{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:OOHQOJ5MMOXOBQYTMV4IPTBMG2","short_pith_number":"pith:OOHQOJ5M","canonical_record":{"source":{"id":"1907.09462","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-07-22T17:55:42Z","cross_cats_sorted":[],"title_canon_sha256":"4681a2311378316f55b74a52ba2d9e2f3b8eabf896301115345a5e78bdbdd961","abstract_canon_sha256":"329d0863aef03575e503011eb6af493d0568ee6596b27cdfde92cfe346ca5b69"},"schema_version":"1.0"},"canonical_sha256":"738f0727ac63aee0c313657887cc2c36a50beb4dcb101dc987f5c202a3944615","source":{"kind":"arxiv","id":"1907.09462","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.09462","created_at":"2026-05-17T23:39:59Z"},{"alias_kind":"arxiv_version","alias_value":"1907.09462v1","created_at":"2026-05-17T23:39:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.09462","created_at":"2026-05-17T23:39:59Z"},{"alias_kind":"pith_short_12","alias_value":"OOHQOJ5MMOXO","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"OOHQOJ5MMOXOBQYT","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"OOHQOJ5M","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:OOHQOJ5MMOXOBQYTMV4IPTBMG2","target":"record","payload":{"canonical_record":{"source":{"id":"1907.09462","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-07-22T17:55:42Z","cross_cats_sorted":[],"title_canon_sha256":"4681a2311378316f55b74a52ba2d9e2f3b8eabf896301115345a5e78bdbdd961","abstract_canon_sha256":"329d0863aef03575e503011eb6af493d0568ee6596b27cdfde92cfe346ca5b69"},"schema_version":"1.0"},"canonical_sha256":"738f0727ac63aee0c313657887cc2c36a50beb4dcb101dc987f5c202a3944615","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:59.166907Z","signature_b64":"ULXxbhEaiv2PS7yZJEzjQCfvq/9I7Gp6c3dqyUUz++la8Bp2EkGsa2Jfg8n1eL+UNVoemTfVYG8R6MhlQJI5Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"738f0727ac63aee0c313657887cc2c36a50beb4dcb101dc987f5c202a3944615","last_reissued_at":"2026-05-17T23:39:59.166386Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:59.166386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.09462","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":"2026-05-17T23:39:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gNlMykaQ/QcMjaUJfj2tDqU2Cm/YFbZS6Ao8sYqUwBSz/OwaswqKKLrPhEZhR6VggoiKrfOibjr86wPsZqVdBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T11:49:02.839419Z"},"content_sha256":"8cbf7eb22c364b9eb871fa79a5f0cbe60d1e2ada328225d92d7b658640305eb2","schema_version":"1.0","event_id":"sha256:8cbf7eb22c364b9eb871fa79a5f0cbe60d1e2ada328225d92d7b658640305eb2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:OOHQOJ5MMOXOBQYTMV4IPTBMG2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On spectral spread of generalized distance matrix of a graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A. Alhevaz, Hilal A. Ganie, M. Baghipur, S. Pirzada","submitted_at":"2019-07-22T17:55:42Z","abstract_excerpt":"For a simple connected graph $G$, let $D(G)$, $Tr(G)$, $D^{L}(G)$ and $D^{Q}(G)$, respectively be the distance matrix, the diagonal matrix of the vertex transmissions, distance Laplacian matrix and the distance signless Laplacian matrix of a graph $G$. The convex linear combinations $D_{\\alpha}(G)$ of $Tr(G)$ and $D(G)$ is defined as $D_{\\alpha}(G)=\\alpha Tr(G)+(1-\\alpha)D(G)$, $0\\leq \\alpha\\leq 1$. As $D_{0}(G)=D(G), ~~~ 2D_{\\frac{1}{2}}(G)=D^{Q}(G), ~~~ D_{1}(G)=Tr(G)$ and $D_{\\alpha}(G)-D_{\\beta}(G)=(\\alpha-\\beta)D^{L}(G)$, this matrix reduces to merging the distance spectral, distance Lapl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.09462","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":"2026-05-17T23:39:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qp6Vey0cEED0ZQFRDHNZl6P6Tdo8o5TXqriDvCO4D2fX8kE6nkyy/mhbOi5RLnZ2p4RVGf0/UFXW4RL8a55YBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T11:49:02.840083Z"},"content_sha256":"ad05b2199f9319e2dc15dcda22b99b8995be4418e45481d8feb3ad5938cbac1f","schema_version":"1.0","event_id":"sha256:ad05b2199f9319e2dc15dcda22b99b8995be4418e45481d8feb3ad5938cbac1f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OOHQOJ5MMOXOBQYTMV4IPTBMG2/bundle.json","state_url":"https://pith.science/pith