(a) an incorrect entry of assessed valuation on an assessment roll or on a tax roll which, because of a mistake in transcription, does not conform to the entry for the same parcel which appears on the property record card, field book or other final work product of the assessor, or the final verified statement of the board of assessment review; or

(b) an entry which is a mathematical error present in the computation of a partial exemption; or

(c) an incorrect entry of assessed valuation on an assessment roll or on a tax roll for a parcel which, except for a failure on the part of the assessor to act on a partial exemption, would be eligible for such partial exemption; or

(d) an entry which is a mathematical error present in the computation or extension of the tax; or

(e) an entry on a tax roll which is incorrect by reason of a mistake in the determination or transcription of a special assessment or other charge based on units of service provided by a special district; or

(f) a duplicate entry on an assessment roll or on a tax roll of the description or assessed valuation, or both, of an entire single parcel; or

(g) an entry on an assessment or tax roll which is incorrect by reason of an arithmetical mistake by the assessor appearing on the property record card, field book or other final work product of the assessor; or

(h) an incorrect entry on a tax roll of a relevied school tax or relevied village tax which has been previously paid; or

(i) an entry on a tax roll which is incorrect by reason of a mistake in the transcription of a relevied school tax or relevied village tax; or

(j) an incorrect entry of assessed valuation on an assessment roll or a tax roll due to an assessor's failure to utilize the required assessment method pursuant to section five hundred eighty-one-a of this article in the valuation of qualifying real property. 3. "Error in essential fact" means:

(a) an incorrect entry on the taxable portion of the assessment roll, or the tax roll, or both, of the assessed valuation of an improvement to real property which was destroyed or removed prior to taxable status date for such assessment roll; or

(b) an incorrect entry on the taxable portion of the assessment roll, or the tax roll, or both, of the assessed valuation of an improvement to real property which was not in existence or which was present on a different parcel; or

(c) an incorrect entry of acreage on the taxable portion of the assessment roll, or the tax roll, or both, which acreage was considered by the assessor in the valuation of the parcel and which resulted in an incorrect assessed valuation, where such acreage is shown to be incorrect on a survey submitted by the applicant; or

(d) the omission of the value of an improvement present on real property prior to taxable status date; or

(e) an incorrect entry of a partial exemption on an assessment roll for a parcel which is not eligible for such partial exemption; provided that the exemption has not been renounced pursuant to section four hundred ninety-six of this chapter; or

(f) an entry pursuant to article nineteen of this chapter on an assessment or tax roll which is incorrect by reason of a misclassification of property which is exclusively used for either residential or non-residential purposes. 4. "Improvement" means real property as defined in paragraph (b) of subdivision twelve of section one hundred two of this chapter, and which has been separately described and valued on the property record card, field book or other final work product of the assessor. 4-a. "Omission" or "omitted real property" means a parcel wholly omitted from the assessment roll or tax roll, taxable real property entered on the roll as wholly exempt real property, or an error in essential fact as defined in paragraph (d) of subdivision three of this section. An omission shall also include taxable real property for which no school district or special district tax was levied because of a failure to include the property within the appropriate taxing district. An "omission" or "omitted real property" shall not include real property assessed pursuant to subdivisions two through five of section five hundred of this article. 5. "Tax levying body" means the governing board of a municipal corporation which annexes a warrant for the collection of taxes to a final assessment roll. 6. "Tax roll" means a final assessment roll upon which taxes have been extended and to which a warrant has been annexed. 7. "Unlawful entry" means:

(a) an entry on the taxable portion of the assessment roll or the tax roll, or both, of the assessed valuation of real property which, except for the provisions of section four hundred ninety of this chapter, is wholly exempt from taxation; or

(b) an entry on an assessment roll or a tax roll, or both, of the assessed valuation of real property which is entirely outside the boundaries of the assessing unit, the school district or the special district in which the real property is designated as being located, but not an entry on an assessment roll or a tax roll, or both, of the assessed valuation of real property assessed pursuant to subdivisions two through five of section five hundred of this article; or

(c) an entry of assessed valuation on an assessment roll or on a tax roll, or both, which has been made by a person or body without the authority to make such entry; or

(d) an entry of assessed valuation of state land subject to taxation on an assessment roll or on a tax roll, or both, which exceeds the assessment of such land approved by the commissioner; or

(e) an entry of assessed valuation of a special franchise on an assessment roll or on a tax roll, or both, which exceeds the final assessment thereof as determined by the commissioner pursuant to subdivision one of section six hundred six of this chapter, or the full value of that special franchise as determined by the commissioner pursuant to subdivision two of section six hundred six of this chapter adjusted by the final state equalization rate established by the commissioner for the assessment roll upon which that value appears.