{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:WN3WQTVKSLL6U72ZQ76TIVEUGR","short_pith_number":"pith:WN3WQTVK","canonical_record":{"source":{"id":"1312.4597","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-12-17T00:22:08Z","cross_cats_sorted":["math.CO","math.MG"],"title_canon_sha256":"336d41f45e1115e136bcf604a12e37723d527d13e1be1b647424e5b6dde6333f","abstract_canon_sha256":"18cd25f82435e92faf5aea2570678cdfdc2161d0ff132c527e4785470a916143"},"schema_version":"1.0"},"canonical_sha256":"b377684eaa92d7ea7f5987fd345494344f232a5266e0ef63653342e2af1fe241","source":{"kind":"arxiv","id":"1312.4597","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.4597","created_at":"2026-05-18T02:24:28Z"},{"alias_kind":"arxiv_version","alias_value":"1312.4597v2","created_at":"2026-05-18T02:24:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.4597","created_at":"2026-05-18T02:24:28Z"},{"alias_kind":"pith_short_12","alias_value":"WN3WQTVKSLL6","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WN3WQTVKSLL6U72Z","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WN3WQTVK","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:WN3WQTVKSLL6U72ZQ76TIVEUGR","target":"record","payload":{"canonical_record":{"source":{"id":"1312.4597","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-12-17T00:22:08Z","cross_cats_sorted":["math.CO","math.MG"],"title_canon_sha256":"336d41f45e1115e136bcf604a12e37723d527d13e1be1b647424e5b6dde6333f","abstract_canon_sha256":"18cd25f82435e92faf5aea2570678cdfdc2161d0ff132c527e4785470a916143"},"schema_version":"1.0"},"canonical_sha256":"b377684eaa92d7ea7f5987fd345494344f232a5266e0ef63653342e2af1fe241","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:24:28.787543Z","signature_b64":"RzjVaBgRASHvfZuMvO027Y61wapPTQvtpeZLEhmy8Y6e8cD698ygiwQiAdoEcVMJAKn8jlttr/UK1Ywrqw7RDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b377684eaa92d7ea7f5987fd345494344f232a5266e0ef63653342e2af1fe241","last_reissued_at":"2026-05-18T02:24:28.786839Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:24:28.786839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.4597","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:24:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yfwDmdgAPnDkBIdPcijCHJ0DJSMYnqF4QSe4UkyNbDw49AZB3yrRNDbxWxAbKs+l0MwspeenFMiMup58SoCIAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T17:38:17.090205Z"},"content_sha256":"c4d7ee73984060e3dbe1f33e38b1e5b220a79d0db9ec20509db33a4aff8d7e27","schema_version":"1.0","event_id":"sha256:c4d7ee73984060e3dbe1f33e38b1e5b220a79d0db9ec20509db33a4aff8d7e27"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:WN3WQTVKSLL6U72ZQ76TIVEUGR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Indecomposable coverings with homothetic polygons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.MG"],"primary_cat":"cs.CG","authors_text":"Istv\\'an Kov\\'acs","submitted_at":"2013-12-17T00:22:08Z","abstract_excerpt":"We prove that for any convex polygon $S$ with at least four sides, or a concave one with no parallel sides, and any $m>0$, there is an $m$-fold covering of the plane with homothetic copies of $S$ that cannot be decomposed into two coverings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4597","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:24:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LFKx/JtdRCWmkqeHG3w9qzi9vtsfl+WM9UGL8FVwrYarqP34O6tACY/3mhhwJEE5H0CUI0RBe4P9EiBZBA4sCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T17:38:17.090915Z"},"content_sha256":"8a39529a49709850ffc5104f4fe37edb87a80f2a5196785a89c3a1619b4d65ec","schema_version":"1.0","event_id":"sha256:8a39529a49709850ffc5104f4fe37edb87a80f2a5196785a89c3a1619b4d65ec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WN3WQTVKSLL6U72ZQ76TIVEUGR/bundle.json","state_url":"https://pith.science