A tax notice arrived: choose the response that fits

D014 FORMULA-02 — Original worked-example repairs

Baseline: October 22, 2026 (America/Los_Angeles) Check date: October 22, 2026, PDT Route: Same regular Chat, GPT-6. No Deep Research invoked.

Scope: Repair the nine original examples supplied in this request, preserving their inputs, assumptions, amounts and original D014 claim IDs. This supplement does not replace or certify the parent research report.

The coordinator's October 22, 2026, 23:25:30 UTC arithmetic audit is retained as attributed evidence. The formulas below are independently recalculated from the supplied inputs. Mathematical correctness is distinguished from legal classification, tax eligibility and IRS acceptance.

1. Repaired original formulas

E01 — Insolvency exclusion with partially taxable COD

Original claims: D014-C035, D014-C037.

Assume $80,000 unsecured debt, $30,000 settlement payment, actual cancellation of the remaining principal, $300,000 total liabilities and $270,000 asset fair market value immediately before cancellation. No higher-priority exclusion applies.

Plain text

Original debt principal = $80,000
Settlement payment = $30,000

Potential cancellation-of-debt income
= $80,000 - $30,000
= $50,000

Immediately-before liabilities = $300,000
Immediately-before asset FMV = $270,000

Amount of insolvency
= $300,000 - $270,000
= $30,000

Potential insolvency exclusion
= minimum($50,000, $30,000)
= $30,000

Potentially taxable COD income
= $50,000 - $30,000
= $20,000

Arithmetic: Pass. Form 982 and subsequent tax-attribute reduction must be considered. Actual cancellation, inclusion of all relevant assets/liabilities, deductible amounts, secured property, joint debt and other exclusions remain factual/legal conditions. The $20,000 is potential gross income, not a calculated tax bill.

E02 — Why insufficient cash does not establish insolvency

Original claim: D014-C035.

Plain text

Cash = $5,000
Other assets at FMV = $100,000

Total immediately-before assets
= $5,000 + $100,000
= $105,000

Total immediately-before liabilities = $70,000

Liabilities minus assets
= $70,000 - $105,000
= -$35,000

Insolvency amount
= maximum($0, -$35,000)
= $0

Arithmetic: Pass. The hypothetical taxpayer has positive net asset value of $35,000, despite only $5,000 cash. Retirement, investment and property interests require appropriate inclusion and valuation; the example does not establish how every actual interest is classified.

E03 — Tax-attribute cost of excluded COD

Original claim: D014-C037.

Assume $20,000 excluded COD, $12,000 reducible NOL, sufficient eligible general-business-credit carryover and no depreciable-property-basis-first election.

Plain text

Excluded COD = $20,000
Reducible NOL = $12,000

NOL reduction
= minimum($20,000, $12,000)
= $12,000

Excluded COD remaining for subsequent attributes
= $20,000 - $12,000
= $8,000

Credit reduction rate = 1/3 dollar per $1

Illustrative general-business-credit reduction
= $8,000 × (1 ÷ 3)
= $2,666.666666...

Rounded illustrative credit reduction
= $2,666.67

Arithmetic: Pass to cents. The $2,666.67 figure is a mathematical illustration; the exact tax-return amount may require statutory rounding conventions. Credit availability, ordering, relevant tax-year attributes and elections must be verified. The credit reduction is not an immediate $2,666.67 cash tax.

E04 — Recourse foreclosure

Original claim: D014-C043.

Assume recourse debt of $250,000, property FMV of $200,000, adjusted basis of $180,000 and complete cancellation of the $50,000 deficiency. Ignore selling expenses and special home provisions.

Plain text

Recourse mortgage balance = $250,000
Property FMV at transfer = $200,000
Adjusted property tax basis = $180,000

Disposition amount realized (assumed)
= $200,000

Disposition gain
= $200,000 - $180,000
= $20,000 gain

Potential canceled deficiency
= $250,000 - $200,000
= $50,000 potential COD

Arithmetic: Pass. The $20,000 is a gain, not a loss. The $50,000 is separately evaluated for COD treatment and exclusions. Recourse classification, actual debt discharge, transfer consideration, basis and property-use rules are legal/factual prerequisites.

E05 — Same property with nonrecourse debt

Original claim: D014-C044.

Plain text

Nonrecourse debt satisfied by foreclosure = $250,000
Property FMV = $200,000
Adjusted property tax basis = $180,000

Assumed amount realized
= $250,000

Disposition gain
= $250,000 - $180,000
= $70,000 gain

Separate COD from this assumed nonrecourse foreclosure
= $0

Arithmetic: Pass. Under the assumed nonrecourse foreclosure classification, the full discharged debt enters amount realized, rather than separating a $50,000 COD component. The $70,000 remains a disposition gain before any other applicable tax provisions. Debt classification and transaction structure require primary-authority confirmation before publication.

E06 — Joint debt with two full-value Forms 1099-C

Original claim: D014-C040.

Assume actual $40,000 cancellation, joint-and-several liability, and a fact-supported 60% allocation to A and 40% to B. A has $10,000 insolvency; B has $30,000.

