C755 — Invert and classify the MT residual field

Question

Which entire interval families survive rounding exactly?

Inputs

{}

Sources

[
  "C754"
]

Opened utc

2026-09-28T01:54:10.979733+00:00

Results

{
  "recovered_e": [
    0,
    -2,
    0,
    0,
    0,
    -2,
    0,
    1,
    -2,
    0,
    0,
    2,
    2,
    1,
    1,
    1,
    0,
    2,
    0,
    0,
    0,
    -2,
    -2,
    2,
    -2,
    0
  ],
  "equal_residual_classes": {
    "-4": [
      "Terah",
      "Abraham",
      "Isaac",
      "Jacob"
    ],
    "-2": [
      "Serug",
      "Nahor",
      "Levi",
      "Amram"
    ],
    "-1": [
      "Reu"
    ],
    "0": [
      "Adam",
      "Seth",
      "Peleg",
      "Kohath",
      "Moses",
      "terminal1406"
    ],
    "1": [
      "Eber"
    ],
    "2": [
      "Enosh",
      "Kenan",
      "Mahalalel",
      "Jared"
    ],
    "3": [
      "Lamech",
      "Shelah"
    ],
    "4": [
      "Enoch",
      "Methuselah"
    ],
    "5": [
      "Noah",
      "Shem",
      "Arphaxad"
    ]
  },
  "interval_rule": "rounded(i,j)-actual(i,j)=D_i-D_j"
}

Finding

Every pair within one residual class preserves its interval. These are consequences of one field, not independent numerical hits. Adjacent differences recover every row residual.

Reassessment

Transfer the full residual operator to LXX and isolate changed row support.

Checks

{
  "inverse": true,
  "interval_identity": true
}

Closed utc

2026-09-28T01:54:10.980078+00:00

Record provenance

Exact record hash: b6b9a4bf00039ec2e00aea2aa885f410548a951dd6d84a46c3b6972ca86ae596

Source journal: Research_Cycles/C0732_C0831/journal.json