[eps^3]",
     "known_zero": null
    },
    {
     "coeff": 1,
     "word_outer_to_inner": [
      "f2b",
      "f2b"
     ],
     "boundary": "b1",
     "boundary_order": 3,
     "boundary_factor": "b1[eps^3]",
     "known_zero": null
    },
    {
     "coeff": -1,
     "word_outer_to_inner": [
      "one",
      "f2a"
     ],
     "boundary": "b2",
     "boundary_order": 3,
     "boundary_factor": "b2[eps^3]",
     "known_zero": null
    },
    {
     "coeff": 2,
     "word_outer_to_inner": [
      "one",
      "f2b"
     ],
     "boundary": "b2",
     "boundary_order": 3,
     "boundary_factor": "b2[eps^3]",
     "known_zero": null
    },
    {
     "coeff": 1,
     "word_outer_to_inner": [
      "one",
      "f4b"
     ],
     "boundary": "b1",
     "boundary_order": 3,
     "boundary_factor": "b1[eps^3]",
     "known_zero": null
    },
    {
     "coeff": 1,
     "word_outer_to_inner": [
      "one",
      "one"
     ],
     "boundary": "b3",
     "boundary_order": 3,
     "boundary_factor": "b3[eps^3]",
     "known_zero": null
    },
    {
     "coeff": 1,
     "word_outer_to_inner": [
      "f2a",
      "f2b",
      "one"
     ],
     "boundary": "b2",
     "boundary_order": 2,
     "boundary_factor": "b2[eps^2]",
     "known_zero": "C_{3,2} = 0 (regularized; CLOSE_K3_A.json MUM_cusp_constants_literature)"
    },
    {
     "coeff": 1,
     "word_outer_to_inner": [
      "f2a",
      "one",
      "f2a"
     ],
     "boundary": "b2",
     "boundary_order": 2,
     "boundary_factor": "b2[eps^2]",
     "known_zero": "C_{3,2} = 0 (regularized; CLOSE_K3_A.json MUM_cusp_constants_literature)"
    },
    {
     "coeff": -2,
     "word_outer_to_inner": [
      "f2a",
      "one",
      "f2b"
     ],
     "boundary": "b2",
     "boundary_order": 2,
     "boundary_factor": "b2[eps^2]",
     "known_zero": "C_{3,2} = 0 (regularized; CLOSE_K3_A.json MUM_cusp_constants_literature)"
    },
    {
     "coeff": -1,
     "word_outer_to_inner": [
      "f2a",
      "one",
      "one"
     ],
     "boundary": "b3",
     "boundary_order": 2,
     "boundary_factor": "b3[eps^2]",
     "known_zero": null
    },
    {
     "coeff": 1,
     "word_outer_to_inner": [
      "f2a",
      "f2a",
      "one"
     ],
     "boundary": "b2",
     "boundary_order": 2,
     "boundary_factor": "b2[eps^2]",
     "known_zero": "C_{3,2} = 0 (regularized; CLOSE_K3_A.json MUM_cusp_constants_literature)"
    },
    {
     "coeff": 1,
     "word_outer_to_inner": [
      "f2b",
      "f2a",
      "one"
     ],
     "boundary": "b2",
     "boundary_order": 2,
     "boundary_factor": "b2[eps^2]",
     "known_zero": "C_{3,2} = 0 (regularized; CLOSE_K3_A.json MUM_cusp_constants_literature)"
    },
    {
     "coeff": 1,
     "word_outer_to_inner": [
      "f2b",
      "one",
      "f2a"
     ],
     "boundary": "b2",
     "boundary_order": 2,
     "boundary_factor": "b2[eps^2]",
     "known_zero": "C_{3,2} = 0 (regularized; CLOSE_K3_A.json MUM_cusp_constants_literature)"
    },
    {
     "coeff": -2,
     "word_outer_to_inner": [
      "f2b",
      "one",
      "f2b"
     ],
     "boundary": "b2",
     "boundary_order": 2,
     "boundary_factor": "b2[eps^2]",
     "known_zero": "C_{3,2} = 0 (regularized; CLOSE_K3_A.json MUM_cusp_constants_literature)"
    },
    {
     "coeff": -1,
     "word_outer_to_inner": [
      "f2b",
      "one",
      "one"
     ],
     "boundary": "b3",
     "boundary_order": 2,
     "boundary_factor": "b3[eps^2]",
     "known_zero": null
    },
    {
     "coeff": 1,
     "word_outer_to_inner": [
      "f2b",
      "f2b",
      "one"
     ],
     "boundary": "b2",
     "boundary_order": 2,
     "boundary_factor": "b2[eps^2]",
     "known_zero": "C_{3,2} = 0 (regularized; CLOSE_K3_A.json MUM_cusp_constants_literature)"
    },
    {
     "coeff": -2,
     "word_outer_to_inner": [
      "one",
