{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:VJGTY3VHD6AQ6GQSL6ORH2UN6M","short_pith_number":"pith:VJGTY3VH","canonical_record":{"source":{"id":"1808.05278","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-15T20:02:33Z","cross_cats_sorted":[],"title_canon_sha256":"ac09036a967eeffeeef3e728aafc1c88a838e9afa2c18a12944a1ae42486bb65","abstract_canon_sha256":"dc6eafe2af21d7c2c92bfe538f5ba1cec1ab06928deaf393dda9f83c3d4d0c10"},"schema_version":"1.0"},"canonical_sha256":"aa4d3c6ea71f810f1a125f9d13ea8df32530c713153a32dc7a977e823d55fc3d","source":{"kind":"arxiv","id":"1808.05278","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.05278","created_at":"2026-05-18T00:07:57Z"},{"alias_kind":"arxiv_version","alias_value":"1808.05278v1","created_at":"2026-05-18T00:07:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.05278","created_at":"2026-05-18T00:07:57Z"},{"alias_kind":"pith_short_12","alias_value":"VJGTY3VHD6AQ","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VJGTY3VHD6AQ6GQS","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VJGTY3VH","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:VJGTY3VHD6AQ6GQSL6ORH2UN6M","target":"record","payload":{"canonical_record":{"source":{"id":"1808.05278","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-15T20:02:33Z","cross_cats_sorted":[],"title_canon_sha256":"ac09036a967eeffeeef3e728aafc1c88a838e9afa2c18a12944a1ae42486bb65","abstract_canon_sha256":"dc6eafe2af21d7c2c92bfe538f5ba1cec1ab06928deaf393dda9f83c3d4d0c10"},"schema_version":"1.0"},"canonical_sha256":"aa4d3c6ea71f810f1a125f9d13ea8df32530c713153a32dc7a977e823d55fc3d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:57.681618Z","signature_b64":"Sy83YrEhmFUrqZd9x4rDHL+dVgSU/ZqgKP2jYdEabhPMuBMAayvd/QiV6wVwOnHc7noVw7/tsNEuDQkDqFSIBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa4d3c6ea71f810f1a125f9d13ea8df32530c713153a32dc7a977e823d55fc3d","last_reissued_at":"2026-05-18T00:07:57.680904Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:57.680904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.05278","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:07:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8C3+2q3OiOh5/SKHDskHzp2chuL07N+mmPD15vAt5JDTaIgFR8bI672tvNBAVVJW9Gt55TLKrSQ7RxLp8Z46AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T11:44:13.818807Z"},"content_sha256":"93055b09aa4461ef28bad768d24493caa5ac3dd09fe7bdcc7dec5050da9ba6a9","schema_version":"1.0","event_id":"sha256:93055b09aa4461ef28bad768d24493caa5ac3dd09fe7bdcc7dec5050da9ba6a9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:VJGTY3VHD6AQ6GQSL6ORH2UN6M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Matrices in the Hosoya triangle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Antara Mukherjee, Matthew Blair, Rigoberto Fl\\'orez","submitted_at":"2018-08-15T20:02:33Z","abstract_excerpt":"In this paper we use well-known results from linear algebra as tools to explore some properties of products of Fibonacci numbers. Specifically, we explore the behavior of the eigenvalues, eigenvectors, characteristic polynomials, determinants, and the norm of non-symmetric matrices embedded in the Hosoya triangle. We discovered that most of these objects either embed again in the Hosoya triangle or they give rise to Fibonacci identities.\n  We also study the nature of these matrices when their entries are taken $\\bmod$ $2$. As a result, we found an infinite family of non-connected graphs. Each "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.05278","kind":"arxiv","version":1},"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":"2026-05-18T00:07:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OKajjMGLpR7JVSzDz1jFwRZK1IOtdREjJ3DCKF3J3HDlwUyWCQJDWs5t8WNn+mTwBomUK6VoO1pA0f2BWDYFCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T11:44:13.819150Z"},"content_sha256":"445f806587c14df79a34f5efb6ba52c6d27338437c32ab10256fa4f6b7e72519","schema_version":"1.0","event_id":"sha256:445f806587c14df79a34f5efb6ba52c6d27338437c32ab10256fa4f6b7e72519"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VJGTY3VHD6AQ6GQSL6ORH2UN6M/bundle.json","state_url":"https://pith.science/pith/