{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:QVX2NMVKEIHIHMHKFR6ZGVBWFP","short_pith_number":"pith:QVX2NMVK","canonical_record":{"source":{"id":"1302.3433","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-02-14T15:34:39Z","cross_cats_sorted":["math.CO","math.SP"],"title_canon_sha256":"73e050e0e47885e17533452ca5f1d7ae3578f89881790fa14fb90ef33db944f4","abstract_canon_sha256":"a475fa4595e74c411b1f069eb95c720f38ccf4cadc62f3899c9f052239c70e95"},"schema_version":"1.0"},"canonical_sha256":"856fa6b2aa220e83b0ea2c7d9354362be26bbd0caeb38e2c35f109cb60182a95","source":{"kind":"arxiv","id":"1302.3433","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.3433","created_at":"2026-05-18T03:33:38Z"},{"alias_kind":"arxiv_version","alias_value":"1302.3433v1","created_at":"2026-05-18T03:33:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.3433","created_at":"2026-05-18T03:33:38Z"},{"alias_kind":"pith_short_12","alias_value":"QVX2NMVKEIHI","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QVX2NMVKEIHIHMHK","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QVX2NMVK","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:QVX2NMVKEIHIHMHKFR6ZGVBWFP","target":"record","payload":{"canonical_record":{"source":{"id":"1302.3433","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-02-14T15:34:39Z","cross_cats_sorted":["math.CO","math.SP"],"title_canon_sha256":"73e050e0e47885e17533452ca5f1d7ae3578f89881790fa14fb90ef33db944f4","abstract_canon_sha256":"a475fa4595e74c411b1f069eb95c720f38ccf4cadc62f3899c9f052239c70e95"},"schema_version":"1.0"},"canonical_sha256":"856fa6b2aa220e83b0ea2c7d9354362be26bbd0caeb38e2c35f109cb60182a95","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:33:38.938072Z","signature_b64":"/7ddR3pQ6kD6O+TQpmcq2PSqAvVUYgFzcjM7z/zHo5uJ5h1/+4dIF5Oxpv0DRBHz7sgVh9xO5XrMKr7LkVuoBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"856fa6b2aa220e83b0ea2c7d9354362be26bbd0caeb38e2c35f109cb60182a95","last_reissued_at":"2026-05-18T03:33:38.937546Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:33:38.937546Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.3433","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":"2026-05-18T03:33:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3FVnq/5706/3hfg3Dx04JyTokWqt1MA1OoO9NT0f49kPuV4SULIUtNyrSbgO2MtfL8Ya9xIC5VVBntH0KIkECg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:49:19.206300Z"},"content_sha256":"b3b1cb0af1bcf02b3add907293215df715dbe60a56f2d6d4096b8279a8f1a84f","schema_version":"1.0","event_id":"sha256:b3b1cb0af1bcf02b3add907293215df715dbe60a56f2d6d4096b8279a8f1a84f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:QVX2NMVKEIHIHMHKFR6ZGVBWFP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Eigenfunctions of the Edge-Based Laplacian on a Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.SP"],"primary_cat":"cs.DM","authors_text":"Edwin R. Hancock, Furqan Aziz, Richard C. Wilson","submitted_at":"2013-02-14T15:34:39Z","abstract_excerpt":"In this paper, we analyze the eigenfunctions of the edge-based Laplacian on a graph and the relationship of these functions to random walks on the graph. We commence by discussing the set of eigenfunctions supported at the vertices, and demonstrate the relationship of these eigenfunctions to the classical random walk on the graph. Then, from an analysis of functions supported only on the interior of edges, we develop a method for explicitly calculating the edge-interior eigenfunctions of the edge-based Laplacian. This reveals a connection between the edge-based Laplacian and the adjacency matr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3433","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":"2026-05-18T03:33:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jgu2siUCtfIkrlKbKaBve6EemCIcE175LkOMzGdk/BbqWJSnDiLHRqavB5uyIf0jEeL3BnVzdeE3zYeGJbikDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:49:19.206653Z"},"content_sha256":"0bf6230e6b3e0332395136e502dd018ddc650b5d42595ecdd4abe95c900ad4da","schema_version":"1.0","event_id":"sha256:0bf6230e6b3e0332395136e502dd018ddc650b5d42595ecdd4abe95c900ad4da"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QVX2NMVKEIHIHMHKFR6ZGVBWFP/bundle.json","state_url":"https://pith