{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:WUXJEPEGFAEBIMDCEBDIQIILKU","short_pith_number":"pith:WUXJEPEG","canonical_record":{"source":{"id":"1608.07939","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-29T07:45:48Z","cross_cats_sorted":[],"title_canon_sha256":"eeaac7e0a482f27e40b0df8ac84a5749e26b11fb90618fcc311796f1bf37f07d","abstract_canon_sha256":"3e988d6d5b27606441d1fbb355d1884a14ad2be453e8bfe69378cdba89ca914f"},"schema_version":"1.0"},"canonical_sha256":"b52e923c862808143062204688210b5505b71d4c055c68a141ac28e3b989cf06","source":{"kind":"arxiv","id":"1608.07939","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.07939","created_at":"2026-05-18T01:07:49Z"},{"alias_kind":"arxiv_version","alias_value":"1608.07939v1","created_at":"2026-05-18T01:07:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.07939","created_at":"2026-05-18T01:07:49Z"},{"alias_kind":"pith_short_12","alias_value":"WUXJEPEGFAEB","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"WUXJEPEGFAEBIMDC","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"WUXJEPEG","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:WUXJEPEGFAEBIMDCEBDIQIILKU","target":"record","payload":{"canonical_record":{"source":{"id":"1608.07939","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-29T07:45:48Z","cross_cats_sorted":[],"title_canon_sha256":"eeaac7e0a482f27e40b0df8ac84a5749e26b11fb90618fcc311796f1bf37f07d","abstract_canon_sha256":"3e988d6d5b27606441d1fbb355d1884a14ad2be453e8bfe69378cdba89ca914f"},"schema_version":"1.0"},"canonical_sha256":"b52e923c862808143062204688210b5505b71d4c055c68a141ac28e3b989cf06","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:49.550199Z","signature_b64":"n8X8NB5IM6G9fjrQ9KUPkH8jpyWH+/g9JKoyEiU09bJVweRWiCC2fHNkHzzkiLPl8IehFd4I4pWn3gYq99FhDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b52e923c862808143062204688210b5505b71d4c055c68a141ac28e3b989cf06","last_reissued_at":"2026-05-18T01:07:49.549730Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:49.549730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.07939","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":"2026-05-18T01:07:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ppKWMTvA4v42QQwLn3qLxKlxI5rx1tnCmz1uYx3L6GEHkKPHC7L2lKFqF2lqOZ4AzEWsKx4IpZEFmE83cuvvBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T20:43:17.006475Z"},"content_sha256":"17c2eacf02ac8e013b6182b369995e057c3b6d6786172b6effcda92e392de338","schema_version":"1.0","event_id":"sha256:17c2eacf02ac8e013b6182b369995e057c3b6d6786172b6effcda92e392de338"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:WUXJEPEGFAEBIMDCEBDIQIILKU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Applications of a theorem by Ky Fan in the theory of weighted Laplacian graph energy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alireza Ataei, Habibeh Panahbar, Reza Sharafdini","submitted_at":"2016-08-29T07:45:48Z","abstract_excerpt":"The energy of a graph $G$ is equal to the sum of the absolute values of the eigenvalues of $G$ , which in turn is equal to the sum of the singular values of the adjacency matrix of $G$. Let $X$, $Y$ and $Z$ be matrices, such that $X+Y= Z$. The Ky Fan theorem establishes an inequality between the sum of the singular values of $Z$ and the sum of the sum of the singular values of $X$ and $Y$. This theorem is applied in the theory of graph energy, resulting in several new inequalities, as well as new proofs of some earlier known inequalities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07939","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":"2026-05-18T01:07:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XXy2We2mcSjHmmRRcwp6Y49jH17buMSLj+I0A1BZyB5njajlRqQE9ZKEPMEk6GnOprIOkswjm7Wzcy+7vwV0DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T20:43:17.006967Z"},"content_sha256":"08d245ee8fe38e70a9f1c718ea6abada91d3c64f969da2f0a9c5256ea02a0f8c","schema_version":"1.0","event_id":"sha256:08d245ee8fe38e70a9f1c718ea6abada91d3c64f969da2f0a9c5256ea02a0f8c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WUXJEPEGFAEBIMDCEBDIQIILKU/bundle.json","state_url":"https://pith.science