Plain text

Total actual debt cancellation = $40,000

Debtor A allocation
= $40,000 × 0.60
= $24,000

Debtor B allocation
= $40,000 × 0.40
= $16,000

Allocation cross-check
= $24,000 + $16,000
= $40,000

A insolvency exclusion
= minimum($24,000, $10,000)
= $10,000

A potentially taxable COD
= $24,000 - $10,000
= $14,000

B insolvency exclusion
= minimum($16,000, $30,000)
= $16,000

B potentially taxable COD
= $16,000 - $16,000
= $0

Arithmetic: Pass. The original 60/40 allocation is preserved. Two information returns showing $40,000 each do not, by themselves, establish $80,000 aggregate taxable income. The 60/40 allocation must be independently supported by actual facts, applicable law and IRS guidance; it is not a default rule.

E07 — Standard Form 656 OIC application cash

Original claim: D014-C010.

Assume one non-low-income-certified individual Form 656 lump-sum offer of $15,000, with the standard $205 application fee.

Plain text

Proposed settlement offer = $15,000
Standard application fee = $205
Initial lump-sum payment rate = 20%

Initial offer payment
= $15,000 × 0.20
= $3,000

Initial cash submitted
= $3,000 + $205
= $3,205

Remaining proposed offer payments
= $15,000 - $3,000
= $12,000

Total cash if accepted and fully paid
= $3,205 + $12,000
= $15,205

Arithmetic: Pass. The $205 fee is separate from the proposed $15,000 compromise. This does not establish acceptance or eligibility.

Form distinction: This example concerns the standard Form 656 procedure. July 2026 Form 656-L doubt-as-to-liability offers require neither the standard application fee nor an initial offer payment. The qualifying low-income exception under Form 656 is also separate.

E08 — Three months of failure-to-pay penalties

Original claims: D014-C014, D014-C017.

Assume $20,000 unpaid individual income tax, a timely filed return, three full chargeable months, unchanged principal, and eligibility for the reduced rate in the second scenario.

Plain text

Unpaid tax = $20,000
Chargeable months = 3

Ordinary monthly rate = 0.5%
Ordinary penalty
= $20,000 × 0.005 × 3
= $300

Qualifying approved-installment monthly rate = 0.25%
Reduced-rate penalty
= $20,000 × 0.0025 × 3
= $150

Illustrative difference
= $300 - $150
= $150

Arithmetic: Pass. The 0.25% rate requires the statutory installment-agreement and timely-return conditions; merely applying for a plan is insufficient. Interest accrues separately. Actual chargeable months, payment timing, rate changes and relief may alter both amounts.

2. Original-example disposition table

All 19 original arithmetic checks supplied by the coordinator are consistent with the repaired formulas. This is not a finding that 19 legal propositions have been verified.

3. Source register and claim qualifications

New supplement source IDs are distinct from the retained original IDs. Direct readings below were performed October 22, 2026 (PDT). IRS publications and webpages are official agency guidance; they are not controlling statutes or court opinions.

Coordinator evidence reuse: The arithmetic audit timestamp 2026-10-22T23:25:30.042416+00:00 and its 19 passing checks were provided directly in this request. The earlier SOURCE-02 findings were reused as existing conversation evidence, not represented as fresh openings.

Claim-level disposition

4. Residual publication holds

The corrected equations may be imported as illustrative arithmetic, with their assumptions and qualifications attached. The following remain held:

1. COD classification: Actual cancellation, timing, principal versus interest, insolvency assets/liabilities, joint allocation and tax attributes.
2. Foreclosure: Recourse/nonrecourse classification, basis, disposition amount, property-use rules and any applicable exclusions.
3. OIC: Form 656 versus Form 656-L, low-income qualification, submission rules and IRS acceptance.
4. Penalties: Return and tax type, full statutory requirements, dates, changing balances, relief and concurrent penalties.
5. Parent report: All other claims, state/local rules, contracts, 2026 tax-year transitions and any unreconciled primary authorities.

Next actions: Open the controlling §108 and §1017 provisions through a functioning official source; reconcile Publication 4681's examples to the actual 2026 law; verify the joint-debt allocation authority; and connect each repaired formula to the parent report's original claim-to-source register. Preserve the original example text as historical output and import these equations as a separately dated correction.

5. Researcher self-check

Recomputed: All supplied original numerical relationships, retaining the $20,000 recourse gain, $70,000 nonrecourse gain, 60/40 joint allocation, $3,205 standard OIC submission and $300/$150 penalty comparison.

Newly opened: IRS Publication 4681, Topic 431, Form 656-B and the IRS failure-to-pay guidance. A direct OLRC §108 request failed and was not counted as verified.

Not established: Complete controlling-law verification of E01–E06, actual taxpayer eligibility, full 2026 applicability, IRS acceptance or any parent-area publication approval.

This is a focused formula and evidence self-check, not an independent review. No local files were written, and no publication, contacts, purchases, account changes or private-data access occurred.

END D014 FORMULA-02