/pith/WN3WQTVKSLL6U72ZQ76TIVEUGR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WN3WQTVKSLL6U72ZQ76TIVEUGR/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-25T17:38:17Z","links":{"resolver":"https://pith.science/pith/WN3WQTVKSLL6U72ZQ76TIVEUGR","bundle":"https://pith.science/pith/WN3WQTVKSLL6U72ZQ76TIVEUGR/bundle.json","state":"https://pith.science/pith/WN3WQTVKSLL6U72ZQ76TIVEUGR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WN3WQTVKSLL6U72ZQ76TIVEUGR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WN3WQTVKSLL6U72ZQ76TIVEUGR","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"18cd25f82435e92faf5aea2570678cdfdc2161d0ff132c527e4785470a916143","cross_cats_sorted":["math.CO","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-12-17T00:22:08Z","title_canon_sha256":"336d41f45e1115e136bcf604a12e37723d527d13e1be1b647424e5b6dde6333f"},"schema_version":"1.0","source":{"id":"1312.4597","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.4597","created_at":"2026-05-18T02:24:28Z"},{"alias_kind":"arxiv_version","alias_value":"1312.4597v2","created_at":"2026-05-18T02:24:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.4597","created_at":"2026-05-18T02:24:28Z"},{"alias_kind":"pith_short_12","alias_value":"WN3WQTVKSLL6","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WN3WQTVKSLL6U72Z","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WN3WQTVK","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:8a39529a49709850ffc5104f4fe37edb87a80f2a5196785a89c3a1619b4d65ec","target":"graph","created_at":"2026-05-18T02:24:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove that for any convex polygon $S$ with at least four sides, or a concave one with no parallel sides, and any $m>0$, there is an $m$-fold covering of the plane with homothetic copies of $S$ that cannot be decomposed into two coverings.","authors_text":"Istv\\'an Kov\\'acs","cross_cats":["math.CO","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-12-17T00:22:08Z","title":"Indecomposable coverings with homothetic polygons"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4597","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c4d7ee73984060e3dbe1f33e38b1e5b220a79d0db9ec20509db33a4aff8d7e27","target":"record","created_at":"2026-05-18T02:24:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"18cd25f82435e92faf5aea2570678cdfdc2161d0ff132c527e4785470a916143","cross_cats_sorted":["math.CO","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-12-17T00:22:08Z","title_canon_sha256":"336d41f45e1115e136bcf604a12e37723d527d13e1be1b647424e5b6dde6333f"},"schema_version":"1.0","source":{"id":"1312.4597","kind":"arxiv","version":2}},"canonical_sha256":"b377684eaa92d7ea7f5987fd345494344f232a5266e0ef63653342e2af1fe241","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b377684eaa92d7ea7f5987fd345494344f232a5266e0ef63653342e2af1fe241","first_computed_at":"2026-05-18T02:24:28.786839Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:28.786839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RzjVaBgRASHvfZuMvO027Y61wapPTQvtpeZLEhmy8Y6e8cD698ygiwQiAdoEcVMJAKn8jlttr/UK1Ywrqw7RDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:28.787543Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.4597","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4d7ee73984060e3dbe1f33e38b1e5b220a79d0db9ec20509db33a4aff8d7e27","sha256:8a39529a49709850ffc5104f4fe37edb87a80f2a5196785a89c3a1619b4d65ec"],"state_sha256":"48ee201ba9d2a8cd0276cf85334f1c7cdf1f173c4d7275f41ae52ebabe62c832"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yb0PBQ6EfqXSnKqKF8QFp+zZ5ptrS3wnKYDdXfRlK0ZgP+2RATofhPRQXdOSS+AahQGhm0ifG1QWnxrqPeHRBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T17:38:17.094908Z","bundle_sha256":"791c306f5b16fad235d78e2840a542b3d925419ef32f671bedc8c9b77495f4e0"}}