      "f2a",
      "f2b"
     ],
     "boundary": "b2",
     "boundary_order": 2,
     "boundary_factor": "b2[eps^2]",
     "known_zero": "C_{3,2} = 0 (regularized; CLOSE_K3_A.json MUM_cusp_constants_literature)"
    },
    {
     "coeff": -1,
     "word_outer_to_inner": [
      "one",
      "f2a",
      "one"
     ],
     "boundary": "b3",
     "boundary_order": 2,
     "boundary_factor": "b3[eps^2]",
     "known_zero": null
    },
    {
     "coeff": 1,
     "word_outer_to_inner": [
      "one",
      "f2a",
      "f2a"
     ],
     "boundary": "b2",
     "boundary_order": 2,
     "boundary_factor": "b2[eps^2]",
     "known_zero": "C_{3,2} = 0 (regularized; CLOSE_K3_A.json MUM_cusp_constants_literature)"
    },
    {
     "coeff": -2,
     "word_outer_to_inner": [
      "one",
      "f2b",
      "f2a"
     ],
     "boundary": "b2",
     "boundary_order": 2,
     "boundary_factor": "b2[eps^2]",
     "known_zero": "C_{3,2} = 0 (regularized; CLOSE_K3_A.json MUM_cusp_constants_literature)"
    },
    {
     "coeff": 2,
     "word_outer_to_inner": [
      "one",
      "f2b",
      "one"
     ],
     "boundary": "b3",
     "boundary_order": 2,
     "boundary_factor": "b3[eps^2]",
     "known_zero": null
    },
    {
     "coeff": 4,
     "word_outer_to_inner": [
      "one",
      "f2b",
      "f2b"
     ],
     "boundary": "b2",
     "boundary_order": 2,
     "boundary_factor": "b2[eps^2]",
     "known_zero": "C_{3,2} = 0 (regularized; CLOSE_K3_A.json MUM_cusp_constants_literature)"
    },
    {
     "coeff": 1,
     "word_outer_to_inner": [
      "one",
      "f4b",
      "one"
     ],
     "boundary": "b2",
     "boundary_order": 2,
     "boundary_factor": "b2[eps^2]",
     "known_zero": "C_{3,2} = 0 (regularized; CLOSE_K3_A.json MUM_cusp_constants_literature)"
    },
    {
     "coeff": -1,
     "word_outer_to_inner": [
      "one",
      "one",
      "f2a"
     ],
     "boundary": "b3",
     "boundary_order": 2,
     "boundary_factor": "b3[eps^2]",
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    },
    {
     "coeff": -1,
     "word_outer_to_inner": [
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      "one",
      "f2b"
     ],
     "boundary": "b3",
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     "boundary_factor": "b3[eps^2]",
     "known_zero": null
    },
    {
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      "one",
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    },
    {
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     "word_outer_to_inner": [
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      "one",
      "f4b"
     ],
     "boundary": "b2",
     "boundary_order": 2,
     "boundary_factor": "b2[eps^2]",
     "known_zero": "C_{3,2} = 0 (regularized; CLOSE_K3_A.json MUM_cusp_constants_literature)"
    },
    {
     "coeff": 1,
     "word_outer_to_inner": [
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      "one",
      "one"
     ],
     "boundary": "b3",
     "boundary_order": 1,
     "boundary_factor": "b3[eps^1]",
     "known_zero": "C_{4,1} = 0 (regularized; CLOSE_K3_A.json MUM_cusp_constants_literature)"
    },
    {
     "coeff": 1,
     "word_outer_to_inner": [
      "f2a",
      "one",
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 },
 "vendoring": {
  "role": "the symbolic companion of banana-evaluate.py --eps1: the words of the Dyson chain over the certified connection that survive at eps^1 of the top master (their t-space sum is what the holomorphic recursion evaluates implicitly)",
  "source_object_sha256": "b949d5715745d9676dbee50002bcd181bf618b8dfcb74a98e6151b512eef350b",
  "edits": [
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   "connection_object.path -> basename",
   "this block appended"
  ],
  "serialization": "json.dump(indent=1), the source's own form and key order"
 }
}