.science/pith/QVX2NMVKEIHIHMHKFR6ZGVBWFP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QVX2NMVKEIHIHMHKFR6ZGVBWFP/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":"2026-06-01T16:49:19Z","links":{"resolver":"https://pith.science/pith/QVX2NMVKEIHIHMHKFR6ZGVBWFP","bundle":"https://pith.science/pith/QVX2NMVKEIHIHMHKFR6ZGVBWFP/bundle.json","state":"https://pith.science/pith/QVX2NMVKEIHIHMHKFR6ZGVBWFP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QVX2NMVKEIHIHMHKFR6ZGVBWFP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QVX2NMVKEIHIHMHKFR6ZGVBWFP","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":"a475fa4595e74c411b1f069eb95c720f38ccf4cadc62f3899c9f052239c70e95","cross_cats_sorted":["math.CO","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-02-14T15:34:39Z","title_canon_sha256":"73e050e0e47885e17533452ca5f1d7ae3578f89881790fa14fb90ef33db944f4"},"schema_version":"1.0","source":{"id":"1302.3433","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.3433","created_at":"2026-05-18T03:33:38Z"},{"alias_kind":"arxiv_version","alias_value":"1302.3433v1","created_at":"2026-05-18T03:33:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.3433","created_at":"2026-05-18T03:33:38Z"},{"alias_kind":"pith_short_12","alias_value":"QVX2NMVKEIHI","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QVX2NMVKEIHIHMHK","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QVX2NMVK","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:0bf6230e6b3e0332395136e502dd018ddc650b5d42595ecdd4abe95c900ad4da","target":"graph","created_at":"2026-05-18T03:33:38Z","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 analyze the eigenfunctions of the edge-based Laplacian on a graph and the relationship of these functions to random walks on the graph. We commence by discussing the set of eigenfunctions supported at the vertices, and demonstrate the relationship of these eigenfunctions to the classical random walk on the graph. Then, from an analysis of functions supported only on the interior of edges, we develop a method for explicitly calculating the edge-interior eigenfunctions of the edge-based Laplacian. This reveals a connection between the edge-based Laplacian and the adjacency matr","authors_text":"Edwin R. Hancock, Furqan Aziz, Richard C. Wilson","cross_cats":["math.CO","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-02-14T15:34:39Z","title":"Eigenfunctions of the Edge-Based Laplacian on a Graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3433","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:b3b1cb0af1bcf02b3add907293215df715dbe60a56f2d6d4096b8279a8f1a84f","target":"record","created_at":"2026-05-18T03:33:38Z","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":"a475fa4595e74c411b1f069eb95c720f38ccf4cadc62f3899c9f052239c70e95","cross_cats_sorted":["math.CO","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-02-14T15:34:39Z","title_canon_sha256":"73e050e0e47885e17533452ca5f1d7ae3578f89881790fa14fb90ef33db944f4"},"schema_version":"1.0","source":{"id":"1302.3433","kind":"arxiv","version":1}},"canonical_sha256":"856fa6b2aa220e83b0ea2c7d9354362be26bbd0caeb38e2c35f109cb60182a95","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"856fa6b2aa220e83b0ea2c7d9354362be26bbd0caeb38e2c35f109cb60182a95","first_computed_at":"2026-05-18T03:33:38.937546Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:38.937546Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/7ddR3pQ6kD6O+TQpmcq2PSqAvVUYgFzcjM7z/zHo5uJ5h1/+4dIF5Oxpv0DRBHz7sgVh9xO5XrMKr7LkVuoBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:38.938072Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.3433","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3b1cb0af1bcf02b3add907293215df715dbe60a56f2d6d4096b8279a8f1a84f","sha256:0bf6230e6b3e0332395136e502dd018ddc650b5d42595ecdd4abe95c900ad4da"],"state_sha256":"73c14848f6928389e0b34167a4a93d74c65b8fd0afd0a38fffd66e33a8cedf35"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aLFdTTU7Pws0q9c9hsajhCTaPfGtWmfTj40LEx8hhF6tqQjz/cHviSQaQDyLTi0twfEfVVQWs3iAHkaCnFOuCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T16:49:19.208618Z","bundle_sha256":"aeffe3f93aaa75bbbba57b14164eb6597b1abaf79c60f48a079beb7dabd6a58c"}}