/pith/WUXJEPEGFAEBIMDCEBDIQIILKU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WUXJEPEGFAEBIMDCEBDIQIILKU/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":"2026-06-01T20:43:17Z","links":{"resolver":"https://pith.science/pith/WUXJEPEGFAEBIMDCEBDIQIILKU","bundle":"https://pith.science/pith/WUXJEPEGFAEBIMDCEBDIQIILKU/bundle.json","state":"https://pith.science/pith/WUXJEPEGFAEBIMDCEBDIQIILKU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WUXJEPEGFAEBIMDCEBDIQIILKU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WUXJEPEGFAEBIMDCEBDIQIILKU","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":"3e988d6d5b27606441d1fbb355d1884a14ad2be453e8bfe69378cdba89ca914f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-29T07:45:48Z","title_canon_sha256":"eeaac7e0a482f27e40b0df8ac84a5749e26b11fb90618fcc311796f1bf37f07d"},"schema_version":"1.0","source":{"id":"1608.07939","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.07939","created_at":"2026-05-18T01:07:49Z"},{"alias_kind":"arxiv_version","alias_value":"1608.07939v1","created_at":"2026-05-18T01:07:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.07939","created_at":"2026-05-18T01:07:49Z"},{"alias_kind":"pith_short_12","alias_value":"WUXJEPEGFAEB","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"WUXJEPEGFAEBIMDC","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"WUXJEPEG","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:08d245ee8fe38e70a9f1c718ea6abada91d3c64f969da2f0a9c5256ea02a0f8c","target":"graph","created_at":"2026-05-18T01:07:49Z","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":"The energy of a graph $G$ is equal to the sum of the absolute values of the eigenvalues of $G$ , which in turn is equal to the sum of the singular values of the adjacency matrix of $G$. Let $X$, $Y$ and $Z$ be matrices, such that $X+Y= Z$. The Ky Fan theorem establishes an inequality between the sum of the singular values of $Z$ and the sum of the sum of the singular values of $X$ and $Y$. This theorem is applied in the theory of graph energy, resulting in several new inequalities, as well as new proofs of some earlier known inequalities.","authors_text":"Alireza Ataei, Habibeh Panahbar, Reza Sharafdini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-29T07:45:48Z","title":"Applications of a theorem by Ky Fan in the theory of weighted Laplacian graph energy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07939","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":"sha256:17c2eacf02ac8e013b6182b369995e057c3b6d6786172b6effcda92e392de338","target":"record","created_at":"2026-05-18T01:07:49Z","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":"3e988d6d5b27606441d1fbb355d1884a14ad2be453e8bfe69378cdba89ca914f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-29T07:45:48Z","title_canon_sha256":"eeaac7e0a482f27e40b0df8ac84a5749e26b11fb90618fcc311796f1bf37f07d"},"schema_version":"1.0","source":{"id":"1608.07939","kind":"arxiv","version":1}},"canonical_sha256":"b52e923c862808143062204688210b5505b71d4c055c68a141ac28e3b989cf06","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b52e923c862808143062204688210b5505b71d4c055c68a141ac28e3b989cf06","first_computed_at":"2026-05-18T01:07:49.549730Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:07:49.549730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n8X8NB5IM6G9fjrQ9KUPkH8jpyWH+/g9JKoyEiU09bJVweRWiCC2fHNkHzzkiLPl8IehFd4I4pWn3gYq99FhDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:07:49.550199Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.07939","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:17c2eacf02ac8e013b6182b369995e057c3b6d6786172b6effcda92e392de338","sha256:08d245ee8fe38e70a9f1c718ea6abada91d3c64f969da2f0a9c5256ea02a0f8c"],"state_sha256":"153f1db62cd6e4a91376db92e15d6297d3c27d09a4a9bf797f01c8e2bad939ed"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sbJFlqnusd7Qb8F7MVAo8BoDGk+z/wG41jtwMKXjAVFX2443qgyoapjz+VVmpoLTFxvQ2QEHaMwVnUGRcrw+Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T20:43:17.009048Z","bundle_sha256":"acc687bf388348cf6d7dbffc5d5adb6f1b7eb574b0548e9e1ad2f0745740e976"}}