{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:7JPF6MNAARZZUJKETAQIFGISKM","short_pith_number":"pith:7JPF6MNA","schema_version":"1.0","canonical_sha256":"fa5e5f31a004739a25449820829912532e3d8695b7a352622199fddb483f1782","source":{"kind":"arxiv","id":"1601.00572","version":2},"attestation_state":"computed","paper":{"title":"Signed tilings by ribbon L n-ominoes, n even, via Groebner bases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.CO","authors_text":"Kenneth Gill, Viorel Nitica","submitted_at":"2016-01-04T17:07:10Z","abstract_excerpt":"Let $\\mathcal{T}_n$ be the set of ribbon $L$-shaped $n$-ominoes for some $n\\ge 4$ even, and let $\\mathcal{T}_n^+$ be $\\mathcal{T}_n$ with an extra $2\\times 2$ square. We investigate signed tilings of rectangles by $\\mathcal{T}_n$ and $\\mathcal{T}_n^+$. We show that a rectangle has a signed tiling by $\\mathcal{T}_n$ if and only if both sides of the rectangle are even and one of them is divisible by $n$, or if one of the sides is odd and the other side is divisible by $n\\left (\\frac{n}{2}-2\\right ).$ We also show that a rectangle has a signed tiling by $\\mathcal{T}_n^+, n\\ge 6$ even, if and only"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1601.00572","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-04T17:07:10Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"930ba871c33e8f2128708374be12c3a8736ef976a251b964102dbf6929fb5fe8","abstract_canon_sha256":"4146fcd085ffde93aa1e95a1ce116a5062eb852a49adbe277f296e6e213483e5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:53.186749Z","signature_b64":"BXjbT8/hsliGGKOE05GgVnfLKzDdUxlCA2V9CJj7R+aa2huVg4kVeJaQbP7yRsTnSjTEb3xI4IgKHTZxhnN0Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa5e5f31a004739a25449820829912532e3d8695b7a352622199fddb483f1782","last_reissued_at":"2026-05-18T01:19:53.186271Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:53.186271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Signed tilings by ribbon L n-ominoes, n even, via Groebner bases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.CO","authors_text":"Kenneth Gill, Viorel Nitica","submitted_at":"2016-01-04T17:07:10Z","abstract_excerpt":"Let $\\mathcal{T}_n$ be the set of ribbon $L$-shaped $n$-ominoes for some $n\\ge 4$ even, and let $\\mathcal{T}_n^+$ be $\\mathcal{T}_n$ with an extra $2\\times 2$ square. We investigate signed tilings of rectangles by $\\mathcal{T}_n$ and $\\mathcal{T}_n^+$. We show that a rectangle has a signed tiling by $\\mathcal{T}_n$ if and only if both sides of the rectangle are even and one of them is divisible by $n$, or if one of the sides is odd and the other side is divisible by $n\\left (\\frac{n}{2}-2\\right ).$ We also show that a rectangle has a signed tiling by $\\mathcal{T}_n^+, n\\ge 6$ even, if and only"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00572","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1601.00572","created_at":"2026-05-18T01:19:53.186343+00:00"},{"alias_kind":"arxiv_version","alias_value":"1601.00572v2","created_at":"2026-05-18T01:19:53.186343+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.00572","created_at":"2026-05-18T01:19:53.186343+00:00"},{"alias_kind":"pith_short_12","alias_value":"7JPF6MNAARZZ","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_16","alias_value":"7JPF6MNAARZZUJKE","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_8","alias_value":"7JPF6MNA","created_at":"2026-05-18T12:30:04.600751+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7JPF6MNAARZZUJKETAQIFGISKM","json":"https://pith.science/pith/7JPF6MNAARZZUJKETAQIFGISKM.json","graph_json":"https://pith.science/api/pith-number/7JPF6MNAARZZUJKETAQIFGISKM/graph.json","events_json":"https://pith.science/api/pith-number/7JPF6MNAARZZUJKETAQIFGISKM/events.json","paper":"https://pith.science/paper/7JPF6MNA"},"agent_actions":{"view_html":"https://pith.science/pith/7JPF6MNAARZZUJKETAQIFGISKM","download_json":"https://pith.science/pith/7JPF6MNAARZZUJKETAQIFGISKM.json","view_paper":"https://pith.science/paper/7JPF6MNA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1601.00572&json=true","fetch_graph":"https://pith.science/api/pith-number/7JPF6MNAARZZUJKETAQIFGISKM/graph.json","fetch_events":"https://pith.science/api/pith-number/7JPF6MNAARZZUJKETAQIFGISKM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7JPF6MNAARZZUJKETAQIFGISKM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7JPF6MNAARZZUJKETAQIFGISKM/action/storage_attestation","attest_author":"https://pith.science/pith/7JPF6MNAARZZUJKETAQIFGISKM/action/author_attestation","sign_citation":"https://pith.science/pith/7JPF6MNAARZZUJKETAQIFGISKM/action/citation_signature","submit_replication":"https://pith.science/pith/7JPF6MNAARZZUJKETAQIFGISKM/action/replication_record"}},"created_at":"2026-05-18T01:19:53.186343+00:00","updated_at":"2026-05-18T01:19:53.186343+00:00"}