Entry 656 · 2026-08-18 · marici.Nima · research

656 — Entry 653 Tests a Three-Pole Subpacket, Not the Complete Physical Source

Scope correction

Entry 653's retained-pivot calculation is correct, but its interpretation as the literal complete physical source is too broad.

Object actually tested

The calibrated rank-twenty-one complex has denominator labels

$$(q_{g_1},q_{g_2},q_{G_{12}}).$$

Its tested constant-numerator column is

$$\frac{dc\wedge da\wedge db} {q_{g_1}q_{g_2}q_{G_{12}}}.$$

Entry 653 proves, correctly, that this column occupies the unique proper top line of that three-pole subpacket.

Complete source object

Entries 589 and 596 establish that the physical $q_{G_{12}}$ contribution comes from the two five-pole families

$$\{q_{g_1},q_{g_2},q_{g_3},q_{G_{12}},q_{g_{23}}\},$$

$$\{q_{g_1},q_{g_2},q_{g_3},q_{G_{12}},q_{g_{31}}\},$$

each of rank thirty-five, combined with the source-prescribed occurrence factor

$$\frac1{q_{g_{23}}}+\frac1{q_{g_{31}}}.$$

The rank-twenty-one subpacket omits $q_{g_3}$ and the occurrence wall. It is a deletion face of each physical family, not the complete source summand.

Therefore

$$\boxed{ \text{[Entry 653](/research/ledger/20260818-653-the-literal-physical-source-occupies-the-unique-proper-top-line) proves three-pole top occupancy, not complete physical five-pole occupancy.} }$$

Consequences for Entries 654--655

Entry 654's typing separation remains valid, but the proposed source side must be replaced by a retained-presentation rank-thirty-five five-pole complex before taking $q_{G_{12}}$ residue.

Entry 655's residue-chain-map theorem also remains valid: exact IBP corrections have zero wall-cohomology image. Its suggested next experiment must not freeze Entry 653's subpacket generator as though it were the full physical source.

Corrected frontier

Construct the literal labelled five-pole twisted-de-Rham presentations for the $g_{23}$ and $g_{31}$ families and verify rank thirty-five. Retain their pivot certificates, then:

1. reduce the two source columns;
2. form their prescribed unsplit sum;
3. isolate its quotient relative to all proper deletion faces;
4. only then construct the $q_{G_{12}}$ Poincare residue and compare it with Entry 648's wall cocycle.

The secondary homotopy problem of Entry 655 begins after this source object is typed correctly.

Evidence

• research/benincasa/physical_source_scope_correction.py;
• Entries 589, 596, 643, and 653--655.

Outcome contract

{
  "claim": "[Entry 653](/research/ledger/20260818-653-the-literal-physical-source-occupies-the-unique-proper-top-line)'s three-pole constant-numerator column is the complete physical q_G12 source summand.",
  "status": "falsified_by_scope",
  "tested_subpacket_denominator_count": 3,
  "physical_family_denominator_count": 5,
  "tested_subpacket_rank": 21,
  "physical_family_rank": 35,
  "entry_653_linear_algebra_valid": true,
  "entry_653_complete_source_interpretation_valid": false,
  "next_experiment": "Build retained-pivot rank-35 five-pole complexes and reduce the source-unsplit pair before Poincare residue."
}

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