/OOHQOJ5MMOXOBQYTMV4IPTBMG2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OOHQOJ5MMOXOBQYTMV4IPTBMG2/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":"2026-06-07T11:49:02Z","links":{"resolver":"https://pith.science/pith/OOHQOJ5MMOXOBQYTMV4IPTBMG2","bundle":"https://pith.science/pith/OOHQOJ5MMOXOBQYTMV4IPTBMG2/bundle.json","state":"https://pith.science/pith/OOHQOJ5MMOXOBQYTMV4IPTBMG2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OOHQOJ5MMOXOBQYTMV4IPTBMG2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:OOHQOJ5MMOXOBQYTMV4IPTBMG2","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":"329d0863aef03575e503011eb6af493d0568ee6596b27cdfde92cfe346ca5b69","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-07-22T17:55:42Z","title_canon_sha256":"4681a2311378316f55b74a52ba2d9e2f3b8eabf896301115345a5e78bdbdd961"},"schema_version":"1.0","source":{"id":"1907.09462","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.09462","created_at":"2026-05-17T23:39:59Z"},{"alias_kind":"arxiv_version","alias_value":"1907.09462v1","created_at":"2026-05-17T23:39:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.09462","created_at":"2026-05-17T23:39:59Z"},{"alias_kind":"pith_short_12","alias_value":"OOHQOJ5MMOXO","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"OOHQOJ5MMOXOBQYT","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"OOHQOJ5M","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:ad05b2199f9319e2dc15dcda22b99b8995be4418e45481d8feb3ad5938cbac1f","target":"graph","created_at":"2026-05-17T23:39:59Z","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":"For a simple connected graph $G$, let $D(G)$, $Tr(G)$, $D^{L}(G)$ and $D^{Q}(G)$, respectively be the distance matrix, the diagonal matrix of the vertex transmissions, distance Laplacian matrix and the distance signless Laplacian matrix of a graph $G$. The convex linear combinations $D_{\\alpha}(G)$ of $Tr(G)$ and $D(G)$ is defined as $D_{\\alpha}(G)=\\alpha Tr(G)+(1-\\alpha)D(G)$, $0\\leq \\alpha\\leq 1$. As $D_{0}(G)=D(G), ~~~ 2D_{\\frac{1}{2}}(G)=D^{Q}(G), ~~~ D_{1}(G)=Tr(G)$ and $D_{\\alpha}(G)-D_{\\beta}(G)=(\\alpha-\\beta)D^{L}(G)$, this matrix reduces to merging the distance spectral, distance Lapl","authors_text":"A. Alhevaz, Hilal A. Ganie, M. Baghipur, S. Pirzada","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-07-22T17:55:42Z","title":"On spectral spread of generalized distance matrix of a graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.09462","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":"sha256:8cbf7eb22c364b9eb871fa79a5f0cbe60d1e2ada328225d92d7b658640305eb2","target":"record","created_at":"2026-05-17T23:39:59Z","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":"329d0863aef03575e503011eb6af493d0568ee6596b27cdfde92cfe346ca5b69","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-07-22T17:55:42Z","title_canon_sha256":"4681a2311378316f55b74a52ba2d9e2f3b8eabf896301115345a5e78bdbdd961"},"schema_version":"1.0","source":{"id":"1907.09462","kind":"arxiv","version":1}},"canonical_sha256":"738f0727ac63aee0c313657887cc2c36a50beb4dcb101dc987f5c202a3944615","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"738f0727ac63aee0c313657887cc2c36a50beb4dcb101dc987f5c202a3944615","first_computed_at":"2026-05-17T23:39:59.166386Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:59.166386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ULXxbhEaiv2PS7yZJEzjQCfvq/9I7Gp6c3dqyUUz++la8Bp2EkGsa2Jfg8n1eL+UNVoemTfVYG8R6MhlQJI5Dg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:59.166907Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.09462","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8cbf7eb22c364b9eb871fa79a5f0cbe60d1e2ada328225d92d7b658640305eb2","sha256:ad05b2199f9319e2dc15dcda22b99b8995be4418e45481d8feb3ad5938cbac1f"],"state_sha256":"980c21eb2c768a2a5f9f49564a0cf04e996f9d67d7d18ee92a5f2ed86a51ec36"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wx1+ii3JgAURS2xSVaXZQhoFVkW/+W/4W88N3grKa0P5KcjHdKuLtwp2qHpW1q1A6tfKsPneTGnNvSwal3erBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T11:49:02.843414Z","bundle_sha256":"0e769c0a7949d44d1ff2e076d328991f8b423b08b71fb7e195b49400f75f7707"}}