VJGTY3VHD6AQ6GQSL6ORH2UN6M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VJGTY3VHD6AQ6GQSL6ORH2UN6M/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":"2026-06-25T11:44:13Z","links":{"resolver":"https://pith.science/pith/VJGTY3VHD6AQ6GQSL6ORH2UN6M","bundle":"https://pith.science/pith/VJGTY3VHD6AQ6GQSL6ORH2UN6M/bundle.json","state":"https://pith.science/pith/VJGTY3VHD6AQ6GQSL6ORH2UN6M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VJGTY3VHD6AQ6GQSL6ORH2UN6M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VJGTY3VHD6AQ6GQSL6ORH2UN6M","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":"dc6eafe2af21d7c2c92bfe538f5ba1cec1ab06928deaf393dda9f83c3d4d0c10","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-15T20:02:33Z","title_canon_sha256":"ac09036a967eeffeeef3e728aafc1c88a838e9afa2c18a12944a1ae42486bb65"},"schema_version":"1.0","source":{"id":"1808.05278","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.05278","created_at":"2026-05-18T00:07:57Z"},{"alias_kind":"arxiv_version","alias_value":"1808.05278v1","created_at":"2026-05-18T00:07:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.05278","created_at":"2026-05-18T00:07:57Z"},{"alias_kind":"pith_short_12","alias_value":"VJGTY3VHD6AQ","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VJGTY3VHD6AQ6GQS","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VJGTY3VH","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:445f806587c14df79a34f5efb6ba52c6d27338437c32ab10256fa4f6b7e72519","target":"graph","created_at":"2026-05-18T00:07:57Z","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":"In this paper we use well-known results from linear algebra as tools to explore some properties of products of Fibonacci numbers. Specifically, we explore the behavior of the eigenvalues, eigenvectors, characteristic polynomials, determinants, and the norm of non-symmetric matrices embedded in the Hosoya triangle. We discovered that most of these objects either embed again in the Hosoya triangle or they give rise to Fibonacci identities.\n  We also study the nature of these matrices when their entries are taken $\\bmod$ $2$. As a result, we found an infinite family of non-connected graphs. Each ","authors_text":"Antara Mukherjee, Matthew Blair, Rigoberto Fl\\'orez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-15T20:02:33Z","title":"Matrices in the Hosoya triangle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.05278","kind":"arxiv","version":1},"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":"sha256:93055b09aa4461ef28bad768d24493caa5ac3dd09fe7bdcc7dec5050da9ba6a9","target":"record","created_at":"2026-05-18T00:07:57Z","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":"dc6eafe2af21d7c2c92bfe538f5ba1cec1ab06928deaf393dda9f83c3d4d0c10","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-15T20:02:33Z","title_canon_sha256":"ac09036a967eeffeeef3e728aafc1c88a838e9afa2c18a12944a1ae42486bb65"},"schema_version":"1.0","source":{"id":"1808.05278","kind":"arxiv","version":1}},"canonical_sha256":"aa4d3c6ea71f810f1a125f9d13ea8df32530c713153a32dc7a977e823d55fc3d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa4d3c6ea71f810f1a125f9d13ea8df32530c713153a32dc7a977e823d55fc3d","first_computed_at":"2026-05-18T00:07:57.680904Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:57.680904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Sy83YrEhmFUrqZd9x4rDHL+dVgSU/ZqgKP2jYdEabhPMuBMAayvd/QiV6wVwOnHc7noVw7/tsNEuDQkDqFSIBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:57.681618Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.05278","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93055b09aa4461ef28bad768d24493caa5ac3dd09fe7bdcc7dec5050da9ba6a9","sha256:445f806587c14df79a34f5efb6ba52c6d27338437c32ab10256fa4f6b7e72519"],"state_sha256":"1e1dbc8b00a691d227330b624b237f39de91577d8a38e79ff1e248fdb5b155cb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iIJJFh2MHP2mbO+e2MzHMQdNn4Q8vJFtjrB4wiIBWKJAztq+swZS9icooapf2lZkP9vzTUrYvRGl3MVAHQqJAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T11:44:13.821114Z","bundle_sha256":"a0756c227d84ff382be1a699fb0e4b3bd5bcda15ac8e97a806e5dc9bf2b5c1b9"}}